optical study of novel perovskitic oxides, with focus on ...€¦ · wael saad mohamed ahmed,...

“Optical study of novel perovskitic oxides, with

focus on their lattice and electronic properties”

Doctoral School in Physics

PhD in Physics - XXVII Cycle

By

Wael Saad Mohamed Ahmed

ID number 1506361

Thesis Advisor Thesis co-Advisor

Prof. Paolo Calvani Dr. Alessandro Nucara

Coordinator

Prof. Massimo Testa

A thesis submitted in partial fulfilment of the requirements for the degree of

Doctor of Philosophy in Physics

October 2014

“Optical study of novel perovskitic oxides, with focus on their lattice and electronic properties” i

Thesis not yet defended

Wael Saad Mohamed Ahmed, “Optical study of novel perovskitic oxides, with focus

on their lattice and electronic properties”.

Ph.D. thesis. Sapienza – University of Rome

©2014 ISBN: 000000000-0

Version: 4 October 2014

Email:[email protected]

ii “Optical study of novel perovskitic oxides, with focus on their lattice and electronic properties”

To my parents, my beloved wife

“Optical study of novel perovskitic oxides, with focus on their lattice and electronic properties” iii

Table of Contents

Table of Contents .............................................................................................. iii

Outline ............................................................................................................... v

Acknowledgment .............................................................................................. vi

Abstract ............................................................................................................ vii

I Basic concepts ...............................................................................................ix

Chapter 1:Basics of optical spectroscopy ....................................................... 11

1.1 Introduction of Optical Spectroscopy ..................................................... 11

1.2 Optical functions ..................................................................................... 15

1.3 Transmittance, reflectance and absorption coefficient ........................... 17

1.4 Kramers Kronig Relations ...................................................................... 18

1.5 Generalization of Reflectance and Transmittance to any angle of

incidence .......................................................................................................... 21

Bibliography....................................................................................................26

Chapter 2: Phenomenology of Manganites and of selected

multiferroics.....................................................................................................27

2.1 Manganites .............................................................................................. 27

2.2 Colossal magnetoresistance (CMR) in manganites ................................ 28

2.3 Structural properties of manganites ........................................................ 30

2.4 Electronic properties of manganites ........................................................ 31

2.5 LaMnO3 and its phase digram ................................................................. 33

2.6 Optical properties of manganites ............................................................ 36

2.7 Multiferroics ............................................................................................ 43

2.8 Optical spectra of multiferroic manganites ............................................ 46

2.9 Multiferroic Germanates ......................................................................... 49

Bibliography....................................................................................................52

Chapter 3: Backgroun Theory ............................................................................. 59

3.1 Introduction ............................................................................................. 59

3.2 Exchange Interaction ............................................................................... 59

3.3 Crystal field theory and JT effect ............................................................ 65

3.4 Modeling the optical conductivity .......................................................... 67

Bibliography....................................................................................................72

iv “Optical study of novel perovskitic oxides, with focus on their lattice and electronic properties”

Chapter 4: Experimental Methods ................................................................. 73

4.1 Introduction ............................................................................................. 73

4.2 Infrared spectroscopy and experimental setup ........................................ 75

4.3 UV-Vis Spectroscopy .............................................................................. 87

4.4 Thin films and single crystal preparation ................................................ 94

Bibliography....................................................................................................97

II Results and Discussion ............................................................................. 98

Chapter 5: Structural, Electronic and Optical properties of LaMn0.5Ga0.5O3 .

..........................................................................................................................99

5.1 Introduction ............................................................................................. 99

5.2 Sample growth and characterization ..................................................... 102

5.3 Transmittance spectra of the LaMn0.5Ga0.5O3 film ............................... 103

5.4 Extraction of the bare film optical functions ........................................ 106

5.5 Analysis of the bare film optical conductivity ...................................... 107

5.6 Drude-Lorentz analysis of the Optical Conductivity ............................ 109

5.7 Conclusion ............................................................................................. 115

Bibliography..................................................................................................117

Chapter 6: Optical study of Insulator to Metal transition in LaxMnO3 thin

films......................... ...................................................................................... 119

6.1 Introduction ........................................................................................... 119

6.2 Sample description and experimental procedure .................................. 121

6.3 Reflectivity spectra of the LaMnxO3 films ............................................ 124

6.4 Extraction of the bare film optical functions ........................................ 125

6.5 Analysis of the bare film optical conductivity ...................................... 126

6.6 Conclusion ............................................................................................. 133

Bibliography..................................................................................................134

Chapter 7: Infrared phonon dynamics of Ba2CuGe2O7 and BiMnO3 ......137

7.1 Infrared phonon spectrum of the tetragonal helimagnet Ba2CuGe2O7...137

7.2 Infrared phonon dynamics of BiMnO3 multiferroic compound............ 155

7.3 Conclusion ............................................................................................. 163

Bibliography..................................................................................................164

Conclusions....................................................................................................167

List of publications ........................................................................................169

“Optical study of novel perovskitic oxides, with focus on their lattice and electronic properties” v

Outline

This thesis is divided into two main sections. After the Acknowledgments and

the Abstract the reader enters the first section, entitled “Basic Concepts”. This

is divided into four chapters: The first chapter is entitled “Basics of Optical

Spectroscopy” which introduces to the readers the fundamentals of

spectroscopy and the basic concepts of light matter interaction. The second

chapter is entitled “Phenomenology of Manganites and of selected

Multiferroics” .its elaborate on the optical and structural properties of

manganites and multiferroics, repectivley. The third one is entitled

“Background theory” which discusses the main theories related to our

investigation. The fourth chapter is entitled “Experimental Methods” which

illustrates the experimental set-ups for different spectroscopic techniques (for

instances: UV spectroscopy and IR spectroscopy set-ups). Additionally, the

fourth chapter reviews the methodologies that are being used in my thesis.

The second section, “Results and Discussion”, contains three chapters and a

conclusion. This section deals with a detailed spectroscopic study of the four

compounds under study (i.e., LaMnO3 and LaMnGaO3 thin films,

Ba2CuGe2O7 and BiMnO3 bulk samples). For all these ensembles we

measured the transmittance and/or reflection. Measurements are taken in the

infrared, visible and ultraviolet spectral range. The range is between 100 and

45000 cm-1

to obtain information on the vibrational, electronic and

multiferroic properties of these correlated perovskites and multiferroics

compounds.

vi “Optical study of novel perovskitic oxides, with focus on their lattice and electronic properties”

Acknowledgment

Thanks to Allah who pushed many of the noble people to help me to

accomplish this work. I am deeply indebted to my Ph.D. supervisor

Prof. Paolo Calvani for accepting me as a PhD student in his group at

Physics Department of the Sapienza University in Rome, for giving me the

opportunity to work and learn in one of the most exciting fields in solid

state physics, that of optical spectroscopy, for his supervision and constant

support through these years.

I would like to thank my tutor, Dr. Alessandro Nucara, for his brilliant

guidance and for the excellent collaboration we had. In these three years he

was always willing to help me during experiments and to explain concepts

when they were not clear to me.

I should also give many thanks to my group staff, in particular Dr. Paola

Maselli and Dr. Michele Ortolani for their great support during the

experiments, for discussions about science and for creating a spectacular

working environment.

I should also give many thanks to my group colleagues at the IRS Group,

Valeria Giliberti, Eugenio Calandrini, Odeta Limaj, Fausto D’Apuzzo , Paola

Dipietro , Marta Autore , Irene Lovecchio and Leonetta Baldassarre and many

more for the wonderful working atmosphere and the nice time we had

together.

I would like to thank the Erasmus Mundus European Commission for

providing financial support for 34 months in framework of FFEEBB 2 project

- Erasmus Mundus Action 2 during my PhD program.

I finish with my family; I would like to thank my parents as well as my

beloved wife for their love, support and encouragement, particularly during my

doctoral studies. Without their vital help over many years, nothing would have

been accomplished.

W.S.M.AHMED

mailto:[email protected]





“Optical study of novel perovskitic oxides, with focus on their lattice and electronic properties” vii

Abstract

Thesis title: “Optical study of novel perovskitic oxides, with focus on

their lattice and electronic properties”

Candidate: Wael Saad Mohamed Ahmed

Physics department - Sapienza University of Rome

The experimental work reported in this thesis consists in a systematic

investigation of various physical properties of epitaxial perovskite manganese

oxide

s films and single crystals with general formula A1-xBxMnO3 where A = La, Bi

and B = Ga and the lattice dynamics of Ba2CuGe2O7 tetragonal helimagnet

compound. In all these systems we measure the transmittance and/or reflection

in the infrared, visible and ultraviolet spectral range, between 100 and 45000

cm-1

to obtain information on the vibrational, electronic and multiferroic

properties of those compounds.

We have measured the transmittance of LaMn0.5Ga0.5O3thin film deposited by

Pulsed Laser Deposition on a LSAT substrate in the visible and near UV

range, from 300 to 10 K. The aim was to shed light on the origin of the

electronic bands in the LMO family through a comparison with the

corresponding spectra collected previously on the parent compound

LaMnO3. Two out of the four bands detected have been assigned to the

intersite d–d transitions between Mn+3

ions. The other ones were ascribed to

the p–d Mn–O charge-transfer transitions. We are thus led to

a“mixed”interpretation where both a Mott–Hubbard and a charge-transfer

approach concur to interpret the electronic spectrum of those manganites.

Lanthanum manganites with a massive concentration of La defects have also

been investigated by optical spectroscopy. They can be stabilized in form of

thin films, by exploiting the structural stress produced by a substrate like

SrTiO3. They undergo an insulator-to-metal transition (IMT) like those doped

viii “Optical study of novel perovskitic oxides, with focus on their lattice and electronic properties”

by divalent ions, but also present peculiar properties. That process is here

studied by determining the optical conductivity of LaxMnO3−δ films with

x=0.66, 0.88, 0.98 and 1.10, and with δ ≃ 0, from the far infrared to the near

ultraviolet, and between 20 and 300 K. We find that the IMT is a slow process

which continues down to 100 K at least, more than 250 K below its onset at

the Curie temperature Tc and at the TIMT Measured in dc from a change of

slope in the resistivity vs. temperature. The metallization is monitored through

the increase of the Drude term and a transfer of spectral weight from a ”hard”

midinfrared band MIR-2 peaked between 3000 and 5000 cm−1

at room

temperature, to a ”soft” midinfrared band MIR-1 at ∼ 1000 cm−1

. We have

also observed that, in these La-defective films, the Drude term at low

temperature is much narrower - and therefore the scattering rate considerably

lower - than in chemically doped manganites with comparable dc

conductivity. This favorable feature persists up to room temperature.

Therefore, this finding may be of interest for potential applications of La-

defective films to conductive devices.

Finally, in this thesis, we have studied the lattice dynamics of two multiferroic

compounds, Ba2CuGe2O7 and BiMnO3, by infrared reflectivity measurements.

The number of the observed phonon lines is consistent with that predicted for

the P 421m cell of Ba2CuGe2O7, and no line splitting has been observed when

cooling the sample to 7 K. Therefore, our spectra confirm that the tetragonal

symmetry is conserved down to the lowest temperatures above TN, with no

appreciable distortion. In collaboration with theorists, the theoretical

frequencies and intensities of about fourty phonon modes have been calculated

and found in good agreement with the observations. The temperature

dependence of the phonons parameters in a BiMnO3 single crystal was probed

by infrared spectroscopy down to 10 K. (i.e., well below the ferromagnetic

transition at TC = 100 K.). The Optical conductivity analyses of the infrared

phonons support the centrosymetric C2/c space group structure of BiMnO3

single crystal.

“Optical study of novel perovskitic oxides, with focus on their lattice and electronic properties” ix

I Basic concepts

Chapter 1:Basics of optical spectroscopy 11

Chapter 1: Basics of optical spectroscopy

1.1 Introduction to Optical Spectroscopy

Optical spectroscopy is one of the oldest techniques used to determine the

properties of materials [1]. Nowadays it is used in an ample variety of fields

(e.g. biology, physics, chemistry, astrophysics, materials science, paint

restoration, forensics) and materials (e.g. polymers, ferromagnets, organics) in

different forms (e.g. solids, liquids, gases) [2-4]. In the work presented in this

thesis, optical spectroscopy has been used in different materials of current

interest in solid state physics and for the purposes of this work, it has been

used to determine the optical conductivity, σ (ω), of the material under study.

In this introductory chapter we describe why optical spectroscopy is a good

tool for understanding the electronic and vibrational properties of matter and

what can be learn from it.

1.1.1 Historical background

In a dictionary-like definition, it is reported that optical spectroscopy is the use

of light to investigate the properties of a material. From a historical viewpoint,

spectroscopy arose in the 17th

century after a famous experiment carried out by

Isaac Newton and published in 1672. Contemporaries thought they were

looking at ghosts and called themselves “ghost watchers.” “Ghost” in Latin is

spectrum, while “watcher” in Greek is scopos – hence the term

“spectroscopy.” In this experiment, Newton observed that sunlight contained

all the colors of the rainbow, with wavelengths that ranged over the entire

visible spectrum (from about 390 nm to 780 nm). At the beginning of the 19th

century, the spectral range provided by the Newton spectrum was extended

with the discovery of new types of electromagnetic radiation that are not

visible; infrared (IR) radiation by Herschel (1800), at the long-wavelength

end, and ultraviolet (UV) radiation by Ritter (1801) at the short-wavelength

end. Both spectral ranges are now of great importance in different areas, such

12 Basics of optical spectroscopy

as environmental science (UV and IR) and communications (IR). The strong

development of optical spectrophotometers during the first half of the 19th

century allowed numerous spectra to be registered, such as those of flame

colors and the rich line spectra that originate from electrical discharges in

atomic gases. With the later development of diffraction gratings, the

complicated spectra of molecular gases were analyzed in detail, so that several

spectral sharp-line series and new fine structure details were observed. This

provided a high-quality step in optical spectroscopy. For a long time, a large

number of spectra were registered but their satisfactory explanation was still

lacking. In 1913, the Danish physicist Niels Bohr elaborated a simple theory

that provided an explanation of the hydrogen atomic spectrum previously

registered by J. J. Balmer (1885). This represented a large impulse for the later

appearance of quantum mechanics; a fundamental step in interpreting a variety

of spectra of atoms and molecules that still lacked a satisfactory explanation.

The interpretation of optical spectra of solids is even more complicated than

for atomic and molecular systems, as it requires a previous understanding of

their atomic and electronic structure. Unlike liquids and gases, the basic units

of solids (atoms or ions) are periodically arranged in long (crystals) or short

(glasses) order. This aspect confers particular characteristics to the

spectroscopic techniques used to analyze solids, and gives rise to solid state

spectroscopy. This new branch of the spectroscopy has led to the appearance

of new spectroscopic techniques, which are increasing day by day [5].

1.1.2 The electromagnetic spectrum

Every day, different types of electromagnetic radiation are invading us; from

the low-frequency radiation generated by an AC circuit (≈ 50 Hz) to the

highest photon energy radiation of gamma rays (with frequencies up to 1022

Hz). These types of radiation are classified according to the electromagnetic

spectrum (see Table 1.1), which spans the above-mentioned wide range of

frequencies. The electromagnetic spectrum is traditionally divided into seven

well-known spectral regions; radio waves, microwaves, infrared, visible and

ultraviolet light, X- (or Roentgen) rays, and γ -rays. All of these radiations

Basics of optical spectroscopy 13

have in common the fact that they propagate through the space as transverse

electromagnetic waves and at the same speed, c ≈ 3 × 108 m s

−1, in a vacuum.

The various spectral regions of the electromagnetic spectrum differ in

wavelength and frequency, which leads to substantial differences in their

generation, detection, and interaction with matter. The limits between the

different regions are fixed by convention rather than by sharp discontinuities

of the physical phenomena involved. Each type of monochromatic

electromagnetic radiation is usually labeled by its frequency, ν, wavelength, λ,

photon energy, E, or wavenumber

˜ . These quantities are interrelated by the

well-known quantization equation

(1.1)

where h = 6.62 × 10−34

J s is the Planck’s constant.

1.1.3 Overview of the spectroscopic techniques

The different spectroscopic techniques operate over limited frequency ranges

within the electromagnetic spectrum, depending on the processes that are

involved and on the magnitude of the energy changes associated with these

processes. Table 1.1 includes the microscopic body probed by the excitation,

as well as some spectroscopic techniques used in each spectral region. In

magnetic resonance techniques (NMR and EPR), radio frequencies and

microwaves, respectively, are used to induce transitions between different

nuclear spin states (Nuclear Magnetic Resonance, NMR) or electron spin

states (Electron Paramagnetic Resonance, EPR) by applying a magnetic field.

NMR transitions are excited by frequencies of about 108 Hz, while EPR

transitions are excited by frequencies of about 1010

Hz. (Obsolete, pulsed

techniques are used in NMR) These techniques are of great relevance in the

study of molecular structures and of local environments in solids.


Spectral

region

Wavelength (cm-1

) energy (eV) Microscopic

excitation

spectroscopy

γ-rays < 109 > 10

5

Atomic

Nucleus

Mossbauer

X-rays 106 - 10

9 10

2 - 10

5 Inner

electrons

XAS,

EXAFS,

XANES,

XRF, etc.

Ultraviolet 50000 - 25000 6.2 - 3 [Electronic

and

vibrational

transition]

Outer

electrons

Molecular

vibrations

and rotation

Optical

(UV, Raman

and IR)

Visible 25000 - 13000 3 - 1.6

Infrared 13000 – 4000 NIR 1.6 - 0.5

NIR

4000- 1000

MIR

0.5 – 0.12

MIR

1000 – 10 FIR 0.12 –

0.001FIR

Microwave 10 – 0. 1 10-3

– 10-5

Electron

Spin

Nuclear

Spin

EPR

NMR

Radio < 0. 1 < 10

-5

Table 1.1: Spectroscopic probes for the different spectral regions. XAS = X-

Ray Absorption Spectroscopy; EXAFS, Extended X-ray Absorption Fin

Structure; XANES = X-Ray Absorption Near-Edge Spectroscopy; XRF =

X-Ray Fluorescence; EPR = Electron Paramagnetic Resonance; NMR =

Nuclear Magnetic Resonance. The shaded region indicates the present

investigation range.


Atoms in solids vibrate at frequencies of approximately 1012 –10

13 Hz. Thus,

vibrational modes can be excited to higher energy states by radiation in this

frequency range; that is, infrared radiation. Infrared absorption and Raman

scattering are the most popular vibrational spectroscopic techniques, together

with neutron scattering and inelastic X-ray scattering. Therefore they are

useful to identify molecular species and vibrating complexes in different

materials, as well as to detect structural changes in solids.

The electronic energy levels are separated by a wide range of energy values.

Electrons located in the outer energy levels involve transitions in a range of

about 1–6 eV. These electrons are commonly called valence electrons and can

be excited with appropriate near-ultraviolet (UV), visible (VIS), or near

infrared (IR) radiation in a wavelength range from about 50000 cm-1

to about

3000 cm-1

. This wavelength range, called the optical range, is investigated by

optical spectroscopy, the technique used in the present thesis. Finally, core

electrons are excited by vacuum-UV and X-ray radiation, while nuclear

transitions involve the absorption or emission of gamma rays.

1.2 Optical functions

The spectroscopic methods available nowadays are numerous. Each of them

is utilized to resolve in an optimal way a specific physical problem. The

choice of the technique depends on the type of excitation (for instance, of

charge or of magnetic origin) to be analyzed, its energy and momentum

domain, anisotropy considerations (polarization dependence), and resolution

requirements. For the analysis of the charge dynamics in solids, the response

to electromagnetic radiation is usually treated in terms of the following

response functions:

the dielectric function )(ˆ = ε1 (ω) + iε2 (ω), (1.2)

the optical conductivity )(ˆ = σ1 (ω) + i σ2 (ω), (1.3)

The complex refractive index )(ˆ N = n (ω) + i k (ω) (1.4)

These optical functions are related with each other through equations derived

from standard electrodynamics (Wooten). Indeed


(1.5)

(1.6)

(1.7)

(1.8)

(1.9)

(1.10)

where )(ˆ is the dielectric function , )(ˆ N is the complex refractive index

,The real part n (ω) (refractive index) modifies the speed of light whereas k

(ω) (extinction index) represents absorption in the solid and )(ˆ is the

optical conductivity.

In the optical range the photon momentum q is much smaller than the typical

electron momentum in solids, hence the optical spectroscopy measures

practically at the q=0 limit. The first step in the quantitative analysis of the

electromagnetic response of a solid is the determination of optical functions

out of the experimental observables. These observables include: reflectance,

transmittance, absorption coefficient, and the so-called ellipsometric angles.

The real and imaginary part of the complex dielectric function )(ˆ ,or the

complex conductivity )(ˆ , can then be inferred by one of the following: (1)

measuring both - reflectivity R(ω) and transmittance T(ω), either by Kramers-

Kronig analysis or modeling of R(ω) or T(ω), (2) by measuring ellipsometric

angles, ψ(ω) and ∆(ω), which are subsequently used to determine the dielectric

function through analytical expressions. It is worth mentioning that one of the

most interesting properties of optical spectroscopy is its capability to probe a

very wide range of photon energies.


1.3 Transmittance, reflectance, and absorption coefficient

1.3.1 Definitions and standard relations

The transmittance is defined through

T() IT ( )

I0( ) (1.11)

where I0 and IT are the intensities of the incident and transmission beams,

respectively.

The reflectance is defined through

R( ) IR ( )

I0( ) (1.12)

where I0 and IR are the intensities of the incident and reflected beams,

respectively.

The absorption coefficient which describes the fractional decrease of

intensity with the distance r [i.e. describes the exponential decay of the

intensity of light inside a medium, Lambert’s law].

= (1.13)

If

I0 is instead the intensity which impinges onto the sample of thickness d

and reflectivity R from an external source, as it is the case in real experiments,

the transmittance is given by

(1.14)

Finally, the absorption coefficient and the dissipative part of the index of

refraction are related by

(1.15)

Where λ is the wavelength of the light. The second exponential factor in Eq.

(1.13) describes a wave traveling with phase velocity c/n, hence the earlier

identification of n as the refractive index.


The reflectance R at normal incidence is related to n and k by the expressions

(1.6)

To determine n and k (and hence )(ˆ from the reflectivity (1.16), one thus

needs a second equation. Two approaches are followed:

1. One can exploit the fact that the real and imaginary part of the dielectric

function is related by the Kramers-Kronig relations. These equations, plus

knowledge of R at all frequencies, permit one, in principle, to find the separate

values of n and k. In practice the numerical analysis can be quite complicated,

and the method has the disadvantage of requiring measurements to be made at

enough frequencies to give reliable extrapolations to the entire frequency

range.

2. One can use the generalization of (1.16) to non-normal angles of incidence.

One then obtains a second expression for the reflectivity at a different angle of

incidence, involving n, k, and the polarization of the incident radiation. By

comparing this expression with the measured reflectivity, one obtains a second

equation involving n and k, and the two can then be extracted.

1.4 Kramers Kronig Relations

Our discussion on the optical properties of solids will be complete with one

more topic; this is the Kramer-Kronig relation. This relation is a mathematical

result that relative the real and the imaginary parts of any complex functions

(i.e., the optical conductivity, the dielectric function, and the refractive index).

Kramers- Kronig relations can be derived by applying the Cauchy integral

formula to a function analytic and bounded in the entire upper half-plane of

its complex argument, and they express the interdependence between the real

and the imaginary parts of such a function [6, 7].

Under the conditions of time and space homogeneity and locality the linear

response of a medium to an electric stimulus can be expressed by the vector of

polarization P (t):


tdtEtttP )()()(0

(1.17)

where )( 'tt is the response function of the medium after an electric field

)(tE had been applied in time t and єo is the permittivity of vacuum. After

Fourier transforming each of the functions involved (1.17) can be rewritten in

the frequency domain as

)()()(0

EP (1.18)

which explicitly expresses the linear response of a medium to a harmonic

component of an electromagnetic wave. The dielectric displacement vector

)()(ˆ)()(1(

)()()(

00

0

EE

PED

(1.19)

where )(ˆ is the complex dielectric function, χ (ω) the electric susceptibility

is analytic and bounded in the upper half-plane of the complex angular

frequency argument. This can be deduced after applying the causality

principle, [i. e. ( )tt = 0 for t < t ], with the expression for closed- contour

integral around the upper half-plane when evaluating the Fourier transform of

this function:

dett tti

)()(2

1)( (1.20)

Application of the Cauchy integral formula on χ (ω) yields the following

equation

di )(

)( (1.21)

after separating its complex components (subscripts r and i will be used for the

real and imaginary parts respectively):

di

r

)(1)( (1.22)


dri

)(1)( (1.23)

Where ω and are real and independent values of the angular frequency and

P denotes the Cauchy principal value of the integral. This pair of equations is

called the Kramers - Kronig relations.

They relate the real (dissipative) with the imaginary (absorptive) parts of the

susceptibility and are also referred to as dispersion relations. χ (t – t ) is a real

quantity. From (4) then follows

)(*)( (1.24)

where * denotes the complex conjugate. Consequently equations (1.22) and

(1.23) reformulated for positive values of frequency read:

diir

0

22

)()(2)( (1.25)

drri

0

22

))((2)( (1.26)

Equivalently they can be written for other material parameters, like the

complex dielectric function )(ˆ , after substituting 1)(ˆ)( or the

complex index of refraction )(ˆ N = n (ω) + i k (ω) for which )(ˆ)(ˆ 2 N .

Using these general relations we can derive various expressions connecting the

real and imaginary parts of different optical parameters and response

functions.

The current J is related to the electric field E by Ohm’s law [J = σ E]; and the

complex conductivity )(ˆ = σ1 (ω) + iσ2 (ω) is the response function

describing this. The dispersion relation which connects the real and imaginary

parts of the complex conductivity is then given by:

d0

22

21

)(2)( ( 1.27)


d0

22

12

)(2)( (1.28)

Since )(ˆ = )(ˆ * and the real part σ1 (−ω) = σ1 (ω) is an even function

and the imaginary part σ2 (−ω) = −σ2 (ω) is an odd function in frequency.

1.5 Generalization of Reflectance and Transmittance to any

angle of incidence

1.5.1 The Fresnel equations

When light moves from a medium of a given refractive index into a second

medium with refractive index , both reflection and refraction of the light

may occur. The Fresnel equations describe what fraction of the light is

reflected and what fraction is refracted (i.e., transmitted). They also describe

the phase shift of the reflected light. The equations assume the interface is flat,

planar, and homogeneous, and that the light is a plane wave. The intensity of

light reflected from the surface of a dielectric, as a function of the angle of

incidence was first obtained by Fresnel in 1827. Since the information about

solid materials is very often obtained from reflectivity R and transmission T

experiments, the propagation of electromagnetic waves across planar

interfaces between materials with different optical properties has to be taken

into account. This is done by considering continuous transitions of the

tangential components of the electric - E and the magnetic - H fields

(boundary conditions to the Maxwell equations), and the conservation of

energy. The result relates the amplitudes of the incident electromagnetic wave

with the transmitted and the reflected waves at the interface between two

media ≠ at average angle of incidence θ, these relations are given by the

Fresnel equations for the complex reflection , and transmission

(amplitude) coefficients. For perpendicular s-, and parallel p

-, polarizations and

semi-infinite media (i.e. no size effects are assumed, see also Fig 1.1), they

read:

https://en.wikipedia.org/wiki/Refractive_index

https://en.wikipedia.org/wiki/Reflection_(physics)

https://en.wikipedia.org/wiki/Refraction

https://en.wikipedia.org/wiki/Phase_(waves)

https://en.wikipedia.org/wiki/Plane_wave


(1.29)

Figure 1.1: Plane of incidence. θ and θ' angles of incidence (reflection) and

refraction. The two media are characterized by complex refractive indices,

and . The electric vectors of the incoming, the reflected and the transmitted

(refracted) beams are Ei Er and Et respectively. S (red) and P (blue) denote the

different polarizations, perpendicular and coplanar with the plane of incidence

[8].


In the general case, all quantities are of course complex: ,

.The generalized Snell’s law:

requires complex quantities for the incidence/refraction angles too.

The reflectivity R is the squared absolute value (norm) of the complex field

:

(1.30)

Hence:

(1.31)

And for the transmission T:

(1.32)

As R and T are defined as ratios of intensities on detecting, if not specially

measured, the phase information Φ is lost.

Under normal incidence (θ → 0) conditions (often realized in experiments),

the distinction between both polarizations (s and p) becomes irrelevant and the

Fresnel expressions are reduced to:

,

(1.33)

With corresponding phase changes upon reflection/ transmission

(1.34)

Assuming now =1 (air), and giving the notation , for the reflectivity

and the transmission we obtain:


(1.35)

(1.36)

1.5.2 Multi-Layer Reflection and transmission

In the following we will discuss the overall reflectivity and transmission of

one thin layer going to double layer system. The analysis of the optical

properties of a sandwich structure consisting of many layers has to start from

fresnel’s formulas as derived in sec. 1.5.1.

(1.37)

For light travelling from medium 1 to medium 2 for a one layer system (i.e. a

material of thickness d, refractive index n and extinction coefficient k which is

Situated between materials labelled by the subscripts 1 and 3), the total

reflection and transmission coefficient are

and

(1.38)

Where the reflection and transmission coefficient of each interface are

calculated according to the previous equations (1.37) and the complex angle

(1.39)


The angle

indicates the phase change on one passing through the

medium of thickness d and refractive index n. here λ is the wavelength in

vacuum, hence β describe the ratio of film thickness and wavelength in

medium. Sometimes it is convenient to combine both to a complex angle Eq.

(1.39). α Is the power absorption coefficient and was defined In Eq. (1.15). as

defined above. Obviously this procedure can be repeated for multilayer

systems. The complex reflection coefficient of the last interface has to be

replaced by total reflection coefficient of two subsequent interfaces according

to (1.38). Thus we obtain after some rearrangement

(1.40)

The corresponding formula, describing transmission of layer 2 and layer 3

between media 1 and media 4 has the form

(1.41)

Where and are complex Fresnel transmission and reflection coefficient

at boundaries between media p and q (with p,q = 1,2,3,4), and the complex

angle

[7,9].

26 Bibliography

Bibliography

[1] E. F. Nichols, Phys. Rev. (Series I) 1, 1 (1893)

[2] P. Calvani "Large polaron absorption in high-Tc cuprates" Physica Status

Solidi 237, 194 (2003)

[3] J. J. Polit, E. M. Sheregii, E. Burattini, A. Marcelli, M. Cestelli Guidi, P.

Calvani, A. Nucara, M. Piccinini, A. Kisiel, J. Konior, E. Sciesinska, J.

Sciesinski, and A. Mycielski. "Analysis of phonon spectra of the Zn(x)Cd(1-

x)Te solid solutions". Journal of Alloys and Compounds 371, 172 (2004)

[4] C. Mirri, P. Calvani, F. M. Vitucci, A. Perucchi, K. W. Yeh, M. K. Wuand

S. Lupi “Optical conductivity of FeTe1-xSe” Superconductor Science &

Technology 25, 045002-1-7 (2012)

[5] J.Garcia Sole, L. E. Bausa, and D. Jaque in “An Introduction to the Optical

Spectroscopy of Inorganic Solids” (Universidad Autonoma de Madrid,

Madrid, Spain 2005)

[6] Ablowitz, M. J. and Fokas, A. S., Complex Vari- ables: Introduction and

Applications, Cambridge Univ. Press, New York, (1997)

[7] M. Dressel and G. Grüner in “Electrodynamics of Solids” Cambridge

University Press (2002)

[8] P. Yordanov “Spectroscopic Study of CaMnO3 / CaRuO3 Superlattices and

YTiO3 Single Crystals” PhD Thesis at Max-Planck-Institut für

Festkörperforschung (2009)

[9] F. Wooten, Optical Properties of Solids (Academic Press, New York and

London, 1972)

Phenomenology of Manganites and of selected Multiferroics 27

Chapter 2: Phenomenology of Manganites

and of selected Multiferroics

2.1 Manganites

Following the discovery of the high Tc superconducting cuprates [1], the

studies on a variety of transition-metal (TM) oxides revived and produced a

great number of scientific results. Modern theoretical and experimental

methods have been used to study both materials which had been fabricated in

earlier times and new and/or doped materials. Among those compounds there

are the manganites [2, 3]. This family of materials is named after the

manganese ion which is a key ingredient of the compounds. The simplest

manganites have the general formula Rl-xAxMn03 (R: a trivalent cation (La+3

,

Pr+3

, Nd+3

, etc.) and A: a divalent cation (Ca+2

, Sr+2

, Ba+2

, etc.)) with

pseudocubic perovskite structure. These materials were first described in 1950

by Jonner and van Santen. Unlike in the usual ferromagnets, the transition of

manganites to ferromagnetic state (at T = TC, where TC is the Curie

temperature) takes place at finite “doping”, x ≠ 0, and is accompanied by a

drastic increase in conductivity. This transition from an insulating to a metallic

and magnetic state is one of the most remarkable fundamental features of these

materials. It is called colossal (negative) magnetoresistance (CMR). One year

later, Zener (1951) explained this unusual correlation between magnetism and

transport properties by introducing a novel concept, so-called “double

exchange” mechanism (DE) [for more details see section 3.1 chapter 3

“theoretical Background”]. Zener’s pioneering work was followed by more

detailed theoretical studies by Anderson and Hasegawa (1955) and de Gennes

(1960). The study of perovskite manganites is undergoing intensive

development, not only because these materials have great potential in

applications related to the CMR effect [4, 5], but also because they offer a

testing ground for theories related to strongly correlated systems.

28 Phenomenology of Manganites and of selected Multiferroics

2.2 Colossal Magnetoresistance (CMR) in manganites

Colossal magnetoresistance (CMR) is a rare phenomenon in which the

electronic resistivity of a material can be decreased by orders of magnitude

upon application of a magnetic field in the proximity of the Curie temperature.

This outstanding property has attracted wide attention in the past decades, as it

was believed that the CMR effect could be the key to a new generation of

magnetic memory devices, magnetic-filed sensors, or transistors [6, 7]. Even if

its applications are not so wide as previously expected, CMR is still playing an

important role in materials science. Negative magnetoresistance [ρ(H) < ρ(0)]

where H is the magnetic field, was first discovered by William Thomson in

1856 but he was unable to lower the electrical resistance of anything by more

than 5%. MR is usually given as a percentage:

(2.1)

where ρ is the resistivity. Then the MR has a maximum value of 100% and MR

for manganites is negative because the application of a magnetic field causes a

decrease of (ρ). In the past century, materials showing both Giant and colossal

magnetoresistance were discovered. The former effect was observed in thin

films composed of alternating ferromagnetic and non magnetic conduction

layers. The effect is observed as a significant change in the electrical

resistance depending on whether the magnetization of adjacent ferromagnetic

layers is in parallel or anti-parallel alignment. The overall resistance is

relatively low for parallel alignment and relatively high for anti parallel

alignment.

Colossal magnetoresistance is instead a property intrinsic to manganese- based

provskite oxides, which – as above mentioned - display changes in resistance

by orders of magnitude upon the application of an external field. CMR is

strictly related to the metal-to-insulator (MIT) transition. For instance, in the

doping region 0.2 < x < 0.5, the ground state of La0.7Ca0.3MnO3 is a

ferromagnetic metal where dρ/dT > 0 while, above Tc, the material displays an


activated temperature dependent resistivity. It is clear that the metal-

insulator transition coincides with the ferromagnetic to paramagnetic

transition. The CMR occurs to TC and is illusrated in Fig. 1.2(a) shows the

resistivity as a function of temperature for several different externally applied

magnetic fields [8]. As the applied field increases, the resistivity drops

dramatically and the resistivity peak shifts to higher temperatures. Figure

1.2(b) shows instead MR% as a function of applied field in. The

magnetoresistance exceeds 99% for modest applied fields around a few Tesla.

Large magnetoresistance effects may not be surprising [9]. The relation

between ferromagnetism and metallicity in manganites and its origin will be

discussed in Section 3.1.

Figure 2-1: Magnetic-field dependent resistivity in (La,Ca)MnO3 for x ≈ 0.3.

(a) Resistivity versus temperature for x = 0.25 at different applied magnetic

field [after Ref. 8]. (b) Magnetoresistance as a function of applied magnetic

field for x = 0.33 [after Ref. 10].


2.3 Structural properties of Manganites

Rare-earth manganites have general chemical formula Rl-xAxMn03 (R is a

trivalent rare-earth (La, Pr, Nd, etc.) and A is a dopant divalent alkali earth

(Ca, Sr, Ba, etc.).These systems belong to the crystallographic class of the

ABO3 perovskites (Fig 2.2). The term perovskite was first used for CaTiO3, in

honor of its discoverer Perovskii. The perovskite structure is represented in

Fig.2-2, where the presence of BO6 octahedra in the structure is evidenced.

These octahedra form the skeleton of the perovskite structure. In rare-earth

manganites, distortions from the ideal cubic perovskite structure are often

observed, with consequent reduction of symmetry from cubic to orthorhombic,

rhombohedral, tetragonal, or monoclinic. These distortions are usually quite

small and one can talk of a pseudocubic structure. The stability of a perovskite

depends on the possibility to form the BO6 array, which is stable only when

the A ion is neither too large nor too small. Indeed the B-O bond lengths and

B-O-B bond angles tend to readjust in order to accommodate the A ion in the

structure. Therefore, there is a limiting value for the dimension of the A ion

for the perovskite structure to be stable, defined by the tolerance factor:

(2-2)

where rA, rB, and rO are the ionic radii of the A, B, and O atoms respectively.

Tf = 1 implies a perfect cubic perovskite, while for Tf < 1 the A ion is too

small to fill the space between the BO6 octahedra which tend to tilt in order to

occupy the available space. On the other hand, for Tf > 1 or Tf <0.75 the

pseudocubic structure is generally unstable.


Figure 2-2: Structure of a cubic ABO3 perovskite

Some ionic radii for the respective elements in perovskite-like structures of

manganites are listed in the table 1-2

Ions Ca2+

Sr2+

Ba2+

Mn3+

Mn4+

O2-

La3+

Nd3+

Sm3+

Radius(Å) 1.34 1.44 1.61 0.645 0.53 1.40 1.36 1.27 1.24

Table 1-2: Ionic radii (in Angstroms) of elements often incorporated in the

perovskite structure of manganites [11].

2.4 Electronic properties of Manganites

The interesting physical properties of manganites are to a considerable extent

related to the Mn cation and its surrounding O octahedron [12].Mn d-electrons

comprise the key players determining the electronic properties of the

manganites. For an isolated Mn atom the 3d levels present a five-fold

degeneracy, but in a manganite crystal six oxygen ions form an octahedron

around the Mn. The effect of the crystal field is to partially lift the degeneracy

into a t2g triplet (dxy, dyz and dzx) and an eg doublet (dx2-y2 and d3z2-r2). The

energy of the t2g levels is lower than for the eg, the difference being of the

order of 1-2 eV [13]. This energy difference stems from the Coulomb

interaction between Mn 3d electrons and oxygen ions: t2g orbitals point away

from the oxygens while eg extend in the direction of oxygens. Due to the

strong Coulomb interactions within t2g levels, double occupation is deterred

and a high-spin state is favored. (Total spin number S=2). The t2g electrons,

less hybridized with 2p states and stabilized by the crystal field splitting, are

viewed as always localized by the strong correlation effect and as forming the

local spin (S=3/2) even in the metallic state. Even the electrons of the eg state,

whose degeneration is removed by the Jahn-Teller effect (see Section 3.2) and

which are hybridized strongly with O 2p states, are affected by such a

correlation effect, and tend to localize in the `carrier-undoped or the parent all-


Mn3+

-based compound, forming the so-called Mott insulator. However, the eg

electrons can be itinerant and hence play a role of conduction electrons, when

electron vacancies or holes are created in the eg orbital states of the crystal.

The latter hole-doping procedure corresponds to creation of mobile Mn4+

species on the Mn sites. The important consequence of the apparent separation

into the spin and charge sectors in the 3d orbital states is the effective strong

coupling between the eg conduction electron spin (S=1/2) and t2g electron local

spin (S=3/2). This on-site ferromagnetic coupling follows the Hund's rule. The

exchange energy JH (Hund's-rule coupling energy) was measured optically for

Nd1-xSrxMnO3 and was found to be 2.2 eV for x=0.05 and 2.1 eV for x=0.10.

It turned out to be 1.7 eV for the La-Ca manganites [14]. Those values exceed

the intersite hopping interaction t0

ij of the eg electron between the neighboring

sites, i and j. In the strong coupling limit JH/tij,→∞, the effective hopping

interaction tij can be expressed in terms of Anderson-Hasegawa relation [12],

as

tij=t0ijcos(θij/2). (2.3)

Thus, the absolute magnitude of the effective hopping depends on the relative

angle (θij) between the neighboring (classical) spins. The ferromagnetic

interaction via the exchange of the (conduction) electron is termed as the

double exchange interaction after the naming by Zener [see section 3.1]. By

creating electron-vacancy sites (or hole doping) the eg electron can hop

depending on the relative configuration of the local spins. The ferromagnetic

metallic state is stabilized by maximizing the kinetic energy of the conduction

electrons (θij=0). When temperature is raised up to near or above the

ferromagnetic transition temperature (TC), the configuration of the spin is

dynamically disordered and, accordingly, the effective hopping interaction is

also subject to disorder and reduced on average. This would lead to

enhancement of the resistivity near and above TC. Therefore, the large MR can

be expected around TC, since the local spins are relatively easily aligned by an

external field and hence the randomness of the eg hopping interaction is


reduced. This is the intuitive explanation of the MR observed for the

manganite around TC in terms of the double-exchange (DE) model.

2.5 LaMnO3 and its phase diagram

Among the manganese oxides, lanthanum manganite (LaMnO3) is particularly

important because it is the parent compound of the family of the manganites

which exhibit the CMR effect [15, 16, 17]. Therefore, a thorough

understanding of this material is indeed a prerequisite to achieve a better

understanding of the family. This system displays a complex correlation

between structural, orbital, magnetic, and electronic degrees of freedom.

LaMnO3 is a basic compound of the ABO3 type perovskite structure [18]. It is

a paramagnetic insulator but shows a paramagnetic to antiferromagnetic

transition at a temperature of about 150 K [18]. At TJT = 750 K, LaMnO3

changes from a static orbital ordered state with cooperative JT distortion to an

orbital disordered state with dynamic, locally JT distorted octahedral [19].

This order-disorder transition is also accompanied by an abrupt decrease in the

electrical resistivity. While there has been considerable effort to decouple

these interactions, many fundamental questions on the interplay and relative

significance of electron-lattice (e-l) and electron-electron (e-e) interactions in

LaMnO3 remain unsolved. The Mott-Hubbard interaction energy, Udd,

required for creating a dn+1

dn-1

excitation in an array of dn ions, lies in range of

4-5 eV. Similarly, the charge-transfer energy, Upd, (energy for creating p5d

n+1

charge excitation from p6d

n) has been estimated around 5eV. Many groups

have estimated the

Udd and Upd between 4-6 eV [20, 21,22]. Since both these energies are of

comparable magnitude, LaMnO3 is believed to posses both Mott-Hubbard type

and charge transfer type insulator character. In 3d transition metal group, the

early oxides are Mott-Hubburd insulators whereas the last members are

charge-transfer insulators. [A detailed review of transition metal oxides has

been given by A.K. Raychaudhuri [23].] This supports that, for an oxide in the

middle of the series such as LaMnO3, both Udd and Upd become comparable. In


undoped LaMnO3, Mn exists in 3+ oxidation states wherein due to doping of

divalent cation, a fraction of Mn3+

state is converted to Mn4+

state. Mn3+

is a

3d ion with four electrons in spin-up orbitals whereas all the spin-down

orbitals are vacant. The five d-orbitals are split by crystal field of oxygen in 3

t2g and 2 eg orbitals. These levels are separated by an energy ~1.5 eV for Mn3+

and 2.4 eV for Mn4+

[24]. The strong Hund’s rule coupling ensures the parallel

alignment of electron spin in 3 t2g and 2 eg energy levels. In principle the pure

compound is supposed to be cubic in structure but the cation mismatch at A-

site cause the structural distortion. When the symmetry is lower than cubic, the

degeneracy of the eg and t2g levels is lifted by Jahn-Teller (J-T) distortion and

JT separation lies in the range ~ 0.5-1 eV [25]. This distortion compresses the

MnO6 octahedra along ab-plane and elongates along the c-axis, thus resulting

in reduced overlap of Mn 3d-orbitals and oxygen p-orbitals. Therefore, due to

the structural distortion of MnO6 octahedra, the conduction in the compounds

having all Mn3+

ions is not possible. The structural distortion caused by Jahn-

Teller effect is long-range order effect and is more effective when the Mn3+

content, upon doping with divalent ions, remains very large. In the absence of

any eg electron, Mn4+

does not create the JT distortion around it. Here, it

should be mentioned that this is volume preserving, whereas the other kind of

distortion called breathing mode distortion is uniaxial and not volume

preserving.

2.5.1 Divalent doping of LaMnO3: mixed-valence manganites

Partial substitution of trivalent cation at A site by a divalent cation results into

a composition with a general formula (R1-xAx) MnO3 (R = La, Pr, Nd, etc.; A =

Ca2+

, Sr2+

, Ba2+

, etc.). This causes an amount (equal to x) of Mn3+

to convert in

Mn4+

state. Since Mn exists in mixed valence state, these compounds are also

known as “mixed-valent manganites”.

The rich phase diagram of La1-xCaxMnO3 [26-33] is shown in Fig. 3.2 as a

function of Ca concentration x and of temperature. The metallic phase only

exists over a narrow range of 0.17≤ x ≤0.50, where the important CMR effect

http://home.gwu.edu/~xqiu/qiu_thesis/node43_ct.htm#fig_ch3_lcmopd


is observed. At low doping levels, the lattice structure in ground state is

orthorhombic, and the magnetic structure is type-A anti-ferromagnetic [30].

This magnetic structure is made up of ferromagnetic planes coupled anti-

ferromagnetically. The proposed canted anti-ferromagnetism (CAF) is

nowadays considered as coming from phase separation at nanometer

scales [34]. It is very interesting to note the coexistence of ferromagnetism and

insulating phase (FI) between 0.1 and 0.17. At rational doping x = 0.375, the

highest Curie temperature ( 260 K) is observed. The 50% doping presents

one particularly interesting case where the type CE charges ordering (CO) is

the stable ground state. The highly doped La1-xCaxMnO3 (x > 0.5) shows

various types of anti ferromagnetism. The end member CaMnO3 has a perfect

cubic lattice structure and type G anti ferromagnetic (AF) structure where

every Mn4+

is coupled anti-ferromagnetically with its six neighboring

Mn4+

ions. There is no JT distortion in CaMnO3 because only Mn4+

O6

octahedra do exist. Other than changing doping or temperature, external

pressure and isotope substitution also considerably modify the phase diagram.

Most studies have been focused on their effects on the resistivity and Curie

temperature [35-38].

Figure 2-3: Phase diagram of the mixed-valence manganite system: La1-

xCaxMnO3. PI – paramagnetic insulating state, FM- ferromagnetic metallic, FI

– ferromagnetic insulating, AF – antiferromagnetic, CAF – canted

antiferromagnetic, CO – charge/orbital ordered state [After Ref. 39].

http://home.gwu.edu/~xqiu/qiu_thesis/node101_ct.htm#schif_prl95

http://home.gwu.edu/~xqiu/qiu_thesis/node101_ct.htm#dagot_b_npsacm


2.6 Optical properties of manganites

Optical absorption studies of the stoichiometric parent compound LaMnO3

(LMO) were studied. However, for LMO, the electronic ground state and the

charge transfer mechanisms are not fully understood.

The optical conductivity of LMO, while featureless in the mid and near-

infrared regions (500−10 000 cm−1

), displays an absorption band centered on 2

eV (16 000 cm−1

) whose origin is controversial. The first observations of the

2-eV band in the optical conductivity assigned this feature to O (2p) → Mn

(3d) transitions, assuming a charge-transfer (CT) character for LMO [40].

Afterwards, the optical conductivity of LMO has been theoretically

reconsidered in a tight-binding approach (TB), where only the eg ordered

orbitals of the Mn ions were involved in the charge dynamics [41].

In the far infrared, basically there are three phonon modes optically active, at

about 200, 400 and 600 cm -1

(the exact frequencies varying with the

compound). They correspond to an A-site mode, an M-O-M bending mode

and a M-O stretching mode, respectively. The bending mode is split in the O′

structure of LaMnO3. There are numerous Raman-active modes [42, 43]

including a broad band at 650 cm-1

(0.085 eV), possibly associated with

magnetic, electronic or Jahn-Teller excitations, and another mode at 2100 cm-1

which could be a plasmon or a single-particle electronic excitation [44]. The

influence of substrate-induced lattice distortion on the infrared phonon mode

was measured in thin films of (La0.7Ca0.3) MnO3 [45]. The optical properties of

the doped manganites are very interesting and puzzling (see Refs. 46 – 55).

The earliest optical characterization of mixed-valence manganites was aimed

at evaluating the materials for magneto-optic recording. There have been

studies of magneto-optic Kerr effect [56, 57] and Faraday Effect [58, 59] as a

function of wavelength. The magneto-optic activity is greatest in the vicinity

of the absorption near 1.8 and 3 eV, associated with intra-atomic d-d

transitions and 2p(O) - 3d (Mn) charge transfer respectively [56, 58],

indicating that spin-polarized Mn-d levels are involved in both these

transitions.


Figure 2-4: Schematic diagrams of σ (ω) for CMR manganites [after Ref.60]

Figure 4-2 shows the schematic diagram of a typical optical conductivity

spectrum for CMR manganites for (a) T>TC and (b) T<<TC. With decreasing

T, a very broad peak near 3.5 eV, which originates from interband transition

between the Hund's rule split bands, decreases. Also a small polaron peak near

0.5 eV changes into a coherent Drude peak and an incoherent mid-infrared

peak. There are also two other T-independent peaks: a broad peak around 4.5

eV, which arises from the charge-transfer transitions between the O 2p and the

Mn d levels, and a peak centered around 1.5 eV, which comes from the inter-

orbital transition at the same Mn3+

site.

Arima and Tokura [61] showed how the main absorption edge due to 2p(O) -

3d(Mn) charge transfer in LaMO3 falls from 6 eV for M = Sc to zero for M=

Ni (LaNiO3 is a metal) (Fig. 5-2).


There is some dispute as to where the charge transfer absorption sets in

forRMnO3. A common view is to associate the absorption edge at 3.1 eV with

this transition, and to assign the weaker absorption feature at about 1.7 eV to

the dipole forbidden eg5 t2g

5 transition of the Mn

+3 ion [56,58], which may

be split by the Jahn-Teller effect [58]. This crystal-field transition corresponds

to promotion of a t2g electron into a vacant eg orbital. However, Arima and

Tokura argue that the stability of the S= 5/2 final state (3d5 L ) depresses the

onset of the 2p (O) 3d (Mn) charge transfer to about 1 eV, and the strong

increase of conductivity above 3 eV is then associated with promoting a spin

down oxygen electron to form an S = 3/2 , t4

2g eg or t32ge

2g excited state which

lies higher in energy by 5/2 JH - Δcf or 5/2 JH respectively, where JH is the

Hund coupling for an electron to the S=2 ion core and Δcf is the crystal-field

splitting. The Hund energy was directly measured in Sr1−xCexMnO3 [14] and

found to be 2.20.1 eV.

Figure 2-5: Excited energy levels of the LaMO3 perovskite series (M= 3d

metal) deduced from optical absorption [After Ref. 61].


Systematic investigations of the optical absorption and optical conductivity of

RMnO3 perovskites have covered frequencies from infrared to ultraviolet.

As derived from a number of different reports, the optical conductivity

spectrum of manganite perovskites can be also understood in terms of two

broad intensive bands centered around 2.0 and 4-5 eV [62-66]. Although the

nature of the lower energy transitions is somewhat controversial [66], it has

been argued recently, based on cluster model calculations, that features around

2.0 eV should be attributed to intersite d-d charge transfer transitions, whereas

the higher-energy transitions should be related to one-center p-d charge

transfer transitions.

A. S. Moskvin et al, 2010, [66]) have performed both theoretical and

experimental studies of optical response of parent perovskite manganites

RMnO3 (R = La, Pr, Nd, Sm, Eu), with the main goal to elucidate nature of

clearly visible optical features. Starting with a simple cluster model approach

they addressed both the one-center (p-d) and two-center (d-d) charge transfer

(CT) transitions. Optical complex dielectric function of single-crystalline

samples of RMnO3 was measured by ellipsometric technique at room

temperature in the spectral range from 1.0 to 5.0 eV for two light

polarizations: E┴ c and E||c (see Fig 4-2), the comparative analysis of the

spectral behavior of ε1 and ε2 is believed to provide a more reliable assignment

of spectral features. They have found an overall agreement between

experimental spectra and theoretical predictions based on the theory of one-

center p-d CT transitions and intersite d-d CT transitions. They claim that the

parent perovskite manganites RMnO3 should rather be sorted neither into the

CT insulator nor the Mott-Hubbard insulator in the Zaanen, Sawatzky, Allen

scheme.


Figure 2-6: Real and imaginary parts of the dielectric function ε in RMnO3.

The left-hand panel presents the spectra for E┴c polarization, the right-hand

panel does for E|| c polarization. The Lorentzian fitting data are shown by

solid lines. A proper Lorentzian decomposition with assignment of all the

peaks is shown for ε2 after [After Ref. 66].

(Nandan pakhira et al. 2011) [67]. Also calculated the optical conductivity σ

(ω) for doped rare-earth manganites, and its temperature dependence for

La0.825Sr0.175MnO3 has been studied (see Fig 5-2) in its metallic ground state.

At low temperatures, the calculated σ(ω) shows a “two-peak” structure

consisting of a far-infrared coherent Drude peak and a broad mid-infrared

polaron peak, as observed in the experiments. Upon heating, the Drude peak

rapidly looses spectral weight, and σ(ω) crosses over to having just a single

broad mid-infrared peak. They also studied the doping dependence of σ(ω) for

the same compound. The integrated spectral weight under the Drude peak

increases rapidly as the doping level is increased from an underdoped,

insulating state (x = 0.1) to a highly doped, metallic state (x = 0.3). From Fig.

5-2 we can see that the height of the Drude peak decreases dramatically with

increasing temperature up to Tc. But for temperatures above Tc there is a slow

building up of the Drude peak in the far-infrared region.


Figure 2.7: Optical conductivity, σ (ω), for the system La1−xSrxMnO3 at

various temperatures as indicated, for x = 0.175 [After Ref. 67]

The optical conductivity has also been reported for the (La1- xCax) MnO3 series

by Kim et al. [68, 69]. For x = 0.3, they find a sharp Drude peak, and a broad

mid-infrared absorption which they associate with a lattice polaron. They also

find the d-d charge transfer and an intra-atomic t2g - eg transition for Mn+3

.

Measurements of optical spectra are useful in probing the electronic structure

of the perovskite-type manganese oxide and explain the spin-charge orbital

coupled and the charge-ordered phase phenomena [70,71].

Charge Ordering (CO) refers to the ordering of the metal ions in different

oxidation states in specific lattice sites of a mixed valence material. Such

ordering generally localizes the electrons in the material, making it insulating

or semiconducting due to the charge localization which in turn restricts the

electron hoping from one cation site to another. In doped manganites which as

above mentioned have the general formula Rl-xAxMn03 (R: a trivalent cation

(La+3

, Pr+3

, Nd+3

, etc.) and A: a divalent cation (Ca+2

, Sr+2

, Ba+2

, etc.)), the


charge-ordered phases are novel manifestations arising from the interaction

between the charge carriers and the phonons where in the Jahn Teller

distortions play a significant role. Charge ordering arises because the carriers

are localized into specific sites below a certain temperature known as charge

ordering temperature, TCO, giving rise to long-range order throughout the

crystal structure. Although, charge ordering would be expected to be favored

when doping level x = 0.5, due to the presence of equal proportions of the

Mn3+

and Mn4+

states, it is found in various compositions in the doping range

0.3 < x < 0.75, depending on the R and A ions. In the charge-ordered (CO)

state, the Mn3+

and Mn4+

ions are regularly arranged in the ab plane with the

associated ordering of the dx2−r2 and dy2−r2 orbitals as shown in fig. 1.

Fig: 2-8: CE-type AFM charge ordering in Pr0.6Ca0.4MnO3. The lobes show

the dx2−r2 or dy2−r2 orbitals [from Okimoto et al ref. 72].


2.7 Multiferroics

The materials which display strong coupling between two at least of the

magnetic, electric, and elastic order parameters, resulting in simultaneous

ferromagnetism, ferroelectricity, and/or ferroelasticity, are known as

multiferroics.

A ferroic is a material that adopts a spontaneous, switchable internal

alignment: In ferromagnetics, the alignment of electron spins can be switched

by a magnetic field; in ferroelectrics, electric dipole-moment alignment can be

switched by an electric field; and in ferroelastics, strain alignment can be

switched by a stress field. Individually, the ferroics are already of great

interest both for their basic physics and for their technological applications.

For example, electrical polarization in ferroelectrics and magnetization in

ferromagnets are exploited in data storage, with opposite orientations of the

polarization or magnetization representing “1” and “0” data bits. Another

example is provided by the ferroelectric ferroelastics that form the basis of

piezoelectric transducers (see figure 7-2). Current convention, however,

applies the term “multiferroic” primarily to materials that combine

ferroelectricity with ferromagnetism or, more loosely, with any kind of

magnetism (magnetoelectricity). The terminology is often extended to include

composites, such as heterostructures of ferroelectrics inter layered with

magnetic materials.

Figure 2-9: Interactions in Multiferroics


The well- established primary ferroic orderings, ferroelectricity (P),

ferromagnetism (M), and ferroelasticity (ε), can be switched by their conjugate

electric (E), magnetic (H), and stress (σ) fields, respectively. Cross coupling

allows those ferroic orderings to also be tuned by fields other than their

conjugates; in magnetoelectric multiferroics, for example, an electric field can

modify magnetism. Physicists are also exploring the possibility of

ferrotoroidics, a promising new ferroic ordering of toroidal moments (T),

which should be switchable by crossed electric and magnetic fields. The “O”

represents other possibilities—such as spontaneous switchable orbital

orderings, vortices, and chiralities—that will likely enrich future research.

(After ref.73)

Magnetoelectric compounds enable the external electric field to change

magnetization and an external magnetic field to change the electric

polarization. The magnetoelectricity may have different origins like structural

distortion (e. g., in BaTiO3), charge ordering (e. g., in LuFe2O4) [74], or

Dzyaloshinskii-Moriya interaction [75], but not all of them are fully

understood. Therefore much effort has been devoted to understand the

interaction between their magnetic and electronic degrees of freedom

(magnetoelectricity) and to exploit its potential for new spintronic devices.

Understanding the origin of magnetoelectric it is a central subject of present

solid state physics. However, the interplay between electricity and magnetism

has fascinated scientists and engineers for centuries, ever since Hans Christian

Oersted noticed in 1820, quite by accident, that a magnetic compass needle

deflected when he switched the current in a nearby battery on or off. Over the

40 years or so following Oersted’s observation, the classical theory of

electromagnetism was worked out, with seminal contributions from the studies

of André Marie Ampère and Michael Faraday; that work culminated in the

1860s with James Maxwell’s unified theory. The implications of those

discoveries for society need no elaboration. One of the very promising

approaches to create novel materials is to combine in one material different

physical properties to achieve richer functionality. The attempts to combine in


one system both the (ferro) magnetic and ferroelectric (FE) properties started

in 1960’s, predominantly by two groups in then the Soviet Union: that of

Smolenskii in St.Petersburg (then Leningrad) [76] and that of Venevtsev in

Moscow [77]. Materials combining these different “ferroic” [78] properties

were later on called “multiferroics” [79].

For some time this field of research was very “quiet’’ and not well known. An

upsurge of interest to these problems started around 2001-2003. This is

probably connected with three factors. First, the technique, especially that of

preparing and studying thin films of oxides, to which most of multiferroics

belong, was developed enormously. This permitted to make very good thin

films of, especially, ferroelectric materials, and opened the perspective to use

these systems [80, 81, 82] for very promising applications, such as e.g.

controlling magnetic memory by electric field or vice versa, new types of

attenuators, etc.

Most of the actively studied multiferroics fall into a class of materials known

as complex oxides, based on two or more transition metal cations (usually 3d)

and oxygen. They are attractive because they are chemically inert and

nontoxic, and because their constituent elements are abundant. Scientifically,

the intermediate ionic–covalent nature of transition-metal–oxygen bonds leads

to strong polarizability a desirable property in ferroelectrics and the highly

localized transition-metal 3d electrons lead to the so-called strong correlation

physics often associated with exotic magnetic behavior. But also worthy of

exploration are other material classes, including fluorides, which featured

prominently in the early history of multiferroics, and organics and selenides,

which are currently showing promising early results.


2.8 Optical spectra of Multiferroic manganites

The interplay between charge, structure, and magnetism is the origin of rich

physics in complex oxides. Because these interactions are so strong, oxides

straddle several competing regions of physical, chemical, and size-shape phase

space. An important consequence of this phase proximity is the opportunity to

drive new functionality via modification of important energy and length scales

in a material. Optical spectroscopy is a well-known probe of charge and

bonding in solids. When charge and spin degrees of freedom are strongly

coupled, it is also sensitive to magnetic excitations and spin ordering

transitions [83,84]. Magnetochromism, the modification of a material’s optical

constants with applied magnetic field, [85,86] is an especially important tool

for understanding magnetoelectric and multiferroic materials,[87,88] for

which the spin-charge interaction is expected to be large.

To understand the extensive physical properties in multiferroic ReMnO3

manganites (Re: rare earth element), it is crucial to know the electronic band

structure. Their crystal structure can be hexagonal, with MnO5 bipyramids. In

contrast with the MnO6 octahedron of the usual orthorhombic structure -

which splits the quintet d levels of Mn3+

ion into t2g and eg , here the crystal

field symmetry leads to two low lying doublets of e2g and e1g (d /d and

d /d 2− 2) states and one singlet a1g (d3z2-r2) state. Therefore, the structural

difference between the hexagonal and orthorhombic phases could be disclosed

by the optical spectra [89, 90].

The first optical measurements in hexagonal YMnO3 were performed by

Kritayakirana et al. in 1969 [91], who observed that a near infrared absorption

edge moves to higher energy with lowering temperature. For the case of

hexagonal ScMnO3 and ErMnO3, the spectra of the real and imaginary parts of

the dielectric function were also measured by Kalashnikova and Pisarev [92].

An abnormally drastic absorption peak in the region 1.57–1.59 eV is the most

pronounced feature in the spectra. This peak exhibits asymmetry and can be

decomposed into two components by peak fitting with the Gaussian functions.

Furthermore, the absorption intensity in the region above 2.2–2.4 eV increases


with photon energy. In addition, hexagonal HoMnO3 [93] and LuMnO3 [94]

also exhibit similar results. It is noteworthy that the near infrared absorption

peak exhibits a substantial blue shift of ~ 0.16 eV from 300K to 10K.

Recently, Choi et al. [95] reported a systematic study on the hexagonal

ReMnO3 (R = Gd, Tb, Dy, and Ho), and the overall features in the spectra are

similar to previous results. The most surprising part of those results is that the

temperature dependent absorption peak at ~ 1.7 eV shows an unexpectedly

large blueshift near TN among the rare-earth ions of Re = Lu, Gd, Tb, Dy, and

Ho. The assignment of the optical absorption peak at ~ 1.7 eV has also been an

issue. One interpretation is that it comes from the charge transfer transition

from the O 2p to the Mn 3d states [92, 96, 97, 98]. The photoemission

spectroscopy (PES) study proposed that the O 2p is the highest occupied state,

while the Mn d3z2−r2 state is mostly unoccupied. Other occupied Mn 3d states

(dxz/dyz, and dxy/dx2−y2) lie deep below EF [97]. The result of the first-principle

electronic structure calculations also suggested that the top of the valence band

is mainly determined by the O 2p states, and the lowest unoccupied band is

formed by the d3z2−r2 of Mn [96, 98]. The other interpretation, which is also an

extensively convincing explanation, is that it comes from on-site d-d transition

between the Mn 3d levels [93, 94, 99,100]. The transition was attributed to the

d-d transition between occupied e2g and e1g (dxz/dyz, and dxy/dx2−y2) orbitals and

the unoccupied e1g (d3z2−r2) orbit, as shown in Figure 10-2. Because of the

selection rule, transitions between d orbitals would be forbidden. However,

this rule is relaxed through the strong hybridization between the O 2p bands

and the transition-metal d bands, which was observed in the hexagonal phase

but not in the orthorhombic phase [89].


Figure 2-10: Schematic diagram of the d-d transition in ReMnO3.The red

arrows indicate electrons reside in the d orbital, and the gray arrow indicates

lowering of e2g band caused by the temperature reduction.[after Ref. 101]


2.9 Multiferroic Germanates

The discovery of a spin-singlet ground state in CuGeO3 [102] and recently

CaCuGe206 [103] triggered the search for model low-dimensional magnetic

systems among transition metal germanates and silicates.

The magnetism of Ba2CuGe207 is due to S = ½ spins localized on the Cu 2 +

sites. The tetragonal crystal structure [space group P 21m, lattice constants

a = 8.466 A˚, c = 5.445 A˚] is non-centrosymmetric. The characteristic feature

is a square-lattice arrangement of Cu 2+

ions in the (a, b) crystallographic plane

with the possibility of super-exchange interactions via the GeO4 tetrahedra

along the diagonals (lnn) and possibly the sides (2nn) of the (a,b)-projected

unit cell. Adjacent Cu-planes are separated by layers of Ba with no obvious

superexchange routes. These structural features suggest that the material may

exhibit quasi-2-D behavior and, possibly, competing in plane

antiferromagnetic (AF) interactions [104].

. A schematic depiction of the unit cell is given in Fig. 11-2 (a). The different

components of the DM vector are sketched for the Cu-Cu bonds along the (1,

1, 0) direction (dashed line). The uniform component Dy points in the same

direction for all bonds. The staggered component Dz is sign alternating.


Figure 2-11: (a) Crystallographic structure of Ba2CuGe2O7 viewed along the

c-axis. (b) Almost AF cycloidal magnetic structure of Ba2CuGe2O7. The

dominant exchance paths J║ and J┴ are indicated by the green and magneta

colored line, respectively [After Ref. 105].

The basic feature of Ba2CuGe2O7 is a square arrangement of Cu2+

ions in the

(a,b)-plane (a depiction of the unit cell is given in Fig. 11-2 (a)). Nearest-

neighbor in-plane AF exchange along the diagonal of the (a, b)-plane is the

dominant magnetic interaction. The interaction between Cu-atoms from

adjacent planes is weak and ferromagnetic (FM). The DM vector consists of

two components: For Cu-bonds along (1, 1, 0), Dy points along the diagonal of

the (a, b)-plane in the (1,-1, 0) direction. Dz is parallel to the tetragonal c-axis

and sign-alternating for neighboring bonds. It has been established by neutron

diffraction [106] that the almost AF cycloid, observed below TN = 3,2K is

stabilized by Dy. The influence of Dz has been neglected in all quantitative

descriptions of Ba2CuGe2O7. A schematic depiction of the cycloidal spin-

structure is given in Fig. 11-2 (b); for the propagation vector q along (1, 1, 0),

spins are confined in (1, −1, 0) plane; the rotation angle β relative to a perfect

antiparallel alignment is 9.7◦ per unit cell. Due to the equivalency of the (1,

±1, 0) directions, two equally populated domains are present.

2.9.1 Optical properties of Ba2CoGe2O7

V. Hutanu et.al. (2012) [107] performed an optical study of lattice vibrations

on the isostructural compound Ba2CoGe2O7. They investigated the

temperature dependence of the phonon spectra across the magnetic transition

from 50 K down to 3.3 K [see fig 12-2]. In the tetragonal SG P-421m, the

factor group analysis yields 28 infrared active phonon modes. Among them,

18 E modes are twofold degenerate and excited by light polarized within the

(a, b) plane, while 10 B2 modes are nondegenerate and active for polarization

along the c axis. In case the lattice symmetry is lowered to orthorhombic,

lifting of the twofold degeneracy should be observed for the E modes. The


weakness of the temperature-induced sharpening and red shift of the modes

indicate negligible thermal expansion below 50 K. No splitting of the E

modes, i.e. no supplementary orthorhombic distortion, related to the magnetic

phase transition at 6.7 K. The Neutron diffraction data and infrared phonon

mode analysis imply no structural phase transition down to 2.2 K.

Figure 2-12: The Reflectivity of of Ba2CoGe2O7 spectra at various

temperatures. Left/right panel: Infrared active phonon modes for polarization

within/perpendicular to the (a, b) plane. The positions of the modes are

indicated by red vertical bars [after Ref.107].

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Chapter 3:Background theory 59

Chapter 3: Background theory

3.1 Introduction

In this chapter, we introduce several models to study the effects of the double

exchange, the Jahn-Teller coupling and the crystal field interaction in

manganites. As we will see, the double exchange mechanism provides the

basis for our understanding of ferromagnetism in doped manganites, while the

Jahn-Teller coupling leads to the electron localization which may explain the

main electronic behavior observed in doped manganites. Also, the Jahn-

Teller coupling and crystal field plays an important role in determining the

nature of the insulating ground state and the metal-insulator transition in

LaMnO3. In order to study the experimental results, we will rely on known

models to distinguish the different contributions to the optical conductivity.

Those models have to comply with the relations presented in the previous

chapters. However, some of the generally used models do not fit to all the

properties of a physical optical conductivity but can still be applicable in a

limited frequency range. It is therefore necessary to combine all of them

together in order to achieve a better understanding of the physics of

manganites.

3.2 Exchange Interactions

According to Pauli Exclusion Principle, there is zero probability of finding

two electrons with the same spins at the same point in space, but opposite

spins can be found at the same point. So the average separation of electrons r

will be larger for parallel spins than anti-parallel spins. The inter-electron

coulomb repulsion energy (e2/4πεor) is smaller for parallel than anti-parallel

spins. This effect is referred to as the exchange interaction. Exchange

interactions lie at the heart of the phenomenon of long range magnetic order.

Exchange interactions being due primarily to electrostatic interactions, arising

because charges of the same sign cost energy when they are close together and

save energy when they are apart. Indeed, in general, the direct magnetic

60 Background theory

interaction between a pair of electrons is negligibly small compared to this

electric interaction. If the electrons on nearest neighbor magnetic atoms

interact via exchange interaction, this is known as direct exchange. The direct

exchange is modeled by the Heisenberg exchange Hamiltonian:

(3.1)

where Jij is the exchange constant between the ith

and jth

spins, distributed on a

regular lattice. Only nearest neighbors are usually included in the summation.

The magnetic properties of the crystal depend on the sign and the strength of

the interaction between spins: if Jij = J > 0 the parallel orientation of the spins

is favored, giving a ferromagnetic state. If Jij = J < 0, the magnetic order is

antiferromagnetic, with the spins of nearest neighbors antiparallel. However

for the manganites, as for many other magnetic materials, it is necessary to

consider some kind of indirect exchange interaction, because the Mn ions are

alternated with O in the lattice.

3.2.1 Super-exchange

Superexchange is an indirect exchange interaction between non-neighbouring

magnetic ions, which is mediated by a non-magnetic ion that is placed in

between them. This interaction was first proposed by Kramers [1] in 1934 to

the aim of finding an explanation for the magnetic properties observed in

insulating transition metal oxides, in which the magnetic ions are so distant

that a direct exchange interaction could not explain the presence of

magnetically ordered states, so the longer-range interaction that is operating in

this case should be “super”. The problem was thereafter treated theoretically

by Anderson [2], who in 1950 gave the first quantitative formulation showing

that the superexchange favours antiferromagnetic order. The insulator FM and

AFM orders are explained by superexchange depending on orbital

configurations. Two magnetic ions (B with part occupied eg orbitals or B′ with

empty eg orbitals) couple through an intermediary non-magnetic ion (e.g. O2−

).

Depending on magnetic ions (B or B′) and orbital coupling orientations

(parallel or orthogonal), there are 5 cases in superexchange interaction (Fig. 3-

Background theory 61

1): (a) strong AFM, (b) weak AFM, (c) weak FM, (d) FM, (e) AFM.

Superexchange effect is successful in explaining the AFM order in many

insulator perovskites. Similar to Antiferroelectricity (AFE) which is a physical

property of certain materials. It is closely related to ferroelectricity; the

relation between antiferroelectricity and ferroelectricity is analogous to the

relation between antiferromagnetism and ferromagnetism. In an

antiferroelectric, unlike a ferroelectric, the total, macroscopic spontaneous

polarization is zero, since the adjacent dipoles cancel each other out. In AFM

materials the magnetic moments exist in AFM but the net magnetic moment in

one magnetic cell is zero because every magnetic moment has an anti-parallel

magnetic moment neighbor. In perovskite compounds, different AFM orders

below magnetic phase transition temperature TN were named after E. O.

Wollan and W. C. Koehler who studied perovskite magnetic orders by neutron

diffraction.

Figure 3-1: Different magnetic orders because of superexchange interaction

[3].

http://en.wikipedia.org/wiki/Ferroelectricity

http://en.wikipedia.org/wiki/Antiferromagnetism

http://en.wikipedia.org/wiki/Ferromagnetism

http://en.wikipedia.org/wiki/Polarization_density

http://en.wikipedia.org/wiki/Polarization_density


3.2.2 Double-Exchange Interaction

The double exchange mechanism is a type of magnetic exchange that may

arise between ions in different oxidation state. In mixed-valence manganites

La1-xАxМnО3, the conduction process between two Mn ions was explained by

C. Zener in 1951 [4,5,6] and therefore, called “Zener-Double Exchange

(ZDE)”. The knowledge of the electronic structure of these materials gives us

the necessary insight for understanding the ZDE conduction in manganites.

Shortly after the discovery of metallic ferromagnetic state in by Jonker and

Van Santen [4] the relation between metallicity and ferromagnetism was

theoretically studied. In there are three 3d electrons in t2g state for the Mn4+

ion, three 3d electrons in the same state and one in the eg state for the Mn3+

ion. The spins of these electrons are aligned parallel to each other because of

the Hund’s coupling. Now, if Mn3+

/Mn4+

ions are neighbors, the eg electron

from Mn3+

can hop onto an empty eg state at the Mn4+

site, thus exchanging

valence, and a resonant process Mn3+

-Mn4+

↔ Mn4+

- Mn3+

occurs. This is

possible only if the spins on both sites are parallel. If they are antiparallel, the

hopping is inhibited by the Hund’s coupling (Fig. 3-2 ). This means that the

ferromagnetism and the metallic state occur cooperatively. The Hamiltonian

describing this interaction is:

(3.2)

Figure 3-2: Schematic of the of the Double-Exchange (DE) mechanism.


In this (DE) Hamiltonian, the eg degeneracy and the electron-lattice

interactions are neglected. The spin, S=3/2, of the three electrons localized in

the t2g states is treated classically. Denote the creation/annihilation operators of

an eg electron with spin σ at site, is the spin operator of the t2g electrons and σ

are the Pauli spin matrices. tij is the hopping integral of the eg electron between

sites, U is the Coulomb interaction between eg electrons and JH is the Hund’s

coupling between eg and t2g spins. For manganites, usual values are U~5-8eV

and JH ~1-2eV [7]. Therefore, the limit of large U and JH is taken and the spin

of the eg electron is always parallel to the t2g spin at each site [8]. In addition,

if the localized spins are treated classically having an angle φ between nearest

neighbors, the effective hopping becomes

(3.3)

as shown by Anderson and Hasegawa [9]. Here t0 is the normal transfer

integral, which depends on the spatial wave functions, the term cos (φ /2) is

due to the spin wave function and φ is the angle between two spins.The

hopping rate is largest if φ = 0 and the hopping is cancelled if φ = π,

corresponding to an antiferromagnetic background.

This expression is different from that of superexchange, where the coupling is

proportional to cos φ. Zener's predictions about stabilization of metallic

conduction by the FМ ordering were based on the single-electron transfer

between the two ions. The problem of the crystal environment was considered

by de Gennes [10]. The dependence of DE on frustration angle, φn – φn+p,

between spin directions of the ions participating in tunneling satisfies the

expression tn, n+p = t cos [(φn – φn+p) /2] [10]. In quasiclassical approximation

the total energy per site, as a function of φ ε is written in the form

(3.4)

where ε(0) is the bottom of conduction band with dispersion ε(k)=tzγ(k); is

the structural factor. For two ion cores S = S1,2 = 3/2, z is the number of the

nearest neighbors from other magnetic sublattices, IAFM = In,n+p, is the constant


of the AFM superexchange interaction between the Мn3+ ion spins. x is the

concentration of doped carriers. As can be seen from Eq. (3-4) the first term

decreases and the second term increases with energy.The minimization of this

energy gives for the angle:

(3.5)

i.e. with the doping (increase of x), the original antiferromagnetic structure

becomes canted and there will be both - antiferromagnetic and ferromagnetic

components in the magnetic order.

Finally, the DE interaction provides changes of the resistivity mechanism

when passing through the PM to FM transition: in the high-temperature PM

phase the spins are disordered and scatter electrons. In the low-temperature

FM phase the spins are ordered with the configuration Mn3+

- O2-

- Mn4+

allowing for high electrical conductivity due to the lack of scattering.

3.2.3 Electron-phonon coupling

According to Millis [11], for a complete description of the transport properties

in manganites, the magnetic degrees of freedom are not sufficient. The

depiction of strong interactions between electronic configuration and structural

symmetry (e.g. JT distortions) fits well the idea of Millis, namely, that a

perturbation of the crystal symmetry (buckling of O-Mn-O bond or rigid

rotation of MnO6 octahedra) might favor an overlap of orbitals. This can be

responsible of a change in the hopping amplitude and, consequently, in the

conductivity. Therefore, the structural degrees of freedom must be taken into

account in the form of electron-lattice interaction. The strong electron-phonon

coupling, relative to the distortion of MnO6 octahedra in the JT effect, may

localize carriers, because the presence of an electron in a given Mn orbital

causes local distortion, which produces a potential minimum: this minimum

tends to trap the electron in that orbital. If the coupling is strong enough,

these tendencies lead to the formation of a “selftrapped” state called polaron

[12]. This short range charge order, which disappears in the FM phase, is


believed to be responsible for the insulating properties of the paramagnetic

phase.

3.3 Crystal field theory and JT Effect

In the cubic environment of the octahedron, hybridization and electrostatic

interaction with oxygen p electrons will create a crystal field for the outer 3d

electrons in Mn3+

(whose strength is often denoted 10Dq). This field lifts the

5-fold degeneracy of d electrons present in free Mn3+ ions by splitting the

energy levels and forming lower lying triply degenerate t2g states and a higher

doublet of eg states, as shown in Fig. 3-3 in the simple ionic framework that

we are assuming here. The t2g triplet consists of the dxy, dxz and dyz-orbitals,

while the eg doublet contains the dx2−y2 and dz2−r2 orbitals.

Further, there may be an additional splitting due to lattice distortions (JT

effect), or other symmetry lowering of some kind. In eg electron systems like

the Mn3+ manganitese compounds, the electronic configuration is t2g 3e1

g

(high-spin state S=2, and 10Dq < JH - Hunds coupling energy) hence the eg

electron occupies an orbital, the lobes of which are directed towards the

nearest-neighbor oxygen ligands establishing a strong lattice coupling. The

Jahn–Teller coupling lifts the degeneracy of the eg orbital by causing a large

deformation of the MnO6 octahedra. The most frequently observed

deformation of the cubic perovskite lattice is an elongation of the z-axis

(apical) oxygen position coupled with the occupied 3dz2–r2 orbital (shown on

Fig. 3-3). Another possible deformation is an elongation of x and y axes (in-

plane) oxygen positions coupled with the occupied x2–y2 orbital. When the eg

band filling is close to 1 (or otherwise to some commensurate value), the

individual Jahn–Teller distortions are cooperatively induced leading to

symmetry lowering of the lattice or even to a new superstructure. Thus, the

peculiar orbital ordering in the manganites is always associated with the

cooperative Jahn–Teller distortion.


Figure 3-3: Crystal field (10Dq) lifts the degeneracy of the d5-electrons of the

Mn3+

- ions into a t2g triplet and an eg doublet. The Jahn-Teller distortion then

further splits the eg level and favors either the dx2−y2 or the d3z2−r2 orbital.

La1-xCaxMnO3 is based on the perovskite structure and is a mixed valent

system due to the random replacement of La3+

ions by Ca2+

which produces

the rich variety of phases. This phase diagram is explained and discussed in

section 2.5.1. The conventional model [13, 14] for the electronic structure of

La1-xCaxMnO3 makes the assumption that the charge distribution corresponds

to the nominal ionic valences, that is to say that La is La3+

, Ca is Ca2+

, O is O2-

and the charge on the Mn ion can be Mn3+

or Mn4+

. Every time a La ion is

replaced by a Ca ion, a Mn3+

ion becomes a Mn4+

ion to maintain charge

neutrality. Thus, the La, Ca and O ions have filled electron shells and it is the

partially filled 3d shell of the Mn ion that determines the behaviour of the

system. A Mn3+

ion has an outer electron configuration of 3d4 and Mn

4+ has

3d3. The electrons in the d shell are thought to be spin aligned because of the

large Hund’s rule coupling energy. The energy levels are split by the

environment of the Mn ion (crystal field splitting) and (in the case of the Mn3+


ion) the Jahn-Teller effect as shown in Figure 3-3. Thus in the mixed valent

state, there are thought to be two types of Mn ion: a Mn4+

ion surrounded by a

regular octahedron of oxygen ions and a Mn3+

ion surrounded by an elongated

octahedron of oxygen ions. At room temperature the itinerant electrons are

thought to be mobile but every time they move to a neighbouring ion, the

distortions of the octahedra have to change. Thus, the electrons can be thought

of as having a lattice distortion associated with them that increases their

effective mass [15]. This combination of electron and lattice distortion is

known as a polaron. In the room temperature insulating, paramagnetic state

has been existed. As the temperature is lowered, the material can become a

ferromagnetic metal as the electrons become more delocalized and the crystal

takes on an average distortion or a charge-ordered insulator where Mn3+

and

Mn4+

ions localize at specific locations within the crystal.

3.4 Modeling the Optical Conductivity

In many situations, a model optical conductivity given by theoretical

considerations is useful or required. The model optical conductivity can be

used for the evaluation of the experimental data, their quantitative description,

reduction of large data set to only a few parameters, etc.

3.4.1 The Drude-Lorentz model

The Drude-Lorentz model [16, 17] dates back to the end of the 19th

century,

and was used, before the development of quantum mechanics, to explain the

dispersion and the absorption of the light in solids. Because of its simplicity,

the model is still used nowadays for a phenomenological description of the

optical properties of metals and insulators. The optical properties of a

material can be described by means of three main frequency- dependent

optical response functions , and [Eqs, 1.2, 1.3 and 1.4].

Generally speaking, in condensed matter those response functions can be

decomposed into a sum of several contributions related to independent

microscopic dynamics (i.e., electronic excitations and phononic contributions),


all of which can be modeled by Drude (for free electrons) or Lorentz (for

bound electrons) terms.

The Lorentz model describes the optical properties of an insulator in a

classical way, by assuming that the valence electrons are bound to specific

atoms in the solid by harmonic forces. Therefore, the solid is considered as a

collection of atomic oscillators, each one with its characteristic natural

frequency ω0 that can be excited by resonant electromagnetic radiation. From

the quantum viewpoint, ω0, may correspond to any electronic transition,

included the ionization to the continuum. In this case, ω0 would correspond to

the gap frequency. In the case of free electrons, the model remains valid with

ω0 = 0 (Drude term).

The interaction of the radiation field at the atom site, Eloc , with the system, is

described by the equation of the forced oscillator :

(3.6)

where is the position vector of the electron, m and e are the electronic

mass and charge, respectively, and Γ is the damping rate. This term arises

from various scattering processes experienced by the valence electrons, In

solids, the dissipation is mostly due to the excitation of acoustical and optical

phonons. Assuming that Eloc, oscillates as e−iωt

, the solution of Equation (3.6 )

is

(3.7)

The resulting, oscillating electric dipole moment is

(3.8)

and the atomic polarizability is

(3.9)


The macroscopic polarization can be written as the sum over all the N atoms

per unit volume, where is the dielectric susceptibility. Since), the Lorentz

contribution to the electric permittivity will be:

(3.10)

The real and imaginary parts of the dielectric function (see Fig. 3-4) are finally

obtained:

(3.11)

(3.12)

Using the relation between we can write the Lorentz expression for the optical

conductivity:

(3.13)

In the general case of more than one valence electron per atom, and allowing

for the possibility of different resonance frequencies instead of a unique

frequency ω0, expression (3.13) is generalized to

(3.14)

Where Nj is the density of valence electrons bound with a resonance frequency

ωj and =N is the total density of valence electrons.

The Drude model for free electrons is a special condition of the classical

Lorentz model with the Hooke’s law force constant equal to zero, so that the

resonant frequency is zero . The Drude model regards metals as a classical

free electron gas executing a diffusive motion characterized at the equilibrium

by a relaxation time τ.


Figure 3-4: Real and imaginary part of the dielectric function for a single

oscillator obtained from equation (3.13). [This curves have been represented

for typical values within the optical range hω=4 eV, h =1 eV and 4 / m

= 60.

The equation of motion for free carriers can be written as:

(3.15)

where is the position vector of the electron, m its mass, γ = 1/τ and (t) the

external electric field. If one solves the differential Equation (3.15) assuming a

harmonic time varying position vector, the contribution to the optical

conductivity will be:

(3.16)

where n is the number of carriers for unit volume and

is the plasma frequency, where e and me are the electron charge and rest mass,

respectively, and vacuum permittivity constant = 8.85 × 10−12

F m−1

.

Therefore, within the framework of the Drude model, the complex

conductivity and consequently all the linear response functions are fully

characterized by two parameters: the plasma frequency and the relaxation rate


γ = 1/τ (in general γ <<). The corresponding electric permittivity for a metal

will be that of plasma:

(3.17)

In conventional metals typical values of the plasma frequency are of the order

of 1015

→ 1016

Hz, therefore in the visible range, while in poor metals like

most oxides it lies in the mid-infrared range. For the scattering rate at room

temperature typical values are τ~10−14

s.

72 Bibliography

Bibliography

[1] H. A. Kramers, Physica 1, 182 (1934)

[2] P. W. Anderson, Phys.Rev. 79, 350 (1950)

[3] Nicolas GUIBLIN. Synthèses, structures et mises en ordre électroniques

d’ordre à valence mixte dans le système Pr-Ca-Mn-O. PhD thesis, Universitè

de Caen, (2002)

[4] G. Jonker & J. Van Santen “Ferromagnetic compounds of manganese with

perovskite structure” Physica 16, 337 (1950)

[5] C. Zener “Interaction between the d-shells in transition metals” Phys. Rev.

81, 440 (1951)

[6] C. Zener “Interaction between the d-shells in the transition metals I”,

“Ferromagnetic compounds of manganese with perovskite structure II” Phys.

Rev. 82, 403 (1951)

[7] S. M ek w e l ”Phy f me l x de ” p ge -Verlag

(2004)

[8] P.W. Anderson and H. Hasegawa “Considerations on double exchange”

Phys. Rev.100 675 (1955)

[9] P.G. de Gennes “Effects of double exchange in magnetic crystals” Phys.

Rev. 118 141 (1960)

[10] A. J. Millis, P. B. Littlewood, B. I. Shraiman, Phys. Rev. Lett. 74, 5144

(1995)

[11] A. J. Millis, Nature 392, 147 (1998)

[12]F. Wooten, Optical properties of solids, Academic Press, New York

(1972)

[13] M.Dressel and G.Gruner, in Electromagnetics of solids,Cambridge

University Press (2002)

Experimental Methods 73

Chapter 4: Experimental Methods

4.1 Introduction

In this chapter we describe the experimental hardware that was used in the

main part of this work. The important and unique aspects of the setup are

described. The purpose of optical spectroscopy is to obtain the material’s

complex response as a function of frequency from that of the Terahertz up to

the near UV, i.e. (10 to 50000 cm-1

). This is a very broad spectral range that

requires the use of different spectroscopic techniques and hardware

configurations to be covered. Two different techniques were used in the

present work to measure near normal-incidence reflectance and transmittance

of thin films and crystals: in the interval from 10 to 10000 cm-1

Fourier

Transform (FT) interferometry, in the range from 10000 to 40000 cm-1

dispersive spectral analysis. Both techniques are described in this chapter and

are summarized in Fig 4-1.

The procedures to obtain from those data the dielectric function (ω) and the

optical conductivity (ω) were discussed in chapter 1.

74 Experimental Methods

Figure 4-1: Summary of the experimental procedures used in this thesis.

Investigation Materials

Manganites Multiferroics

La1-xMnxO3

x=0.66, 0.88, 0.98 and 1.10

La0.5Ga0.5MnO3 Ba2CuGe2O7 + BiMnO3

Bulk Samples made by

Floating Zone Method (FZ)

Thin films made by

Pulsed Laser Deposition

(PLD)

Thin films made by

Pulsed Laser

Deposition (PLD)

The reflectance (R) was

measured in IR range

between 100 to 104 cm

-1,

from 300 to 10 K. (R)

was collected with

incident radiation with

or without polarization

along the (a, b) plane and

c axis of the crystal.

The reflectance (R)

was measured in

1- Visible and UV

range between 104

to 4x104 cm

-1.

2- IR range between

100 and 104 cm

-1,

from 300 to 10 K.

The transmittance

(T) was measured in

visible and UV range

between 104 and

4x104 cm

-1, from 300

to 10 K. by UV-Vis

Optical setup.

Data Analysis “Multilayer Transmittance and Reflection Model” or “KK

Transformations”

“KK Transformations” “Multilayer Transmittance and Reflection Model”

Optical Conductivity σ1 (ω)


4.2 Infrared Spectroscopy and experimental setup

Infrared spectroscopy has been a workhorse technique for materials analysis

for more than a hundred years. In the solid phase, an infrared spectrum

represents a fingerprint of a sample with absorption peaks which correspond to

the frequencies of vibrations between the bonds of the atoms making up the

material. Because each material is a unique combination of atoms, no pair of

compounds produce the same infrared spectrum. Therefore, infrared

spectroscopy results in an unambiguous identification (qualitative analysis) of

every different kind of material. With modern software algorithms, infrared is

an excellent tool for quantitative analysis.

In this section we provide basic information on infrared spectroscopy and on

the way it has been applied to the measurements of this thesis.

4.2.1 Fourier-Transform IR Spectroscopy

Fourier-transform infrared (FTIR) spectroscopy, [e.g., see Refs. [1–4] for an

overview] is based on the interference between two radiation beams to obtain

an interferogram. This latter is a signal which changes as a function of the path

length difference between the two beams. The interferogram provides the

spectrum by applying the mathematical operation of Fourier transform.

The basic components of an FTIR spectrometer are shown schematically in

Fig.4-2. The radiation emerging from the source is passed through an

interferometer to the sample before reaching a detector. Upon amplification of

the signal, where the high-frequency contributions have been eliminated by a

filter, the data are converted to digital form by an analog-to-digital converter

and transferred to the computer for Fourier transformation.

Figure 4-2: Basic components of an FTIR spectrometer.

Source Computer Analog-to-

digital

converter

Interferomete

r

Sample Detector Amplifie

r


The most common interferometer used in FTIR spectrometry is the Michelson

Interferometer, Figure 4-3. Energy from a conventional source is directed

towards a beamsplitter. The beamsplitter creates two separate optical paths by

partially reflecting and partially transmitting the incident light. One part of the

beam is then reflected by a fixed mirror, while the other part impinges on a

movable mirror that translates back and forth. The two beams are then

recombined at the beamsplitter before reaching the detector. When the

distances between the beamsplitter and the fixed and movable mirrors are the

same, the optical path length traveled by the two beams is the same (zero-path

difference, ZPD). When the movable mirror is moved, the optical path

difference δ becomes nonzero.

Figure 4-3: Sketch of a Michelson interferometer. On the down, from the

Interferogram I (δ) a Fast Fourier Transform (FFT) algorithm produces the

power spectrum B (ω).


Figure 4.4: Interferograms and related spectra for (a) a monochromatic light

and (b) a broadband light.

In the case of a monochromatic light source, the interferogram is a periodic

sine function and the spectrum is a delta function centered at the frequency of

the light (Figure 4.4 a). In the more realistic case of broadband radiation, the

interferogram has an oscillating shape, sharply peaked at the zero-path-

difference (ZPD) position and the related spectrum is a superposition of all the

radiation frequencies, as can be seen in Figure 4.4b.

As δ is increased, the signal from the detector - the interferogram - goes

through a series of maxima and minima. The maxima occur when δ is an

integral multiple of wavelengths of the emitting source (i.e., δ = nλ; n= 0, ±1,

±2, etc.), the minima when δ is an odd multiple or half wavelengths (i.e., δ =

[n+1/2 λ]). A complete formal discussion of FTIR can be found in Refs. [5, 6].

Hence, the FT spectrometer measures an interferogram I (δ) :

(4.1)


where B(ω) is the spectral power density at a particular wave number ,

where in turn

dIB )2cos()()(

(4.2)

Eq. 4-2 provides the spectrum, namely the intensity as a function of

wavenumber.

FT-IR spectroscopy presents three main advantages with respect to the more

traditional spectroscopic techniques employing a dispersive medium (prism,

grating) to separate the spectral components of the light.

• Connes advantage: The position of the scanning mirror is measured by

means of a laser light. The measurement of the optical path difference δ is

therefore determined with optical precision.

• Fellget advantage:

One single measurement of I (δ) contains information on the entire spectral

range. The acquisition and average of n interferograms improves the signal to

noise ratio by a factor of n1/2

with respect to the same spectrum acquired with

a dispersive technique.

• Jacquinot advantage:

FT-IR spectroscopy allows one to use circular apertures. This results in an

enhancement of the light intensity with respect to dispersive techniques,

where narrow slits are necessary to guarantee a good resolution.

4.2.2 Bruker IFS 66v/S interferometer

The majority of the experiments reported in this thesis have been realized

using the Bruker IFS 66v/S Fourier transform spectrometer. A detailed

scheme of the instrument is displayed in Fig. 4-5. The Bruker spectrometer

offers high resolution and excellent sensitivity. Its modular construction allows

the system to be easily configured for specialized applications. The specially

designed permanently aligned interferometer provides high sensitivity and

stability. The spectrometer has a resolution of better than 0.05 cm−1

, and a

spectral range from 10 cm−1

in the far-IR to above 10,000 cm−1

in the near


infrared (with wavelengths from 1 mm to 1 micron). The optics bench works

at a pressure of a few Torr for eliminating moisture but allowing the mirror to

move on an air cushion.

In Principle, with some modifications and a proper component [i.e. the

radiation source, the beam splitter… etc], The Bruker IFS 66v/S

interferometer is able to investigate the radiation spectrum from the Far

Infrared (5 cm−1

) up to the visible (30.000 cm−1

).

The instrument is equipped with a liquid helium cooled bolometer for the far

infrared, which can be replaced by a room-temperature DTGS detector, a

liquid nitrogen cooled mercury-cadmium-tellurium (MCT) detector for the

mid infrared, a Si diode detector for the near infrared.

All the optical component can be remotely controlled via software so that

different measurement configurations can be set without any need to ventilate

the interferometer, which anyway is divided into several independent

compartments (Figure 4-5). In the A compartment there is the building block

of the interferometer, composed by the radiation sources, the beam splitter, a

fixed mirror and a mobile mirror capable of moving on the air-cushion; In the

B compartment is placed the setup for transmittance or reflectivity

measurements where the sample under investigation will be housed. The C

compartment contains all the internal detectors and the E section contains the

building block of the electronics of the instrument. As reported in panel L in

Fig. 4-4 the radiation source is in one of the two focal points of an elliptical

mirror. Light coming from the source is driven into the aperture wheels toward

a parabolic mirror which converts it in a plane wavefront. After passing

through the beamsplitter and covering the optical path in the two arms of the

interferometer, it is focused by a second parabolic mirror in the sample

compartment and then reaches the detector. Depending on the spectral range

under investigation, different configurations and optical components provided

by the interferometer manufacturer have to be used. In Table 4-1 the main

measurement configurations are reported for several frequency ranges.


1) KBr window 14) HeNe Laser

2) Globar Source 15) Laser Power Supply Connection

3) Beam Spliter 16) Connection for sources cooling system

4) Interferometer 17) Connection to vacuum sensor

5) Pump Connection 18) Connection for gas supply to mobile mirror

6) Aperture Wheel 19) Vacuum Pump Connections

7) Focus 20) Switch for Sources Power Supply

8) Mobile Mirror Compartment 21) Master Switch

9) Flange 22) Lower Cooling Level

10) Bolometer Connection 23) Upper Cooling Level

11) MCT Detector

12) DTGS Detector

13) Laser Support

Figure 4-5: Schematics of the Bruker interferometer.


Range

ωL ÷ ωH

cm-1

Source

Beam

splitter

Polarizer

window

Detector

window

Far-IR 10-60 Hg arc Mylar

50 μm

polyethylene

Bolometer

1.6 K

20-100 Hg arc Mylar

25 μm

polyethylene

Bolometer

1.6 K

30-220 Hg arc Mylar

12 μm

polyethylene

Bolometer

4.2 K

190-660 Globar Mylar

3 μm

polyethylene

Bolometer

4.2 K

30-660 Hg arc

Si-

covered

My 6μm

polyethylene

Bolometer

4.2 K

Mid-IR 450-

6000 Globar

Ge on

KBr KRS5

HgCdTe

77K

Near-IR 4000-

12000

Quartz-

halo

Fe2O3 on

Quartz NaI/ KRS5

HgCdTe

77K

Table 4-1: Experimental setup for each of the infrared ranges investigated,

defined by the frequency interval ωL ÷ ωH. To be noticed that many infrared

ranges overlap so that independent measurements can be taken.


4.2.3 Reflectivity measurements

The optical setup to measure the reflectivity of the sample

(4.3)

where IR is the reflected, and I0 the incident intensity, is illustrated in Fig. 4-6.

In our IR reflectance spectroscopy measurements, the spectra are collected in

near-normal incidence configuration (Fig. 4-6) with polarized or un-polarized

light .The set-up is built with two flat mirrors and two spherical mirrors.

Figure 4-6: Near-normal reflectance configuration.


The radiation is deflected into the horizontal plane of the sample chamber by a

mirror in the interferometer. The first plane mirror in Fig. 4-6 deflects the

beam to the spherical off-axis mirror that focuses the light spot onto the

sample. The reflected radiation is collected by a second focusing mirror and a

plane mirror. The symmetry of the system ensures that the image at the

detector is that of the source, thereby allowing maximum collection of the

light package with minimal distortion of the contained information. The two

plane mirrors and the aperture position are only adjustable when the bench is

purged, or at atmospheric pressure. Fine tuning of the beam path can be

achieved when the optical bench is under vacuum however, using servo

controlled motors on the adjustment pins of the two off-axis mirrors.

Figure 4-7: Photography of the experimental FTIR setup mounted at the IRS

Group Lab. of the Physics Department in Rome.


Considerable efforts have been devoted to improve the signal to noise ratio for

small samples and to reduce the low frequency limit. One improvement of our

setup consists in using a Hg-arc source, which is more brilliant than the

globar source below 100 cm-1

, and a bolometer as a detector (see fig 4-7),

which, in particular conditions, can measure down to 4 cm − 1

. The bolometer

is a thermal detector, used in the FIR, made of a doped semiconductor which,

when hit by electromagnetic radiation, changes its resistivity with the variation

of temperature. The semiconductor is in thermal contact with a chamber where

liquid helium is inserted, so its starting working temperature is 4.2 K. When

FIR electromagnetic radiation is sent on the semiconductor its resistivity

decreases and this can be measured by looking at the variation of the potential

difference while a constant current flows through the semiconductor. The

amplified output of the bolometer provides the interferogram.

We performed measurements at several temperatures from 7 K to 300 K using

a cryostat and the heating system described in the next Section.

Liquid Helium cryostat

A commercial cryostat shown in Fig. 4-7 has been used for our IR

measurements. This continuous L He (liquid He) flow cryostat operates with

the sample in a vacuum. A needle valve regulates the flow of LHe from the

dewar to the cryostat (see Fig 4-7). The sample was kept at fixed temperature

between 7 and 300 K by a controller Model VARIOTEMP HR1 89072.

The inner part can be rotated around its vertical axis, to expose the sample

either to the radiation or the gold evaporator for making the reference. The

cryostat is fixed on a flange on the sample compartment of Bruker IFS 66v/S

spectrometer which does remains under its working pressure of a few torr. For

reflectivity measurements we should comply with several requirements: (1) all

radiation not reflected by the sample should be directed off the detector, (2)

the sample must be cooled sufficiently, and (3) the reflective surfaces of the

measured and the reference sample have to be exactly parallel to each other.

This can be accomplished in two ways: either evaporating gold (infrared

reflectivity nearly equal to 1) directly on the sample, if this is a crystal, or


inserting a small golden mirror close to the sample if this is a thin film, whose

surface would be destroyed by gold ablation after the measurement. In the

latter case, the delicate alignment of sample and mirror is made by

superimposing on a screen, at a distance of several meters, the images of an

external laser source reflected by the sample and the golden reference mirror.

In both cases one thus obtains from the golden surface the reference

interferogram I0.

Sample holder

Both thin films and bulk samples have been glued by silver paint on a brass

cone to reflect away the radiation which does not hit the sample surface

(see figure 4-8).

Figure 4-8: Photography of the liquid helium cryostat sample holder with (left

panel) and without (right panel) the thermal screen


Evaporation process

Reflectivity measurements require a reference signal from which the absolute

value of the reflectivity R is obtained, in the case of bulk samples they were

covered by a film of evaporated gold that provides (with suitable corrections)

the reflectivity reference. In Fig 4-9 the evaporation process is shown.

Figure 4-9: schematic diagram of the evaporation process.

The inner part of the cryostat can be rotated around its longitudinal axis, so

that the sample can be placed in front of the evaporator to start the evaporation

procedure. When a current of about 3 A passes through the tungsten filament,

a gold wire on the filament evaporates and a thin gold film is deposited on the

sample surface. It is common experience that the best deposition occurs with

the sample at room temperature. Another 180° rotation places the reference in

front of the window for the determination of I0.


4.3 VIS-UV spectroscopy

For the visible-ultraviolet (Vis-UV) range, the domain of electronic

transitions, we used a commercial Czerny-Turner monochromator, whose

principle of operation is recalled in Fig. 4-10

Figure 4-10: Czerny-Turner Grating Monochromator

Polychromatic radiation enters the monochromator through the entrance slit.

The beam is collimated by a spherical mirror and then strikes the grating at a

fixed or varying angle, depending on the detector. If this latter is a CCD

camera, as in our case, the grating does not move. The spectral components

split by the grating are focused again on the exit slit by the second spherical

mirror. In our optical setup we use a model SP-300i which has a 300 mm focal

length. f/4- aperture, and is equipped with a triple grating turret, carrying in

our case 600 and 1200 div/mm gratings.

A large 14 x 27-mm focal plane allows to host multichannel CCD devices

with shutters installed. A summary of SpectraPro-300i specifications is

reported in Table 4-2.


Specifications(1200-g/mm grating)

Focal Length 300 mm

Aperture ratio F/4

Optical design imaging Czerny-Turner with

aspheric mirrors

Scan Range 0 to 1400- nm mechanical range

Usable range 200 to 1000 nm

Resolution 0.1 nm at 435.8 nm

Dispersion 2.7 nm/mm (nominal)

Accuracy ±0.2 nm

Repeatability ±0.05 nm

Drive step size 0.0025 nm

Focal plane size 27 mm wide x 14 mm high

Standard slits Adjustable from 10 µm to 3 mm

wide. 4- or 14-mm slit heights;

Graiting size 68 x 68 mm

Grating mount triple-grating turret

Grating change time Less than 20 seconds

Table 4-2: Specifications of SpectraPro-300i

Light source

We utilized in the UV-VIS range a quartz tungsten filament lamp for visible

and near-IR wavelengths (350 - 2500 nm), and a deuterium lamp for UV

wavelengths (180 nm to 370 nm). It is important that the power of the

radiation source does not change over its wavelength range.

Detection system (CCD detector)

Since the invention of the Charge-Coupled Device [fig 4-11] by Willard Boyle

and George Smith at Bell Labs in 1970, CCD’s have become familiar to

consumers in a variety of applications. In dispersive spectroscopy, they have


replaced single-channel detectors like photomultipliers, allowing for keeping

the grating fixed. This has hugely increased the acquisition speed and has

bypassed all problems related to its motion, like the mechanical stability and

the linearity of the frequency scale.

Most of scientific CCDs are cooled for optimal performance. Cooled operation

results in a CCD read noise that is 2-5 times lower.

Our SpectraPro-300i CCD- detector is cooled down by a Peltier device

regulated by a temperature sensor, which is built in the CCD head and

controlled by software. CCD resolution is 0.1 nm with (1200-g/mm grating) .

The usable detection range is 200- 1000 nm.

Figure 4-11: Picture of the charge-coupled device.

Sample chamber (Low Temperature Cryostat)

In the Vis-UV setup the sample was cooled by a closed-cycle cryostat Model

LEYBOLD RD 210 (Figure 4-12), and kept at fixed temperature between 20

and 300 K by a controller Model VARIOTEMP HR1 89072. Inside the

cryostat the pressure of 10-5

Torr was ensured by the two stage scroll vacuum

pump.


Figure 4-12: low temperature setup schematic diagram

Optical scheme

Fiber optics transports the light reflected or transmitted from the sample to the

entrance slit of the spectrometer. The optical fiber consists of an outer

cladding material and an inner core material (see Fig. 4-13), having different

indexes of refraction. This produces a numerical aperture (NA) for the optical

fiber, given by

2/12

1

2

0 )()()sin( nnANA (4.4)

where: n0 = index of refraction of the core and n1= index of refraction of the

cladding. At both ends of the fiber, a quartz lens is applied to focus the

radiation.


Figure 4-13: Single optical fiber illuminating a Surface

The optical setup for reflectance and transmittance measurements in the Vis-

UV region is illustrated in Figs 4-14 and 4-15, respectively. The red line tracks

the light beam. We are using different configurations to acquire both T and R

of the sample. The light emitted by the source first passes through a slit, then

to lens and mirrors which focus the light onto the sample or the reference (the

aluminum mirror or a hole for reflectivity and transmittance measurements,

respectively). The detector finally receives the reflected or transmitted light by

other lenses or mirrors.


Figure 4-14: Schematic diagram of the optical setup for reflection

measurements.


Figure 4-15: Schematic diagram of the optical setup for transmission

measurements.


4.4 Thin-films and single crystal preparation

Most of the technologically interesting compounds must be reduced in form of

thin films to allow for their practical use [7, 8]. These are produced by ion

beam sputtering, MOCVD (Molecular chemical vapor deposition), molecular

beam epitaxy (MBE), chemical solution deposition (CSD), pulsed laser

deposition (PLD), etc. Among all these techniques, PLD has emerged as most

efficient and convenient technique for deposition of thin films of mixed-

valence oxide compounds, like manganites. In our work, PLD was used for the

deposition of thin films like LaMnO3 and LaMnGaO3.

On the other hand, single crystals are most suitable for basic investigations of

new materials, and in particular for optical spectroscopy due to the absence of

the substrate. The crystals of Ba2CuGe2O7 here investigated were grown by

the Floating Zone method. We will illustrate both the above techniques in the

following two sections.

4.4.1 Pulsed Laser Deposition (PLD)

The Pulsed Laser Deposition (PLD) method is described in Refs. [9, 10].

Indeed the laser, due to its high precision, reliability and spatial resolution, is

widely used for the deposition of the thin film, modification of materials, heat

treatment, welding and micro-patterning [11, 12]. In PLD, or more

specifically in Physical Vapor Deposition, PVD) (Fig. 4-16) high-energy laser

pulses are focused onto the target material, which has the nominal composition

of the desired film, resulting in its ablation and ejection of a plume of ionized

particles. By controlling the geometry of the laser beam and target, it is

possible to direct the path of the plume, creating a thin film on the desired

substrate surface. The creation and expansion of the plume is a very complex

process with many competing mechanisms. During the growth of the film,

both the target and substrate are held in vacuum. This ensures that the ejected

material does not interact with air, preventing scattering of the plume and the

deposition of unwanted species on the substrate.

http://en.wikipedia.org/wiki/Physical_vapor_deposition


Figure 4-16: Schematic diagram of the Pulsed Laser deposition set up.

4.4.2 Floating Zone Method (FZ)

In the floating-zone process (FZ), a rod of polycrystalline material is melt by

the focused radiation emitted by halogen lamps and is solidified again around

a crystalline seed [13]. After its first application to silicon, it has been used for

growing many materials, including any sort of oxides [14, 15]

As the crystals grown by FZ are of high quality but relatively small (usually

not bigger than few mm in diameter and few cm long), most of the work has

concentrated on new materials, mainly for research purposes. Y3Fe3O12 [15,

16] and TiO2 [17] are the only oxides grown by FZ for industrial applications.

The most obvious advantages of the floating zone technique come from the

fact that:

1- No crucible is necessary.

2- Both congruently and incongruently melting materials can be grown

3- Oxides melting at temperatures as high as 2500 ºC can be grown.

4- The growth can be performed at high pressure (up to 10 atm) and in

specific atmosphere.

5- Solid solutions with controlled chemical composition can be prepared.


6- In contrast to crucible methods, a steady state can be achieved. This is

beneficial for crystal growth of doped materials (with distribution

coefficient different than 1) and for incongruent crystallization.

Figure 4-17: Basic concept of the floating zone method.

Figure 4-17 illustrates the basic concept of the floating zone method. The heat

is concentrated to one point in space by some technique to form the melt zone,

which is literally floated and held in space only by the surface tension of the

melt itself. Therefore, if the heated region is too long, the melt zone will

collapse due to the increased self-weight. Crystal growth is effected by

moving melt zone up or down, when melting occur at the interface between

the feed rod and the melt zone, and simultaneously solidification occurs at

the interface between the melt zone and the crystal. Both the feed rod and

the crystal are usually counter-rotated in order to homogenize the melt zone

thermally and compositionally.

Bibliography 97

Bibliography

[1] R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic Press,

New York, 1972)

[2] P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared

Spectrometry (Wiley, New York, 1986)

[3] J. B. Bates, Science 191, 31 (1976)

[4] W. D. Perkins, J. Chem. Educ. 63, A5 (1986)

[5] P.R. Griffiths and J. A. De Haseth, Fourier Transform Infrared

Spectrocopyed. by John Wiley and sons, p. 147 (1986)

[6] A. J. LaRocca, in the Infrared Handbook, ed. by G. Zissis and W. Wolfe of

IRIA (1978)

[7] A.M. Haghiri- Gosnet and J.P. Renard, CMR manganites: Physics, thin

films and devices, J. Phys. D: Appl. Phys. 36, R127-R150 (2003)

[8] T. Venktesan, M. Rajeshwari, Zi-Wen Dong, S.B. Ogale, R. Ramesh,

Phil.Trans. R. Soc. Lond. A 356, 1661 (1998)

[9] T. Ohnishi, K. Shibuya, T. Yamamoto, M. Lippmaa, Journal of Applied

Physics 103, 103703 (2008)

[10] J. D. Ferguson, G. Arikan, D. S. Dale, A. R. Woll, J. D. Brock, Phys.

Rev. Letters 103(25): 256103 (2009)

[11] A. Ohtomo, H. Hwang, Journal of Applied Physics 102 (8): 083704

(2007)

[12] M. Lippmaa, , N. Nakagawa, K. M. awasaki, S. Ohashi, H.

Koinuma, Applied Physics Letters 76 (17): 2439 (2000)

[13] R. P. Poplawsky: J. Appl. Phys. 33 1616 (1962)

[14] S. Kimura, K. Kitamura, J.Am. Ceram.Soc., 75 [6] 1140-46 (1992)

[15] A. Revcolevschi, A. Muiznieks, J. Virbulis, Journal of Crystal Grouth

180 372-380 (1997)

[16] I. Shindo, K. Kitamura, and S. Kimura, Journal of Crystal Growth 46

307-313 (1979)

[17] M. Higuchi, K. Kodaria, Journal of Crystal Growth 123 495-499 (1992)

98 II Results and Discussion

II Results and Discussion

Structural, Electronic and Optical properties of LaMn0.5Ga0.5O3 99

Chapter 5: Structural, Electronic and Optical

properties of LaMn0.5Ga0.5O3

5.1 Introduction

Mixed oxides of manganese and rare earths have been the object of a

systematic investigation in the last decades. This is not only due to the

discovery of colossal magnetoresistance (CMR) in some compounds of this

family [1, 2], but also to a strong interplay among orbital, lattice, magnetism

and transport properties. A remarkable property of these materials is the

possibility to induce ferromagnetism by cationic substitutions on the different

sites of the antiferromagnetic parent compound LaMnO3. The most famous

illustration of this mechanism is the substitution of alkaline-earth ions such as

Ca2+

or Sr2+

on the A-site of LaMnO3, which can lead to the appearance of a

paramagnetic–ferromagnetic transition coupled to an insulator-to-metal

transition and therefore to negative and high magnetoresistance values [3, 4].

However, substitutions on the Mn site are also very interesting, from a

theoretical point of view, due to the prominent role played by the manganese–

oxygen network in the physics of these materials [5, 6]. Introducing foreign

cations on the Mn site of mixed-valent manganites La1-xAxMnO3 is known to

lead to severe modifications of the physical properties, as well in conductive

ferromagnetic manganites [7–9] as in insulating charge-ordered compounds

[10,11]. The single-valent parent compound LaMnO3 is also very sensitive to

Mn-site substitution [6, 12, 13].

The antiferromagnetic orbitally ordered state of LaMnO3 is easily destroyed to

give way to ferromagnetism. However, this ferromagnetic behavior can result

from several mechanisms: depending on the nature of the substituting cation

and on the substitution level, the physical properties derived from a complex

interplay between exchange interactions, orbital ordering and Jahn–Teller

distortion [14, 15].

Ga substitution is a clean tool to study the effect of a replacement of Mn+3

by a

100 Structural, Electronic and Optical properties of LaMn0.5Ga0.5O3

non-magnetic (diamagnetic) ion without introducing lattice distortion and any

additional magnetic exchange interaction due to the replacement. Indeed, Ga+3

has no magnetic moment and its ionic size (0.62 Å) is very similar to that of

Mn+3

(0.65 Å). Moreover, Ga+3

has a 3d10

filled-shell configuration so that eg

orbitals are neither involved in exchange interactions, nor in charge transport.

However, Gallium substituted manganites are predicted to be ferromagnetic at

low temperature, since Ga+3

ion in the B sites of the lattice is expected to

change the orbital order of the neighbors Mn3+

ions along the c-direction.

Consequently, the Jahn-Teller (JT) orbital ordering is destroyed at high Ga

content, and the ferromagnetic (FM) exchange between Mn3+

ions is favored

in the scale of few atomic shells. As Gallium concentration ranges between

0.4-0.6, a 3-dimensional FM ground state is expected at low temperature. It is

worth to notice that even in the FM state, these compounds are insulators.

Concerning the magnetic properties, bulk LMGO undergoes a paramagnetic

(PM)-to-ferromagnetic (FM) transition at Tc ≈ 75 K, with a

magnetization M=3.9μB per formula unit at 5 K [16,17]. This ferromagnetic

phase has been attributed to a destruction of the eg orbital order along the c-

axis, which favors the ferromagnetic exchange between the stacked ab

planes [18]. At variance with other doped manganites, in LaMn0.5Ga0.5O3 the

ferromagnetic phase does not promote the double-exchange mechanism and

therefore, as mentioned before, the system remains insulating below Tc.

J. Blasco et al., (2002) [19] studied the crystal and magnetic structure of

LaMn1-xGaxO3 (0.9 ≥ x ≥ 0.05). This study has shown the evolution of the

structural and magnetic ground state for the LaMn1-xGaxO3 series. Figure 5-1

displays the structural-magnetic phase diagram of the LMGO series. The

replacement of Mn by Ga induces a continuous decrease of the tetragonal

distortion of the MO6 (M=Mn,Ga) octahedron, which becomes practically

regular for x > 0.6. Simultaneously, the Ga substitution induces a

ferromagnetic component explained in terms of a canting of the A-type

antiferromagnetic structure. The ferromagnetic component increases with

increasing the Ga content up to x = 0.5. Neutron diffraction has clearly shown

that Ga substitution also induces a continuous canting of the Mn magnetic

http://www.sciencedirect.com/science/article/pii/S0921452613006480#bib10



moments into the z-direction. Therefore, the A-type AFM structure of

LaMnO3 evolves into collinear ferromagnetism for x = 0.5.

Figure 5-1: Magnetic phase diagram for the LaMn1-xGaxO3 series. A-AFM

denotes antiferromagnetic ordering of type A. CAF, CF, and FM indicate

canted antiferromagnetic, canted ferromagnetic, and ferromagnetic ordering,

respectively. PM is the paramagnetic region, SP means superparamagnet, and

BSP is the superparamagnet below the blocking temperature. O’ and O refer to

the orthorhombic crystallographic structures [After Ref.19].


Optical spectroscopy has played a central role in revealing the peculiar

electronic states of the strongly correlated electron systems. In particular, the

optical properties of the doped manganites are very interesting and their

interpretation is still controversial. Optical absorption studies of the

stoichiometric parent compound LaMnO3 (LMO) were studied. However, for

LMO, the electronic ground state and the charge transfer mechanisms are not

fully understood [see chapter 2].

In the present chapter we present a detailed analysis of the optical bands

observed in a thin film of LaMn0.5Ga0.5O3 (LMGO) as a function of

temperature, and we compare these results with those on pure LMO that were

reported previously [20]. The concurrent absence of JT distortion, double-

exchange, and orbital order at low temperature gives LMGO an intrinsic

simplicity, and the opportunity to neglect excitations like orbitons [21] and JT

polarons [22] in the interpretation of the optical spectra. This opportunity will

be exploited here to obtain – through the comparison with LMO – further

evidence for the interpretation of the absorption spectra of the lanthanum

manganites in the visible and near UV frequency range.

5.2 Sample growth and characterization

LaMn0.5Ga0.5O3 Epitaxial film (200 nm in thickness) were grown on (001)

oriented (LaAlO3)0.3(SrAl0.5Ta0.5O3)0.7 (LSAT) substrates by RHEED assisted

pulsed laser deposition with a KrF excimer laser. [A brief description of

experimental growth techniques were reported in chapter 4]. A high degree of

epitaxy can be expected on low lattice-mismatch substrates such as LSAT.

Hence, most manganite thin film devices presented in literature are grown on

LSAT substrates, which moreover have a low optical absorption in the range

of interest. One half of the substrate was covered by a shadow mask in order to

allow subtraction of the substrate absorption contribution. Deposition

temperature was 700 °C, deposition pressure was 10−3

mbar O2 and the laser

fluence was about 2 J/cm2. Manganite film growth conditions were optimized

through plume imaging and optical emission spectroscopy [23,24]. In order to

avoid the effects of oxygen excess (which has been shown to significantly







affect the optical properties of LMO thin films in the spectral region of interest

[25], the sample was post-annealed in vacuum for 1 h at 700 °C. Sample

resistivity was too high to be measured in our setup. X-ray diffraction (XRD)

showed that the films were single-phase and epitaxial, with an out-of-plane

pseudocubic lattice parameter c=0.394 nm. Wavelength dispersive

spectroscopy (WDS) was performed in the wavelength range from 0.12 to

0.24 nm. The estimated occupation of the perovskite B-site was Mn 47%, Ga

53%, in good agreement with expectations. This demonstrates that no

preferential Ga evaporation is taking place in our deposition conditions [26].

XRD and WDS data are reported in Fig.5-2.

5.3 Transmittance spectra of the LaMn0.5Ga0.5O3 film

The transmittance T(ω) of an LaMn0.5Ga0.5O3 (LMGO) film deposited on

LSAT has been measured at near normal incident in the range between 10 000

and 40 000 cm-1

. The measurements have been performed by means of the

experimental setup described in chapter 4 between 10 K and 300 K.

Figure 5-3 shows the transmittance data of the two-layer (LMGO-LSAT)

system in the whole measured frequency range at selected temperatures

between 10k and 300k. A first inspection to data in Fig. 5-3 shows a broad

absorption feature between 10 000 and 25 000 cm−1

, and an intense band

above 35 000 cm−1

. The latter feature could not be studied in detail, being

partially masked by the intense absorption of the substrate at those

frequencies. The two-layer transmittance increases as the temperature

approaches 200 K, especially in the region around 18 000 cm−1

. In the same

spectral region but for temperatures lower than 200 K, the transmittance

gradually decreases. A similar behavior, even if less evident, is observed

around 33 000 cm−1

.



http://www.sciencedirect.com/science/article/pii/S0921452613006480#f0005



Figure 5-2: Top: example of X-ray diffraction pattern of a well-oriented film

pointing out the epitaxy of the sample and the absence of spurious phases. The

unfiltered Kβ peak from the (002) substrate reflection is marked by an asterisk.

Bottom: WDS scan in the wavelength range 1.2–2.4 Å. The intensity data

collected from Mn and Ga elements are visible. For each acquired element the

peak position is indicated by the element symbol while the backgrounds are

indicated by the element symbol with − or + for the lower and upper

backgrounds, respectively.


Figure 5-3: Raw transmittance of the two-layer system (LMGO+LSAT) at

different temperatures.


5.4 Extraction of the bare film optical functions

The analysis of the data in Fig. 5-3 has been performed by using a standard

model for the multilayer transmittance, namely Eq. (1-41) of chapter 1.

(1.41)

In the fitting procedure we used the complex refractive index of LSAT as

obtained from a measurement of its transmittance spectrum and we assumed

a Drude–Lorentz expansion for the complex dielectric function of the LMGO

film [27]:

(5.1)

In Equation (5-1) SJ, ωJ, and γJ are the intensity, the central frequency and

the width of the J th DL contribution, respectively. Figure 5-4 shows an

instance of the fitting data according to Eq. (5-1). The imaginary part ε2 of

the LMGO dielectric function, as obtained from the fit, was then used to

extract the real part of the optical conductivity for the bare LMGO film,

σ (ω) = ε2(ω)*ω/60 (in Ω−1 cm−1

).

Figure 5-4: Example of fit to the data (in black) of Eq.5-1 (red line) at 10 K.




5.5 Analysis of the bare film optical conductivity

This section presents a comparison of the optical conductivity derived from

transmittance measurements of the LMGO film, with that previously measured

in a LMO film as a function of temperature and for photon energies up to 5

eV.

The resulting optical conductivity is reported at two temperatures in Fig. 5-

5 together with the four Lorentzian bands obtained from the fits to Eq. (5-1).

Three out of them, called s1, s2 and s3, build up the broad feature around

16 000 cm−1

and are centered at 13 000 cm−1

, 16 000 cm−1

and 20 700 cm−1

,

respectively. Attempts to fit the results in this spectral range by a lower

number of Lorentz oscillators did not provide acceptable results. Even if the

high frequency part of the conductivity is dominated by the temperature-

independent substrate absorption, after its subtraction a contribution from the

film centered at 33 000 cm−1

, s4, had to be included. We could thus better

reproduce the high-frequency tail of the spectra, and account for its

temperature dependence. Finally, the low-frequency side of a strong band at

higher frequency, s5 (dashed line) had to be included. This is probably the tail

of the intense bands around 5 eV due to the charge-transfer O–Mn transitions.

A comparison between the optical conductivity of LMGO and that of a LMO

film of similar thickness measured previously [20] is also shown in Fig. 5-5.

In LMGO around 2 eV (~16 000 cm−1

), it is lower and red-shifted with respect

to that of LMO. In both films, the high-frequency conductivity is dominated

by that of the LMGO substrate.



http://www.sciencedirect.com/science/article/pii/S0921452613006480#eq0005




Figure 5-5: Optical conductivity and Drude–Lorentz contributions of the

LMGO thin film as obtained from the fit to the transmittance data. The long-

dashed curves describe the high-frequency, T-independent σ(ω) of the LSAT

substrate. The optical conductivity of a pure LMO film of similar thickness,

and at the same temperatures [20] is reported for comparison by short-dashed

lines.



5.6 Drude-Lorentz analysis of the Optical Conductivity

In the following we discuss the individual contributions to σ (ω) in Fig. 5-5,

starting from the bands indicated in the figure as s2 and s4. The s2 band at 2 eV

shows a pronounced variation with temperature. Its integrated intensity

equation (5-2)

(5.2)

which is proportional to the spectral weight W is reported vs. temperature

in Fig. 5-6. Therein, one can distinguish three different regimes: (i) when

cooling the sample down to 200 K, Is2 steeply decreases, (ii) between 200 K

and 75 K it is approximately constant, and, (iii) below about 70 K it increases

slightly but significantly. The latter behavior (enlarged in the inset of Fig. 5-6)

provides useful information on the origin of s2: as it occurs close to the

ferromagnetic transition at T=75 K, this band can be assigned to the HS

intersite transition between neighboring Mn ions. A fit to Is2 with a sigmoid

function, shown in the inset of Fig. 5-6, places the ferromagnetic transition

at Tc ≈ 63 K, to be compared with the Tc ≈ 75 K reported in Ref. [16]. As

shown in the same inset, the transition monitored by Is2 in LMGO at Tc looks

much sharper than that in LMO at TN. This may be attributed to the role of the

inhomogeneities in the magnetic transition, already observed in several

manganites [20] and [21], which tend to promote a first-order magnetic

transition with a discontinuity of the order parameter. We note from the inset

that the intensity of the s2 band in LMGO is similar to that of LMO, despite a

50% lower Mn concentration. This can be explained by considering

that Is2 depends also on the strength of the hopping integral t. This in turn

strongly depends either on the Mn–O distance or on the Mn–O–Mn bending

angle, which in LMGO are both more favorable to the overlap of eg orbitals

than in LMO. The average frequency ω2 of the s2 band is 16 000 cm−1

at the

lowest temperatures, with a red-shift (0.35 eV) ∆ =2800cm-1

with respect to

the corresponding band in LMO. In a tight-binding approach involving the 3d

levels of manganese, this shift should be entirely attributed to the disappearing









of the Jahn–Teller distortion energy of Mn+3

, namely EJT=2Δ=0.7 eV. This

value is consistent with that (0.6 eV) reported in Ref. [20].

The increase in the s2 intensity detected above 200 K, in the paramagnetic

phase, is likely due to subtle structural changes. Indeed, neutron scattering

experiments detected two orthorhombic phases in Ga substituted

manganites [16]: at low Ga content, the stable phase belongs to the O′ spatial

symmetry due to cooperative Jahn–Teller distortion, but above 50% Ga, the

symmetry becomes O. Therein, a=b and both are smaller than the

corresponding lattice constants of the O′ phase. Therefore the electronic

overlap between neighboring Mn+3

ions should benefit of this symmetry

change. One may speculate that this effect increases the intersite matrix

element and then the intensity of transitions like s2 in LaMn0.5Ga0.5O3, which

may include large domains of O symmetry.

Figure 5-6: Integrated intensity of the s2 contribution of the LMGO optical

conductivity. The dotted line is a guide to the eye. In the inset, the low-

temperature intensity of s2 is enlarged and compared to both a fit to data (solid

line) and to the corresponding behavior in LMO [20] (dashed line).





The s2 bandwidth γ2 of LMGO is larger than that of LMO (see Fig. 5-7) and,

unlike this latter, is independent of temperature within errors. In LMO, the

broadening of this band below TN=140 K was ascribed to the increase in the

electron kinetic energy (in a tight-binding framework) due to the

ferromagnetic ordering of the ab planes. Here, the random distribution of Ga

ions probably causes an inhomogeneous broadening of the t2g→eg splittings,

which prevents to observe any T-dependence of the s2 bandwidth.

Figure 5-7: The bandwidth of the s2 contribution in LMGO (red diamonds)

and LMO (black squares). Dashed lines are guides to the eye. Data of LMO

are taken from Ref. [20].

The intensity of the s4 band, Is4 (T), is reported vs. temperature in Fig. 5-8: at

variance with Is2 (T), it decreases below Tc. This is a clear indication that





the s4 transition is inhibited by the onset of the ferromagnetic order. Therefore

it can be assigned to the Low Spin (LS) intersite transition between Mn+3

ions.

Similar to Is2, Is4 (T) exhibits a steep decrease when T decreases below 200 K.

By the same argument as above, this step can be tentatively attributed to the

structural transition which occurs for 50% Ga.

Figure 5-8: Integrated intensity of the s4 contribution to the LMGO optical

conductivity. The dotted line is a guide to the eye. The low-temperature region

is enlarged in the inset, where also a fit to data is reported (solid line). The

dashed line is the corresponding fit for LMO from Ref. [20].



As remarked above for the HS transition, also the bandwidth γ4 is much

broader than in LMO, and does not display appreciable temperature

dependence, at odds with the steep decrease across TN =140 K in LMO

(see Fig. 5-9). Also in this case, γ4 probably reflects the inhomogeneous

broadening of the electronic transition in LMGO.

Figure 5-9: The bandwidth of the s4 contribution in LMGO (red diamonds)

and LMO (black squares). The dashed lines are guides to the eye.

Let us now discuss the s1 and s3 contributions, peaked at 13 000 cm−1

and

21 000 cm−1

, respectively. Both their intensities are independent of

temperature within the experimental errors; that of s3, for example, is reported

in Fig. 5-10 in comparison with that of the same band in LMO. For this

reason, the s1 and s3 bands were attributed [20] to t2g→ e1

g and t2g→ e2

g on-

site transitions, respectively, which are separated in energy by the Jahn–Teller





term. However, in the present case of LMGO, where the average distortion of

the MnO6 octahedra is small and the eg levels are nearly degenerate, the above

assignment would lead to a single band placed between those of LMO. This is

at odds with the present data.

Figure 5-10: Integrated intensity of the s3 band in LMGO (red diamonds) and

LMO (black squares). The dashed lines are guides to the eye.


An alternative origin for s1 and s3 may be found in the manifold of charge-

transfer p–d transitions within the MnO6 octahedra [3] and [4]. Therein, the

dipole-allowed t2u (π) → t2g and the forbidden t1g (π) → t2g should fall in the

energies range 18 000 ÷ 22 000 cm-1

and 11 000 ÷ 15 000 cm-1

, respectively.

They could be reasonable candidates for s3 and s1, because the latter transition

occurs only if phonon-assisted. As a consequence, its intensity should increase

by a bare 10% in the range of temperature here investigated, a variation which

could be hardly appreciated in Fig. 5-10. However, the comparison in Fig. 5-

10 between the intensity Is3(T) of the band in LMGO and that in LMO seems

in contradiction with an Mn–O mechanism for S3. As it should scale with the

Ga concentration, in LGMO it should be smaller by 50% than in LMO.

However, the decrease of the Mn–O average distance in LMGO results in an

enhancement of the effective dipole matrix element [28]〈t2u(π)|d|t2g〉 by a

factor of 1.5 along the Mn(3d)–O(2pπ) bond, and therefore of the absorbed

intensity by about a factor of 2. This should shift again the ratio between the

two intensities to a value close to 1, and explain the result of Fig. 5-10.

5.7 Conclusion

The origin of the electronic optical absorption in manganites is still a

controversial topic: in the visible and near UV range one observes four bands,

of which two change with temperature, while two other do not. In the

literature one finds papers in favor of a Mn–O charge-transfer attribution of

those bands, at variance with others which privilege the intrasite and intersite

Mn–Mn transitions. The latter approach must take into account both the Jahn–

Teller distortion and Hund's energy, resulting in a view of the manganites as

Mott–Hubbard insulators. Here, we have tried to distinguish those two models

by studying the electronic spectrum of a LaMn0.5Ga0.5O3 thin film, from about

1 eV to about 5 eV and comparing with that of LaMnO3. Two out of the four

bands (those peaked at 16 000 and 33 000 cm−1

) exhibit a pronounced

temperature dependence that are sensitive to the ferromagnetic transition.

They are confirmed to be due to Mn–Mn intersite transitions of HS and LS

types. Remarkably, in LGMO the bandwidth of these bands is larger than in









LMO and nearly independent of temperature, a behavior which reveals an

inhomogeneous broadening due to the random distribution of Ga ions. The

weaker bands peaked at 13 000 and 22 000 cm−1

are instead temperature

independent. When observed previously in LMO films, this behavior led us to

assign them to Mn and

on-site transitions. However, such

assignment seems at variance with the observation of both bands in the present

spectra of LGMO, where the eg Jahn–Teller splitting should be strongly

reduced by Ga. Therefore we have considered an assignment of these

contributions in terms of p–d Mn–O charge-transfer. Their nearly equal

intensity in LMGO and LMO may be explained by assuming that the

transition dipole strength, which in the former compound is larger by 50% for

the smaller size of the MnO6 octahedra, compensates the 50% reduction in the

Mn concentration.

We are thus led to a “mixed” interpretation of the electronic spectra in the La

manganites, where the d–d Mn–Mn transitions dominate the visible–UV

region but p–d charge-transfer Mn–O transitions are also present. This result

suggests that both a Mott–Hubbard and a charge-transfer picture may coexist

in such intriguing systems.

Bibliography 117

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Optical study of insulator to metal transition in LaxMnO3 thin films 119

Chapter 6: Optical study of insulator to metal

transition in LaxMnO3 thin films

6.1 Introduction

The phase diagram of the mixed-valence A1-xBxMnO3 manganites - where A is

trivalent lanthanide and B is a divalent cation - is known to include an

impressive variety of different phases, which span from ferromagnetic metals

to ferromagnetic and antiferromagnetic insulators, with the latter ones which

may also exhibit charge and orbital order [1]. In bulk materials the transitions

between those phases are governed by two parameters only, the temperature T

and the nominal hole doping x. This in turn controls (in a simple ionic model)

the relative concentration of Mn3+

and Mn4+

states, whose simultaneous

presence allows for electrical transport through the double-exchange

mechanism [2,3] between collinearly spin-oriented Mn ions. As the Mn3+

ions

locally distort the surrounding oxygen octahedral through the Jahn-Teller e

ect, the carriers strongly interact with phonons and their transfer between Mn3+

and Mn4+

ions causes alternating distortions and relaxations. Therefore the

conduction mechanism in metallic manganites is dominated by polaronic

effects [4]. When passing to the corresponding thin films, which are much

more interesting than bulk materials for the potential applications [5,6] , not

only temperature and doping play a major role, but also the film thickness and

the stress due to the lattice mismatch with the substrate. Indeed, both latter

factors heavily affect the properties of manganites, to the extent that

heterostructures made of two insulators, like alternating layers (LaMnO3)

2n/(SrMnO3)n , be-come metallic below a critical value of n [7,8]. In thin films

of manganites it was also found [9] that, thanks to the structural stress, one can

stabilize La-decient phases LaxMnO3 (x <1) which would be hardly obtained

in bulk samples. Those films exhibit a ferromagnetic transition at a Curie

temeprature Tc which varies between 330 and more than 380 K for x changing

in the interval 0.98 - 0.66 [10]. Correspondingly, an insulator-to-metal

120 Optical study of insulator to metal transition in LaxMnO3 thin films

transition (IMT) is observed at a T IMT ~ Tc, through a sharp change of slope in

the T-dependence of the resistivity. [11,12] TIMT is sensitive to both the La/Mn

ratio and the oxygen concentration. Indeed, LMO films optimally oxygenated

by postannealing, with x= 0.88, have a TIMT = 387 K, higher than that

measured in the as-grown samples (355 K) [11,12] , and magnetotransport

properties closer to those found in La1- xSrxMnO3 . Around Tc those films also

display negative magnetoresistance, similarly to the manganites chemically

doped [9] . Another important finding is that obtained by X-ray Absorption

Spectroscopy (XAS) in LaxMnO3 films with x <1, namely, evidence for the

presence of ions Mn2+

Indeed, their XAS spectra include a line very similar to

that detected in MnO, which is absent in the manganites doped by divalent

ions [13,14] . It has then been suggested that Mn2+

replace, either partly or

fully, he missing La3+

ions at the A sites. This replacement would considerably

reduce the structural disorder created by La vacancies. One should also

remember that the Mn2+

ions, with their filled eg orbitals, neither provide

electrons to the conduction mechanism, nor produce Jahn-Teller distortions.

The other Mn ions will be partly Mn3+

, with Jahn-Teller distorted oxygen

octahedra around them, partly Mn4+

, as in chemically-doped manganites. In

the present work we have measured the optical spectra of three LaxMnO3 films

with x < 1, and one with x > 1, with the aim to study the

effect of La non-stoichiometry on the electrodynamics of LaMnO3. Our focus

is on the spectral changes observed in the La-deficient films at temperatures

below the TIMT, to understand the mechanism which triggers the metallization

of the La-deficient samples. Our observations support a polaronic landscape

with phase separation, where the spectral weight of large polarons in

ferromagnetic islands increases below TIMT at the expense of those from small

polarons in a magnetically disorder background. Meanwhile, a Drude term

grows up in the far infrared, much narrower than in chemically doped

manganites like La1-xSrxMnO3 . This feature indicates a lower disorder in these

La-defective films than in the chemically doped manganites, which may be

interesting for potential applications. Finally, in the visible range we identify

an absorption characteristic of the Mn2+

ions in both most La-defective films,


which confirms the result of previous X-ray experiments. The lm with La

excess is insulating at all temperatures and does not present spectral features

much different from those reported in the literature for the stoichiometric

material.

6.2 Sample description and experimental procedure

Four LaxMnO3 thin films, with La/Mn ratios x= 0.66, 0.88, 0.98, and

1.10, were grown on SrTiO3(STO) (100) substrates by Molecular Beam

Epitaxy (MBE), a technique which easily allows one to change the La/Mn

ratio by changing the evaporation rate of the individual elements. All the

depositions were performed under an oxygen pressure of about 2x10- 6

mbar,

and the average film thickness was d~35 nm. During the substrate heating

before deposition, the chamber was kept under an oxygen pressure of about

10 -7

mbar in order to avoid any reduction of STO which might affect the

optical spectra in the midinfrared. The composition of the samples was

determined by electron dispersive spectroscopy (EDS) measurements on twin

samples (i.e., grown in the same deposition run) but on MgO substrates, in

order to minimize the substrate interference with the film spectrum. [11] X-ray

direction (XRD) analyses showed that all the investigated LMO samples are

in-plane matched with STO substrates and revealed no trace [14] of secondary

spurious phases like Mn3O4. [15] The oxygen content was increased by

postannealing all the LMO samples, until no longer process could affect their

metallicity. Even though a reliable measurement of oxygen content was not

possible, such observation led us to conclude that in our samples ∂ ~ 0.As

reported above, it has been proposed that a partial occupancy of Mn ions at

perovskite A-site, rather than the promotion of structural vacancies, better

addresses the structural and electronic properties of La-defective samples.

According to such a substitutional model, [16] the La and Mn atomic

occupancies at perovskite A- and B-sites are those listed in Table 6-1 for the

four films. Therein, their measured TIMT's are also reported. For the film with x

>1, the data in Table 6-1 are also based on the results of XRD, XAS and RIXS

measurements, see Refs. 10,14,16. They rule out spurious phases related to


other La compounds and show the presence of both Mn3+

and Mn+4

ions in the

sample, in addition to vacancies at the Mn site.

La

at A-site

Mn-A

at A-site

Mn-B

at B-sitea

TIMT

(K)

x = 0.66 0.80 0.20 1.00 > 430

x = 0.88 0.94 0.06 1.00 387

x = 0.98 0.99 0.01 1.00 370

x = 1.10 1.00 0 0.91 240

Table 6-1: Stoichiometric composition of LMO films according to

asubstitutional model.

a All data with x <1 are normalized to Mn-B content, while the sample with x

>1 is intended to have vacancies at B-site.

As already mentioned, for x <1 the Mn ions at the A-site are expected to be in

the +2 state, while those at the B-sites will be partially in the +3 state, and the

remainders in the +4 state. The corresponding nominal concentrations can be

easily calculated in the purely ionic model we are using, if one assumes that

oxygen is stoichiometric, that all the missing La3+

ions are replaced by Mn2+

,

and that the valence is +2, +3, and -2 for Mn-A, La and O, respectively. From

the neutrality condition

(6.1)

one thus obtains the average electronic valence Mn-B of Mn ions at perovskite

B-site. The results for the LMO films with x <1 are reported in Table 6-2.

Therein, the Mn3+

/Mn4+

ionic ratio is 4 and 16 for x= 0.66 and 0.88,


respectively, in both cases sizably different from those reported in chemically

doped manganites (where optimum doping is obtained for Mn3+

/Mn4+

~ 2).

Moreover, in real La-defective thin films, even though the highest TIMT is

recorded at x= 0.66, the lowest resistivity at low temperature is observed at x=

0.88 [12] .This may imply that, for decreasing x, not all the La vacancies can

be filled by Mn ions. This on one hand will strongly influence the x3+ / x4+

ratio; on the other hand will increase the disorder due to the vacancies, which

limits the electrical conductivity.

Mn2+

at A-site

(%)

VMn-B

at B-site

Mn3+

at B-site

(%)

Mn4+

at B-site

(%)

x = 0.66 20 3.20 80 20

x = 0.88 6 3.06 94 6

x = 0.98 1 3.01 99 1

Table 6-2: Distribution of the Mn+ states in the lattice of La-defective thin

films and average electronic valence VMn-B at the B sites.

6.3 Reflectivity spectra of the LaMnxO3 films

The optical properties of the four thin films described above have been studied

by measuring their reflectivity R (ω) from 40 to 45000 cm-1

at quasi-normal

incidence, between 20 and 300 K, in helium-flow cryostat. In the whole

infrared range the spectra were collected by a Michelson interferometer and

using an Au mirror as reference, in the visible and UV domains by a

monochromator and an Al mirror as reference. The raw reflectivity of the

films is shown in Fig. 6-1.


Figure 6-1: (Color online). Raw reflectivity data for the four LaxMnO3 films

on SrTiO3 substrates, at different temperatures. The fits to the highest and

lowest temperature spectra are shown by the dashed lines.

In the far infrared it is dominated by the phonons of the STO substrate, which

include the well-known soft mode whose peak frequency decreases from 88

cm -1

at room temperature [19] to about 20 cm -1

at the liquid helium

temperatures. [20] Superimposed to the absorption of STO, phonon lines due

to the manganite itself are detected, which evolve with temperature as it will

be discussed below. Strong and T-dependent bands are exhibited by the La-

defective films also in the midinfrared (MIR) and the near infrared (NIR),

which can be fully ascribed to the manganite as the reflectivity of STO is low

and featureless up to ~ 25,000 cm -1

. Finally, an electronic absorption with an

edge at ~ 18,000 cm -1

is observed in the visible and UV ranges.


6.4 Extraction of the bare film optical functions

To extract the optical conductivity from R(ω) we fit to data the usual [17]

Equation for a triple-layer system consisting in a vacuum, a film of thickness

d, and a semi-infinite substrate [18] namely

(6.2)

where

(6.3)

Here, n0=1 is the refractive index of a vacuum; is the complex refractive

index of the film, and that of the substrate, that is obtained from data in the

literature [20]. Particular care was devoted to the soft phonon of STO, whose

intensity strongly increases, and whose peak frequency changes from 90 to 20

cm-1

, when cooling the sample from 300 to 20 K. The film refraction index

is modeled through the Drude-Lorentz dielectric function.

(6.4)

All quantities in the right-hand side of Eq. 6-4 are free parameters. Therein,

replaces all contributions at energies higher than the measuring range,

while the second term is the Drude contribution with plasma frequency ωp and

relaxation rate . The sum on j includes the phonon contributions with

oscillator strength Sj and width j, while the sum on k describes the broad

oscillators detected above the phonon region, up to the UV range. In the

present case it includes two midinfrared bands, MIR-1 and MIR-2, and from

four to six electronic transitions in the near infrared, visible, and near-UV

range, depending on x. In the infrared range the film thickness used in the fits

was that measured after the growth, d= 35±1 nm. At short wavelengths, where

the radiation penetration depth becomes comparable with the film thickness or

shorter, the film tends to be seen as a semi-infinite medium, and keeping x


fixed in the fits would produce artifacts. Therefore, in the near infrared and

the visible, the fixed d was replaced by an "effective thickness" left free to

vary.

6-5 Analysis of the bare film optical conductivity

The real part of the bare film optical conductivity σ1 (ω) related to the

dielectric function in Eq. 4-6 by

is shown in Fig. 6-2

for all samples at different temperatures. The dots on the vertical axis are the

σ1(0) values extracted from resistivity measurements on similar films, at the

same temperatures [12]. The agreement between dc and infrared

measurements is rather good, considering the errors involved in both

techniques and the fact that the samples in the two experiments had equal

nominal composition but were not the same. In the bottom panel (Fig. 6-2-d),

the film with La excess (x= 1.10) shows a spectrum typical of a good insulator

at all temperatures, at variance with a film with x= 1.10 which exhibited an

IMT at 240 K [14]. Indeed, there is no Drude term indicating the presence of

free carriers at any temperature, and also that the midinfrared absorption is

negligible. Eight phonon lines are detected in the far infrared, more than the

three observed in doped pseudocubic manganites, but much less than the 25

modes predicted for the orthorhombic cell (space group Pnma) of pure

LaMnO3 [23]. At higher frequencies, strong and broad peaks around 12000

and 30000 cm-1

are well evident. The latter band results in turn from the

superposition of four different contributions, as it will be discussed further on.


Figure 6-2: (Color online). Real part of the optical conductivity of the bare

LMO films, as extracted from the reflectivity of the three-layer system by use

of Eqs. 1-3.The dots on the vertical axis are the σ1 (0) values extracted from

resistivity measurements on films with the same nominal composition, at the

same temperatures.


For the three sample with La deficiency one expects a completely

different response, as they are metallic at all temperatures of the present

experiment, being their Tc 's well above 350 K. [12,14] Indeed, in Figs. 6-2-a,

-b, and -c., σ1 (ω) reaches high values in the FIR due to a Drude absorption

which increases steadily for decreasing temperatures. As a result, the phonons

are efficiently shielded except for the strong pair at the highest frequency,

which disappears only in the sample at optimum doping (x= 0.88) at low

temperature. Moreover, broad absorption bands appear in the midinfrared

which strongly changes with temperature, both in intensity and peak

frequency. This process can be better understood in Fig. 6-3, where σ1 (ω) is

decomposed in Lorentzian oscillators, through Eq. 6-4, at the highest and

lowest measuring temperature. In addition to the phonons and the Drude term,

all samples exhibit two well defined contributions in the midinfrared: a "soft"

band peaked around 1000 cm-1

that we call MIR-1, and a "hard" band called

MIR-2. This is centered between 2000 and 5000 cm-1

, depending on doping

and temperature. Similar midinfrared pairs, of polaronic origin [25] have been

observed in a number of oxides, like SrTiO3 [26] and many superconducting

cuprates at low doping. [27] In the latter compounds, a band similar to MIR-1

drives the IMT by transferring part of its spectral weight, for increasing

doping, to the free-carrier Drude term. [28].

In the present case of the manganites, the existence of two midinfrared bands

which co-exist in such a broad range of temperatures below the IMT can be

explained recalling that phase separation is a common characteristic of

manganites around the insulator-to-metal transition [30]. In this framework,

the complex infrared spectrum of the manganites which undergo an IMT

transition driven by magnetic ordering [31,32] can be explained by polaronic

models like that proposed in Ref. 29. On this basis, the "soft" band can be

assigned to islands of high electron density, where itinerant large polarons

form ferromagnetic domains through the double-exchange mechanism, while

the "hard" band should be due to localized small polarons. Their insulating

domains may be either paramagnetic or antiferromagnetic, depending on the


temperature, and the frequency difference between the two bands is related to

the Hund's energy [33].

Figure 6-3: (Colour online). Evolution of the midinfrared bands MIR-1 and

MIR-2 and of the Drude absorption for lowering temperature in the thin

LaxMnO3 film with x= 0.88.

As temperature decreases and the magnetization increases, the conducting

domains slowly expand at the expense of the insulating ones, causing the

transfer of spectral weight from MIR-2 to MIR-1 in Fig. 6-3, which thus

directly monitors the transition. This process is illustrated in further detail in

Fig. 6-4 for the case x= 0.88. Therein, one can see how the intensity of both

MIR-1 and Drude gradually increases for T 0, while MIR-2 increasingly

looses intensity. Indeed, a f- sum rule is respected within a 20% uncertainty,

as one obtains at all temperatures from 300 to 20 K, for the film with x = 0.88

(6-5)

Here, being the integral extended over the whole infrared range (ω0= 15000

cm-1

), it includes the Drude term, MIR-1, and MIR-2. As one can see in Fig. 6-

4, MIR-2 also markedly softens, indicating that, in the insulating regions, also


the binding energy of the small polarons decreases. This dynamics tends to

saturate only around 50 K, i.e., more than 300 K below the Tc of this film.

The plasma frequency of the Drude term, which measures the

concentration n of the free carriers, is reported for the three films which

undergo the transition in Fig. 6-5. All of them are already in the metallic phase

at the highest temperature of the experiment, consistently with the dc

measurements, but ωp still increases by a factor of two for T → 0, depending

on the sample. Though rather strong, this Drude term, as one may notice in

Fig.6-2, is surprisingly narrow. Its width is just ~ 100 cm-1

at 7 K, for x =

0.66 and 0.88. This value is better than the lowest Drude widths measured in

divalent-ion doped single crystals of manganites: for example, one had ~ 150

cm-1

at 9 K in La0.825Sr0.175MnO3 (Tc = 283 K) [31]. This result at low

temperature indicates a structural disorder, in the present films, much lower

than that expected in the presence of a large number of La defects and is

consistent with the prediction that the La missing ions are replaced by other

ions (Mn2+

,according to both diffraction and magnetic measurements [10] ).

Figure 6-4: (Coloronline) Temperature dependence of the Drude spectral

weight W in the three LaxMnO3 films with x <1.


Finally, the high-frequency part of the spectra is shown in Fig. 6-5 and

decomposed into Lorentzian oscillators. The film with x= 1.10 shows four

bands in the VIS-UV range, at about 25,000, 28,000, 33000, and 41000 cm-1

;

in that at with x= 0.98 four contribitutionsare resolved at about 20,000, 23,000,

28000, and 36000 cm-1

, while both samples with the most numerous La

defects have well resolved lines at about 16500, 18000, 20,000, 23,000,

28000, and 36000 cm-1

. The latter can be compared, by taking into account

small shifts due to possible deviations in the crystal structures caused by the

La vacancies, to the five bands found in stoichiometric LMO thin films at

16800, 19500, 22,000, 28,000, and 33000 cm-1

, which therein were called s1,

s2, s3, s4 and s5, respectively [35] . s1 and s3 were assigned to intrasite →

and →

transitions, respectively, where the t and e levels are

separated by the crystal field and the e doublet is split by the Jahn-Teller

distortion. s2 and s4 , which in LMO appreciably changes across the Neel

temperature, were attributed to intersite transitions within the t2g - eg manifold;

s5 to charge transfer transitions. The most interesting one in the present

context is however the lowest-energy band, that we may call s0 , which is

marked with the red line in Fig. 6-6. This contribution appears in the most La-

deficient samples only and is peaked at 16500 cm- 1

, a frequency close to that

of a line observed in MnO at 16400 cm-1

[36] . For those two reasons, we

assign it to an electronic transitions of the Mn2+

ions, whose presence in the

most La-defective samples is thus confermed by infrared spectroscopy.


Figure 6-5: (Color online). Decomposition of the visible-UV conductivity in

terms of Lorentzian oscillators in the four films at 20 K. The band marked

with the red line is the contribution at 16500 cm-1

that we assign to the

Mn2+

ions.


6-6 Conclusion

We have exploited the opportunity to stabilize in thin films highly defective

structures that cannot be obtained in the bulk samples, to investigate by optical

spectroscopy the electronic properties of manganites with strong La non-

stoichiometry. In particular, we have studied the slow metallization process

that LaxMnO3 undergoes for decreasing temperatures, in films with x <1. We

have found that, as in other oxides, the insulator-to-metal transition is driven

by a continuous transfer of spectral weight from a "hard" band MIR-2 peaked

between 3000 and 5000 cm-1

at room temperature, to a softer band (MIR-1)

observed around 1000 cm-1

which acts as a "reservoir" for the Drude term of

the free carriers. This process continues down to 100 K at least, more than 250

K below its onset at the Curie temperature Tc and at the TIMT where the curve

of the resistivity vs. T changes its slope. These observations are fully

consistent with a phase separation model where MIR-2 is attributed to

localized charges strongly interacting with the lattice (small polarons), and

MIR-1 to itinerant large polarons in zones richer of electrons. We have also

observed that, in these La-defective films, the Drude term at low temperature

is narrow as in the best divalent-ion doped manganites, and therefore the

scattering rate is rather low. This finding may be of interest for potential

applications of La-defective films to conductive devices.

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Infrared phonon dynamics of Ba2CuGe2O7 and BiMnO3 137

Chapter 7: Infrared phonon dynamics of

Ba2CuGe2O7 and BiMnO3

7.1 Infrared phonon spectrum of the tetragonal

helimagnet Ba2CuGe2O7

Multiferroics, defined for those multifunctional materials in which two or

more kinds of fundamental ferrocities coexist, have become one of the hottest

topics of condensed matter physics and materials science in recent years. The

coexistence of several order parameters in multiferroics brings out novel

physical phenomena and offers possibilities for new device functions. The

revival of research activities on multiferroics is evidenced by some novel

discoveries and concepts, both experimentally and theoretically. Ba2CuGe2O7

one of the magnetoelectric compounds which below a critical temperature

simultaneously display ferroelectricity and some kind of magnetic order -

several mechanisms that can couple magnetism to a macroscopic polarization

have been identified. Among them, one of the most interesting is the

Dzyaloshinsky-Moriya (DM) effect [1,2] , which gives rise to helical spin

structures through an exchange Hamiltonian which depends on the vector

product between adjacent spins. Such magnetism can also be associated with

an electric polarization whose expression contains the same vectorial term

[3]. The compound here studied, Ba2CuGe2O7 (BCGO), is the only member

of Ba2XGe2O7 family which develops helical magnetism at liquid helium

temperatures via the DM mechanism [4–6]. Indeed, for X =Mn (spin S = 5/2)

and Co (S = 3/2) the insulator is antiferromagnetic (AF) below a Ne el

temperature TN = 4.0 and 6.7 K, respectively [3,7,8] . Below TN these systems

develop magnetoelectricity due to the spin-dependent hybridization between

the d orbitals of the transition metal and the p orbitals of oxygen [9,10].

Ba2CuGe2O7 instead, having the Cu2+

ion S = 1/2, is magnetically much less

anisotropic. Below TN = 3.2 K, it thus displays a quasi-AF cycloidal,

incommensurate magnetism. However, despite the absence of a center of

138 Infrared phonon dynamics of Ba2CuGe2O7 and BiMnO3

inversion symmetry in the crystal structure, it does not develop spontaneous

ferroelectricity [8]. Nevertheless, a macroscopic electric polarization can be

induced in BCGO by an external magnetic field [11]. As the magnetoelectric

properties of Ba2CuGe2O7 have been extensively discussed in Refs. [3,9,11],

the present work is focused on its lattice dynamics, both from an experimental

and from a theoretical point of view. We have thus measured the reflectivity

R(ω) of a single crystal of this compound, from 80 to 6000 cm−1

and from 7 to

300 K, with the radiation polarized both along the a (or b) axis and along the c

axis of the tetragonal unit cell. For both polarizations, the real part σ (ω) of the

optical conductivity extracted from R(ω) displays in the far infrared a number

of well defined phonon peaks, as Ba2CuGe2O7 is an excellent insulator,. The

measured frequencies and intensities have been compared with the predictions

of shell-model calculations.

7.1.1 Ba2CuGe2O7 Single crystal growth

Single crystals of Ba2CuGe2O7 were grown by the float zone technique at a

pressure of 3 bar in an oxygen gas atmosphere with the growth speed of 0.5

mm/hour [13]. The morphology, phase composition, and purity of the grown

crystals were inspected by high-resolution x-ray diffraction and scanning

electron microscopy combined with energy dispersive spectroscopy. The

crystal orientation was determined by the x-ray back-reflection Laue method

showing well defined; neither distorted nor smeared-out spots. Moreover, the

crystals used in this work were cut in such a way that the largest surface

contained the a (or b) and the c axes. This surface was finely polished with

polycrystalline diamond suspension down to 0.3μm in grain size, while the

orientation of the a (or b-c) axes with respect to the sample edges was assessed

by the electron back-scattered Kikuchi diffraction technique. The dimensions

of the crystals employed in this work were approximately 3×2×1 mm. In the

visible range, they look transparent and colorless, like a piece of glass.


7.1.2 Ba2CuGe2O7 structure

The insulator Ba2CuGe2O7 crystallizes in the noncentrosymmetric tetragonal

space group P421m, with lattice parameters a = 0.8466 nm and c = 0.5445 nm,

these values are presumably measured at room temperature, and no structural

changes induced by temperature are reported in the literature at best of our

knowledge. A schematic view of its unit cell is reported in Fig. 7-1, which

reproduces that reported in Ref. 5. The Ba2+

planes, orthogonal to the c axis,

separate the layers made of corner-sharing GeO4 and CuO4 tetrahedra. It is in

the resulting two-dimensional square lattice of Cu2+

ions, that the Cu spins

interact through the DM mechanism and the helical magnetic structure takes

place.

Figure 7-1: Color online. Lattice structure of Ba2CuGe2O7 (reelaborated from

Ref. 12 with the graphical tools reported in Ref. 14). The oxygen tetrahedra

contain a copper atom if blue, a germanium atom if grey.


7.1.3 Infrared Reflectivity measurements on Ba2CuGe2O7

The reflectivity R (ω) of BCGO was measured with a rapid-scanning

Michelson interferometer at a resolution of 2 cm−1

. Two different polarizations

of the radiation field were used, one along the a (b) axis (which will be

simply indicated as the ab plane further on) and the other one along the c axis.

The sample was mounted on the cold finger of a helium-flow cryostat. Even if

the phonon region is limited to 850 cm −1

, R(ω) was measured by a rapid-

scanning interferometer up to 6000 cm−1

in order to perform on it accurate

Kramers-Kronig (KK) transformations. The reference was a gold film

evaporated in-situ onto the sample. As the crystal is nearly transparent in the

midinfrared, to avoid interference fringes its back surface was left unpolished

and wedged [15] with respect to the front surface. The real part σ1 (ω) of the

optical conductivity was then extracted from R (ω) by standard KK transforms.

The reflectivity was extrapolated to ω → ∞ by an inverse power law of ω, and

to ω = 0 by Lorentzian fits. The raw reflectivity data of Ba2CuGe2O7 are

shown in Fig. 7-2 in the frequency range of the MIR and FIR ranges, for the

radiation polarized both in the ab plane (top) and along the c axis (bottom).

Fig 7-3 shows the reflectivity of Ba2CuGe2O7, in the far infrared range of

frequencies at the lowest and highest measured temperatures, 7 K (solid line)

and 300 K (dashed line) respectively, with the radiation polarized along the

axis (a) and along the c axis (b).

According to Fig.7-3 both spectra look very similar to the corresponding

reflectivities of Ba2CoGe2O7 reported in the same frequency range in Ref. 16.

They are typical of an insulating crystal, with a number of phonon lines in the

far infrared, and a flat and very low reflectivity (6-7 %) at higher frequencies.

This behavior continues in the whole midinfrared range (see Fig 7-2).


Figure 7-2: Reflectivity of Ba2CuGe2O7 between 7 K to 300 K in the MIR and

FIR ranges (6 meV-0.74 eV), with radiation polarized along a axis (top) and

along c axis (bottom) in logarithmic scale.


Figure 7-3: Reflectivity of Ba2CuGe2O7, in the far infrared range of

frequencies at 7 K (solid line) and 300 K (dashed line), with the radiation

polarized along the axis (a) and along the c axis (b).


7.1.4 Factor group analysis of the infrared phonons

The optical conductivity extracted from the data of Fig. 7-3 is shown in Figs.

7-4 (a) and 7-5 (a) for the a,b plane and the c axis, respectively, in the far

infrared region at both the lowest and highest measured temperatures. The

absence of lines common to both polarizations confirms that the polarizer was

correctly oriented and that the sample was a single crystal. A factor group

analysis predicts for the unit cell of Ba2CuGe2O7, which includes two

formula units, the vibrational representation

(7.1)

where the E modes are doubly degenerate. One B2 mode and one E mode are

acoustic, the six A2 modes are silent, and all of the others are optical, Raman-

active phonons. Among them, the 18 E and the ten B2 modes are also infrared

active and can be observed with the radiation polarized in the ab plane or

along the c axis, respectively. Figures 7-4 (a) and 7-5 (a) show that 14

transverse optical (TO) phonon modes belonging to the ab plane and nine

belonging to the c axis could be detected in the present experiment. Their

frequencies will be listed in Tables 7-2 and 7-3 , respectively.

7.1.5 Shell-Model calculations

In order to understand the complex phonon spectrum of BCGO, we have used

a shell model (SM) calculations which performed by the cooperation with our

colleagues (i.e, S. Koval (Instituto de Fısica Rosario, Universidad Nacional de

Rosario, Argentina) and J. Lorenzana (Dipartimento di Fisica, Universit` a di

Roma “La Sapienza”-Roma-Italy). (SM) calculations enabled us to perform

lattice dynamical calculations and to compare the results with the measured σ1

(ω). The SM has been successfully applied to different compounds (oxides and

hydrides) where the effects of the anion polarizability turned out to be

important for a proper description of the vibrational properties [17–20]. The

ionic polarizability is taken into account by considering electronic shells with

charge Y coupled harmonically by a force constant k to an atomic core.


The SM includes long-range Coulomb interactions between all charged shells

and cores, and shell-shell short-range interactions arising from the wave-

function overlap between neighbouring ions.

They have considered short-range interactions of the Born-Mayer type, A exp

(−r/ρ), for the Cu-O, Ba-O, and Ge-O bonds. The lattice constants and the

atomic positions were taken from the experimental data of Ref. [12].

Figure 7- 4: a) Optical conductivity of Ba2CuGe2O7 , in the far infrared range

of frequencies at 7 K (solid line) and 300 K (dashed line), with the radiation

polarized in the ab plane. b) Shell-model results for the vibrational modes of

the ab plane. The bar length is proportional to the calculated strength Sj [th].


Figure 7- 5: a) Optical conductivity of Ba2CuGe2O7, in the far infrared range

of frequencies at 7 K (solid line) and 300 K (dashed line), with the radiation

polarized in the ab plane andalong the c axis. b) Shell-model results for the

vibrational modes of the ab plane. The bar length is proportional to the

calculated strength Sj [th].


To calculate the oscillator frequencies and strengths, they have fixed the total

charges Z of the ions to their nominal values, i.e., ZO= −2, ZCu= 2, ZBa= 2, and

ZGe= 4. The model contains 14 adjustable parameters. The initial parameter

values were taken from Refs. [21,22] and were subsequently modified in order

to fit the measured infrared phonon frequencies at the Brillouin-zone center.

The calculations were carried out with the help of the GULP code [23].Due to

the complexity of the structure and consequently of the developed SM, the use

of automatic searches for parameters included in the code turned out to be

ineffective [20]. Thus, the adjustment of the parameters was made by hand.

The final set of SM parameters which gave the best fit to data is shown in

Table 7-1. An important effect of the ionic polarizabilities is that they modify

the oscillator strengths of the optical absorption, an effect that is often

accounted for by using the concept of Born effective charges. The theoretical

frequencies Ωjth of the transverse optical (TO) infrared phonons obtained with

the model are shown in Table 7-2 for the ab plane and in Table7-3 for the c

axis. Also shown are the calculated oscillator strengths Sjth for each jth TO

infrared mode [23,24]. The resulting components of the dielectric function

tensor, which is diagonal here and also symmetric in the ab plane, are reported

in Table 7-4 in both limits of zero frequency and high frequency.

Interaction A (eV) Ion Y (e)

Ba-O

Cu-O

Ge-O

915

900

3000

0.397

0.305

0.280

Ba

Cu

Ge

O

-2

4

0

-2.59

251

175

1000

50

Table 7-1: Shell-model potential parameters (A,ρ), shell charges (Y), and on-

site core-shell force constants (k).


Phonon (j) Ωj (th) Ωj (7 K) Ωj (300 K) Sj [th] Sj [7 K] Sj [300 K] Γj [7 k] Γj [300 k]

1 59 13400

2 75 84 82 6700 27000 12500 2 5

3 108 103 102 1700 8000 2300 2 3

4 129 11800

5 142 152 146 3500 14500 9500 7.5 15

6 179 187 182 2600 30000 26500 4 18

7 224 217 212 8750 26000 19000 4 11

8 258 257 258 970 33000 32000 21 25

9 261 274 270 11100 40000 22600 6 15

10 319 310 305 126000 89000 39000 11 20

11 334 315 313 46000 111000 120000 4 15

12 374 367 371 1700 26000 17000 8 30

13 443 30

14 489 450

15 766 710 707 21500 213000 153000 7 17

16 776 714 724 64000 64000 42000 10 23

17 786 772 772 2500 5300 3000 8 8

18 836 844 838 16500 24000 12000 7 10

Table 7-2: The ab plane calculated phonon frequencies Ωj[th] and oscillator

strengths Sj[th] are compared with the frequencies Ωj, oscillator strengths Sj,

and widths Γj, obtained by fitting to Eq. (2) the experimental σ1 (ω) at 7 and

300 K. Ωj and Γj are given in cm−1

, Sj is given in cm−2

.


Phonon (j) Ωj (th) Ωj (7 K) Ωj (300 K) Sj [th] Sj [7 K] Sj [300 K] Γj [7 k] Γj [300 k]

1 137 109 100 19400 17000 24000 7 22

2 157 130 131 5600 6500 7500 5 10

3 198 147 146 43000 121000 66000 3 16

4 267 278 269 1600 1900 3300 4 19

5 318 321 320 100 700 300 10 12

6 412 390 391 21600 58000 30000 15 19

448 446 36000 43000 11 27

7 488 488 485 56400 74000 47000 9 18

8 559 8500

9 781 775 771 32000 174000 91000 7 9

10 794 791 786 41800 84000 81000 17 21

Table 2: The c axis calculated phonon frequencies Ωj[th] and oscillator

strengths Sj[th] are compared with the frequencies Ωj, oscillator strengths Sj,

and widths Γj, obtained by fitting to Eq. (2) the experimental σ1 (ω) at 7 and

300 K. Ωj and Γj are given in cm−1


.


7.1.6 Comparison between theory and experiment

In Tables 7-2 and 7-3, the theoretical frequencies and oscillator strengths of

the phonon modes are compared with the corresponding values obtained by

fitting to the experimental optical conductivity the Lorentzian expression

(7.2)

In Eq. (7-2), σ1 (ω) is measured in Ω-1

cm−1

, while Ωj and Γj are the central

frequency in cm−1

, and the linewidth of the jth transverse optical mode

respectively,Sj is the oscillator strength in cm−2

. The atomic displacements for

selected phonons of the ab plane are shown in Fig.7-5. They are labelled by

their number in Table 7-2 and by the theoretical frequency in cm−1

(also, see

Supplemental Material [25]). Surprisingly, we find that in many modes, the

CuO tetrahedra and the GeO tetrahedra have a similar pattern, and this is the

case of the four modes shown in Fig.7-5. This behavior is probably due to the

similarity of the Ge and the Cu mass which makes the tetrahedral “molecules”

vibrate at similar frequencies and appreciably mix their modes in the solid.

Therefore, we shall discuss the pattern by referring to the tetrahedra without

specifying the central atom.

In the 129 cm−1

mode [Fig.7-5(a)], the atom at the center of the tetrahedra and

three vertex oxygens move approximately in the same direction, while a fourth

vertex oxygen moves in a quasiperpendicular direction. Thus the angle of only

one Cu-O (or Ge-O) bond is significantly perturbed. In the 224 cm−1

mode

[Fig.7-5(b)], two oxygens move approximately parallel to the central atom and

two others move in a quasiopposite direction, causing a larger distortion of the

tetrahedra even if, again, mainly in the internal angles. In the 319 cm−1

Mode

[Fig. 7-5(c)], the pattern is again similar for the Cu and Ge tetrahedra but they

move out of phase. The central Cu moves toward a vertex O when the central

Ge moves away from a vertex O. As the other atoms move perpendicular to

the bonds, they mainly change their angles, causing the mode to be a mixture

of bending and stretching. This explains its relatively large energy.


The 776 cm−1

mode [Fig.7-5(d)] has a stronger stretching character, as shown

by its high energy, although one never finds in BCGO either purely stretching

or purely bending modes, as is the case in higher-symmetry solids. This also

explains why here, at variance with many oxides where the highest vibrational

frequency corresponds to a pure oxygen stretching mode, the highest-energy

lines do not shift appreciably when decreasing the temperature.

Figure 7-5: (Color online) Atomic displacements for selected modes of

Ba2CuGe2O7 along the ab plane. Each mode is identified by its number in

Table 7-2 and by its calculated frequency, in cm−1

.


Finally, Fig.7-6 shows selected phonon modes polarized along the c axis. They

are labelled by their number in Table 7-3 and theoretical frequency in cm−1

.

The mode [Fig.7-6 (a)] at 137 cm−1

shows a rigid motion of the Cu tetrahedra

with the Ba in antiphase. The Ge ions practically do not move and act as

“nodes” of the vibration. In most other modes, instead, the two kinds of

tetrahedra show very similar displacements, as discussed above for the ab

plane. In the mode [Fig.7-6 (b)] at 198 cm−1

, the Cu and Ge tetrahedral

“molecules” move in antiphase and the Ba ions have smaller displacements.

The mode [Fig.7-6 (c)] at 488 cm−1

is a mixture of stretching and bending,

similar to the mode of Fig.7-5 (c). Finally, in the mode [Fig.7-6 (d)] at 794

cm−1

, the stretching character of the bonds bridging the O’s to the center of the

tetrahedra prevails.

Figure 7-6: (Color online) Atomic displacements for selected modes of

Ba2CuGe2O7 along the c axis. Each mode is identified by its number in Table

7-3 and by its calculated frequency, in cm−1

.


As one can see in Tables 7-2 and 7-3, as well as inFigs.7-3 and 7-4, there is a

good agreement—within the experimental linewidths—between the

observations and the theoretical predictions, as far as the phonon frequencies

are concerned. The main discrepancies concern phonons 15 and 16 of the ab

plane and modes 1–3 of the c axis, where the calculated frequencies are much

higher than the observed ones. This may be ascribed either to anharmonic

effects which particularly affect those modes, not taken into account in the

model, or to an overestimation of the shell-shell repulsive interactions. The

latter problem may be specifically present in the Cu-O and/or Ge-O bonds in

the case of the ab-polarized phonons 15 and 16, and in the Ba-O bond in the

case of the c-polarized modes 1–3. Moreover, four modes of the ab plane were

not observed: mode 1 is out of the measuring range, 13 and 14 are too weak,

while modes 4 and 5 are probably unresolved, as one can see by comparing

their total intensity with the intensity of the observed line. In the spectrum of

the c axis, the bump at 448 cm−1

, not predicted by the theory, might be a

shoulder of the closest mode 7, while mode 8 was not resolved. Concerning

the oscillator strengths, most calculated values reported in the same tables and

figures match the order of magnitude of those measured in the real system, but

are systematically lower. This may be mainly due to the so-called charged-

phonon effect [25], by which phonons acquire an anomalously large spectral

weight due to interatomic movement of charge associated with their

displacement pattern. Such effect is not included in the shell model, which

only takes into account on-site distortions of the atomic cloud. This results in a

transfer of spectral weight to the far-infrared region from the electronic bands

in the near-infrared and the visible region. Similar “dressed phonons” were

observed in several perovskites with high polarizability [26,27] through a

strong increase of the phonon intensities at low temperature, especially for the

lowest frequency modes, and through the failure of the f-sum rule,

(7.3)

when, as in Eq. (7-3), it is restricted to the far-infrared (FIR) region. Indeed, in

Ba2CuGe2O7, both the O and Cu ions are largely polarizable as shown by the


large shell charges and the small core-shell force constants (see Table 7-1)

required by the model fitting of the observed spectra. We therefore compared

with each other the intensities provided by the fits at the lowest and highest

temperatures of the experiment. As shown in Tables 7-2 and 7-3, most

phonons are more intense at low temperature, so that is larger than

by about 40% for the ab plane and 45% for the c axis. This

effect, which “dresses” the phonons, is not taken into account in the shell

model employed here, and may explain most of the discrepancies between

theory and experiment which emerge in Tables 7-2 and 7-3. The f-sum-rule

violation also has the interesting implication that the dielectric constant of

Ba2CuGe2O7, which is related to [26], is higher than the theoretical

values in Table 7-4 and should also increase when cooling the system below

room temperature. As is shown in Fig.7-7, the phonon strengthening for

decreasing temperature saturates around 200 K for the ab plane and around

100 K for the c axis: in both cases, at T >>TN. Moreover, it occurs gradually

and without any discontinuity, which may suggest a transition of any sort.

10.34 4.67 1.96 1.77

Table 7-4: Calculated values of the dielectric constant ϵ0 and of the high-

frequency dielectric function ϵ∞ in the ab plane and along the c axis.


Figure 7-7: (Color online) the total oscillator strength of the phonons

polarized in the ab plane of Ba2CuGe2O7 (squares) and along its c axis

(circles) is plotted vs temperature. The lines are guides to the eye.


7.2 Far-infrared spectra of the multiferroic BiMnO3

BiMnO3 is among the best known multiferroic materials, namely those which

display at least two simultaneous properties among (anti)ferromagnetism,

ferroelectricity, and ferroelasticity. Such materials, which are rather rare, are

of great interest for applications which span from giant electric transformers to

small computer memory devices, tiny sensors, electric field controlled

ferromagnetic resonance devices, and variable transducers [28]. BiMnO3 is

perhaps the most fundamental multiferroic and has been referred to as the

“hydrogen atom” of multiferroics [29]. In BiMnO3 (BMO), as in BiFeO3, the

6s2 lone pair on the Bi ion leads to the displacement of that ion from the

centrosymmetric position at the A-site of a perovskite unit cell. The resultant

distortion leads to an FM interaction between the Mn ions at the B-site in

BMO [30,31]. In bulk form, BMO has been observed to be both FM and FE

[32]. Polycrystalline BMO can be grown under high pressure and within a

very narrow range of growth conditions. While thin films of BMO have been

grown by various groups, few such films have shown magnetic properties

similar to bulk BMO and high enough resistivities, that is, low leakage

currents to allow clear measurement of FE properties [33–35]. A possible

reason for the low resistivities of BMO thin films is the substrate induced

strain, which triggers the growth of a highly distorted perovskite structure.

Investigations of BiMnO3 allow for the study of the fundamentals of

multiferroism without the problems associated with simulating compounds

containing many atoms per formula unit.

7.2.1 Properties and crystal structure of BiMnO3

BiMnO3 has a highly distorted perovskite-type structure. Among ABO3-type

multiferroic oxides, BiMnO3 is the only one that displays true ferromagnetic

behaviors with a Curie temperature (TC) of ~100 K [36]. BiMnO3 is also

expected to be ferroelectric according to first-principle calculations [37,38].

Ferroelectricity requires that the crystal structure must be noncentrosymmetric

and the ferroelectric transition is directly related to the structural phase

transformation. There is no doubt in literature about the ferromagnetic order


in BiMnO3. The Curie temperature was determined between 99 and 102 K and

the saturated magnetization reaches 3.9μB at 5 K, which is close to the

expected value of 4.0 μB. Magnetization is oriented along the monoclinic b-

axis. Ferroelectricity in BiMnO3is still controversial. More than 10 years ago

it was presented as a multiferroic system, i.e., a ferroelectric and

ferromagnetic material at low temperature, basing on electrical polarization

hysteresis loops measured on bulk polycrystalline samples [39]. In addition, in

the first crystallographic studies of BMO, the structure was refined in a

noncentrosymmetric space group, C2, which allows ferroelectricity [40].

Nevertheless, the reported nonsaturation of the polarization loops and the fact

that this measurement was not reproduced in bulk samples rise doubts on its

ferroelectric nature. Several more recent studies based on electron and neutron

diffraction [41,42] on polycrystalline samples have questioned the C2 initial

choice and have pointed towards a centrosymmetric space group,C2/c, which

excludes ferroelectricity.

Based on the electron diffraction information, the crystal structure of

BiMnO3 was refined from powder neutron diffraction data to be a C2

monoclinic structure with a = 9.53 Å, b = 5.61 Å, c = 9.85 Å, and β = 110.67°

[Atou, 1999]. This structure is now commonly accepted and used as a

fundamental model for the interpretation of the observed physical phenomena.

The crystallographic unit cell, containing two formula units, is shown in Fig 7-

8. To have more insight into the physics of this material, it is often helpful to

view it as having a perovskite structure. Indeed, the triclinic distortion from

the ideal perovskite structure is rather small. The cell parameters of this

pseudo-perovskite phase are a = 3.950 Å, b = 3.995 Å, c = 3.919 Å, α = 90.7º,

β= 90.9º and γ= 91.0º [Faqir, 1999]. The pseudo-perovskite unit cell,

containing one formula unit, is shown in Figure 7.8(b). Upon cooling from

high temperatures, BiMnO3 undergoes several phase transitions. Above 500

ºC, BiMnO3 has an orthorhombic Pbnm structure. Around 500 ºC there is a

phase transition from the high-temperature orthorhombic Pbnm phase to the

low-temperature monoclinic C2 phase. The C2 phase allows ferroelectricity to

occur (it is non-centrosymmetric), but it is unsure whether the ferroelectric


ordering also occurs at this temperature. There is another phase transition at

180 ºC and there are indications that this (second-order) transition is the

paraelectric-to-ferroelectric transition. At this transition the crystallographic

phase does not change, but the lattice parameters change abruptly, possibly

indicating ordering of the bismuth ions.

Figure 7-8: Unit cell of BiMnO3, (a) monoclinic [Atou, 1999] and (b)pseudo-

perovskite.

The magnetism of BiMnO3 is in sharp contrast with that of LaMnO3.A simple

consideration of the nominal ionic valence gives that, in both materials, the

Mn 3d state is formally given by the

configuration(Mn3+

3d4) and thus is

Jahn–Teller (JT) active. Furthermore, the ionic radii of Bi and La are very

close to each other. Despite these resemblances, their magnetic structures are

completely different. It is well established for LaMnO3 that the orbital

ordering among the eg states takes place and stabilizes the A-type

antiferromagnetic spin arrangement. By contrast, a different type of orbital

order may occur in BiMnO3, which makes ferromagnetic spin order favorable,

and which might have correlation with the off-centred displacement that is not

seen in LaMnO3.


7.2.2 Infrared reflectivity spectra of BiMnO3

The optical properties of the bulk BiMnO3 have been studied here by

measuring its reflectivity R (ω). Even if the phonon region is limited to 850

cm −1

, R (ω) was measured by a rapid-scanning interferometer up to 10000

cm−1

in order to perform on it accurate Kramers-Kronig (KK) transformations,

in the whole infrared range the spectra were collected between 10 and 300 K

by a Michelson interferometer at a resolution of 2 cm−1

and using an Au mirror

as reference. The raw reflectivity data of bulk BiMnO3 are shown in Fig. 7-9

in the frequency range of the infrared range. A gradual decrease of the band

intensity with increasing temperature is seen [Figs. 7-9]. This is caused by

an increase of the phonon damping with temperature. At high temperatures

some phonons become overlapped and, therefore, they disappear from the

spectra. According to Fig.7-9 both spectra look very similar to those reported

for BiMnO3 in the same frequency range in Ref. [43]. They are typical of an

insulating crystal, with a number of phonon lines in the far infrared, and a flat

and very low reflectivity (2-3 %) at higher frequencies. This behavior

continues in the whole midinfrared range.

Figure 7-9: IR reflectivity spectra of bulk BiMnO3 taken at different

temperatures.


7.2.3 Optical conductivity of the infrared phonons

The analysis of the data in Fig. 7-9 has been performed by using the Kramers-

Kronig (KK) transformations (i.e, section (1-4) of chapter 1).Fig. 7-10 displays

the real part of the optical conductivity at different temperatures. The

temperature dependence of the phonon lines give us hints about the structural

properties of BiMnO3 and allow us to understand if the structure is modified

by the different magnetic and charge orders.

7.2.4 Factor group analysis

A factor group analysis predicts for the non-centrosymmetric C2 space group

of BiMnO3 below 475 K with 8 formula units per unit cell as found in ref. [43]

gives the following:

(7.4)

of which 57 phonons are both IR and Raman active (additional 1A and 2B

modes are acoustic). In the centrosymmetric space group C2/c, which excludes

ferroelectricity, the factor group analysis according to [43] gives instead

(7.5)

of which the 14 Ag and 16Bg modes are only Raman active; while 13Au and

14Bu modes are only IR active (additional 1Au and 2Bu modes are acoustic

phonons).



Figure 7-10: Temperature dependence of the optical conductivity spectra of

bulk BiMnO3, in the far infrared range of frequencies.

7.2.3 Drude-Lorentz analusis of the Infrared phonons

A simple sum of Lorentz oscillators given by Eq. (7.2) for the real part of the

optical conductivity σ1 (ω) measured in Ω-1

cm−1

fits the IR conductivity

spectra. Ωj and Γj are the central frequency in cm−1

, and the linewidth of the jth

transverse optical mode respectively, Sj is the oscillator strength in cm−2

. Fig

(7-11) displays the fitting of the optical conductivityof BiMnO3, in the far

infrared range at 10 K and 300 K. Table 7-4 lists the phonon parameters

resulting from a Lorentz fit to the measured σ1 (ω) at 10K and 300K. We used

23 oscillators to fit the curve at 10 K. At higher temperature 300 K some

oscillators are strongly damped, so that we used only 18 oscillators to fit the

300 K data [see table 7-4].

Attempts to fit the results by a lower number of Lorentz oscillators did not

provide acceptable results. The observed modes are most of those predicted by

group theory analysis in C2/c space group. Then our experimental results

support the centrosymetric C2/c space group structure of BiMnO3.


Figure 7-11: the optical conductivity (solid lines) of BiMnO3, in the far

infrared range with the fitting curves (dotted lines) which provide the

parameters listed in table 7-4. at (a) 10 K and (b) 300 K.


10 k 300 k

No. Ωj (cm-1

) Sj (cm-2

) Γj (cm-1

) Ωj (cm-1

) Sj (cm-2

) Γj (cm-1

)

1 53 5000 2.7 53 53000 45

2 67 53000 8 61 6000 6

3 75 15000 7 72 11000 8

4 100 141000 24 91 17000 14

5 117 46000 18 117 41000 22

6 142 54000 22 138 42000 30

7 159 25000 16 156 18000 20

8 196 57000 22 192 16000 18

9 219 49000 17 215 28000 22

10 237 12000 10

11 260 79000 29

12 284 178000 30 281 192000 69

13 307 110000 22

14 320 94000 18 322 180000 37

15 345 217000 29

16 367 111000 31 365 252000 51

17 407 9000 13

18 427 43000 29 420 55000 48

19 462 53000 24 468 98000 44

20 488 188000 39 497 100000 49

21 544 83000 30 546 101000 39

22 565 76000 28 567 117000 42

23 627 17000 24 630 13000 28

Table 7-4: The calculated phonon frequencies Ωj , oscillator strengths Sj and

widths Γj, obtained by fitting to Eq. (2) the experimental σ1 (ω) at 7 and 300 K.

Ωj and Γj are given in cm−1


.


7.3 Conclusion

In the present chapter, we have described the lattice dynamics of both

Ba2CuGe2O7 and BiMnO3 by infrared reflectivity measurements. In

Ba2CuGe2O7 we investigated the infrared spectra with polarized radiation,

down to temperatures close to those where a helimagnetic phase takes place

via the Dzyaloshinsky-Moriya mechanism. The number of the observed

phonon lines is lower than that predicted for the P421m cell of Ba2CuGe2O7,

and no line splitting has been observed when cooling the sample to 7 K.

Therefore, our spectra confirm that the tetragonal symmetry is conserved

down to the lowest temperatures above TN, with no appreciable distortion. The

optical conductivity extracted from R (ω) has been fit by a sum of Lorentzians,

and their parameters have been compared with the results of shell-model

calculations. These have correctly predicted the observed frequencies, within

the experimental linewidths, except for a few modes where the theoretical

values are systematically higher. The discrepancy may be due either to

anharmonic effects, not taken into account in the model, or to an

overestimation of the shell-shell repulsive interactions. A systematic

underestimation with respect to the observed values is instead exhibited by the

calculated oscillator strengths. We have tentatively explained this effect by

considering that “charged-phonon” effects—not considered in the model—can

increase the dipole moment of those vibrations due to the distortion of the

electron clouds going beyond one atom. Such interpretation is consistent both

with the strong increase observed in the phonon intensities for decreasing

temperature and with the failure of the optical sum rule when it is restricted to

the phonon region.

Finally, we have preliminarily investigated the temperature dependence of the

phonon parameters in a BiMnO3 crystal, down to 10 K. (i.e., below the

ferromagnetic transition at TC = 100 K.), the Optical conductivity analysis of

the infrared phonons support the centrosymetric C2/c space group structure

of BiMnO3.

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Conclusion 167

Conclusion

In this thesis, optical spectroscopy has been used to get an insight in the

physical properties of various strongly correlated systems through the

determination of the optical conductivity, σ (ω), of the material under study.

Generally speaking, σ (ω) provides useful information on the intra-band, inter-

band transitions, phonons, and localized electronic states. Especially important

are the transitions driven by the electron – electron interactions (correlation

effects) and by the electron – phonon interactions.

This is for example the case of LaMnO3 with strong La non-

stoichiometry, where we have studied the slow metallization process that

LaxMnO3 undergoes for decreasing temperatures, in films with x <1. We have

found that, as in other oxides, the insulator-to-metal transition is driven by a

continuous transfer of spectral weight from a "hard" band MIR-2 peaked

between 3000 and 5000 cm-1

at room temperature, to a softer band (MIR-1)

observed around 1000 cm-1

which acts as a "reservoir" for the Drude term of

the free carriers. These observations are fully consistent with a phase

separation model where MIR-2 is attributed to localized charges strongly

interacting with the lattice (small polarons), and MIR-1 to itinerant large

polarons in zones richer of electrons.

The far-infrared range has been explored especially in Ba2CuGe2O7 and

BiMnO3 to study the phonon spectrum of these multiferroics. In the

helimagnet Ba2CuGe2O7 we have investigated the infrared spectra with

polarized radiation, down to temperatures close to those where a helimagnetic

phase takes place via the Dzyaloshinsky-Moriya mechanism. The number of

the observed phonon lines is lower than that predicted for the P421m cell of

Ba2CuGe2O7, and no line splitting has been observed when cooling the sample

to 7 K. Therefore, our spectra confirm that the tetragonal symmetry is

conserved down to the lowest temperatures above TN, with no appreciable

distortion. The optical conductivity extracted from R(ω) has been fit by a sum

168 Conclusion

of Lorentzians, and their parameters have been compared with the results of

shell-model calculations. These have correctly predicted the observed

frequencies, within the experimental linewidths, except for a few modes where

the theoretical values are systematically higher. The discrepancy may be due

either to anharmonic effects, not taken into account in the model, or to an

overestimation of the shell-shell repulsive interactions. Finally, we have

preliminarily investigated the temperature dependence of the phonon

parameters in a BiMnO3 crystal, down to 10 K. (i.e., below the ferromagnetic

transition at TC = 100 K.), the Optical conductivity analysis of the infrared

phonons support the centrosymetric C2/c space group structure of BiMnO3.

Concerning the electronic properties of manganites, we have presented

an optical study of the electronic bands of La0.5Ga0.5MnO3, in comparison with

those of pure LMO, aimed at solving a long-standing problem on the

assignment of the bands around 2 eV. Two out of the four observed bands

(those peaked at 16 000 and 33 000 cm−1

) exhibit a pronounced temperature

dependence that is sensitive to the ferromagnetic transition and therefore are

confirmed to be due to Mn–Mn intersite transitions of high-spin and low-spin

type, respectively. The weaker bands peaked at 13 000 and 22 000 cm−1

are

instead temperature independent. When observed previously in LMO films,

this behavior led us to assign them to Mn and

on-site

transitions. However, such assignment seems at variance with the observation

of both bands in the present spectra of LMGO, where the eg Jahn–Teller

splitting should be strongly reduced by Ga. Therefore we have explained them

in terms of p–d Mn–O charge-transfer. We are thus led to a “mixed”

interpretation of the electronic spectra in the La manganites, where the d–d

Mn–Mn transitions dominate the visible–UV region but p–d charge-transfer

Mn–O transitions are also present. This result suggests that both a Mott–

Hubbard and a charge-transfer picture may coexist in such intriguing systems.

List of publications 169

List of publications

1- W. S. Mohamed, P. Maselli, P. Calvani, L. Baldassarre, P. Orgiani, A.

Galdi, L. Maritato, and A. Nucara “Optical study of the insulator-to-

metal transition in LaxMnO3 thin films" , Mater. Res. Express 1

036406 (2014).

2- A. Nucara, W. S. Mohamed, L. Baldassarre, S. Koval, J. Lorenzana, R.

Fittipaldi, G. Balakrishnan,A. Vecchione and P. Calvani ,“Infrared

phonon spectrum of the tetragonal helimagnet Ba2CuGe2O7”

,Phy.Rev. B 90, 014304 (2014).

3- A. Nucara , F. Miletto Granozio, W.S. Mohamed , A. Vecchione, R.

Fittipaldi ,P.P. Perna , M. Radovic , F.M. Vitucci , P. Calvani, “Optical

spectra of LaMn0.5Ga0.5O3: A contribution to the assignment of the

electronic transitions in manganites” Physica B 433 102–106 (2014).

optical study of novel perovskitic oxides, with focus on ...€¦ · wael saad mohamed ahmed,...

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