Phononic and magnetic excitations in the quasi-one-dimensional Heisenberg antiferromagnet KCuF3

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  • Phononic and magnetic excitations in the quasi-one-dimensional Heisenbergantiferromagnet KCuF3V. Gnezdilov, J. Deisenhofer, P. Lemmens, D. Wulferding, O. Afanasiev, P. Ghigna, A. Loidl, and A. Yeremenko Citation: Low Temperature Physics 38, 419 (2012); doi: 10.1063/1.4709772 View online: http://dx.doi.org/10.1063/1.4709772 View Table of Contents: http://scitation.aip.org/content/aip/journal/ltp/38/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Magnetic interactions in a quasi-one-dimensional antiferromagnet Cu(H2O)2(en)SO4 J. Appl. Phys. 115, 17B305 (2014); 10.1063/1.4865323 Magnetism of A 2 Cu 2 Mo 3 O 12 ( A = Rb or Cs): Model compounds of a one-dimensional spin- 1 2 Heisenbergsystem with ferromagnetic first-nearest-neighbor and antiferromagnetic second-nearest-neighbor interactions J. Appl. Phys. 97, 10B303 (2005); 10.1063/1.1851675 Light scattering on phonons in quasi-one-dimensional antiferromagnet CsFeCl 3 2 H 2 O induced by magneticordering Low Temp. Phys. 28, 516 (2002); 10.1063/1.1496660 Magnetization measurement on the S=1 quasi-one-dimensional Heisenberg antiferromagnet Ni(C 5 H 14 N 2 ) 2 N 3(PF 6 ) J. Appl. Phys. 89, 7338 (2001); 10.1063/1.1361264 NiCl 2 H 2 O : A quasi-one-dimensional Heisenberg antiferromagnet J. Appl. Phys. 87, 6052 (2000); 10.1063/1.372609

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  • Phononic and magnetic excitations in the quasi-one-dimensional Heisenbergantiferromagnet KCuF3

    V. Gnezdilova)

    B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences ofUkraine, 47 Lenin Ave., Kharkov 61103, Ukraine and Institute for Condensed Matter Physics, BraunschweigUniversity of Technology, D-38106 Braunschweig, Germany

    J. Deisenhofer

    Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, D-86135Augsburg, Germany

    P. Lemmens and D. Wulferding

    Institute for Condensed Matter Physics, Braunschweig University of Technology, D-38106 Braunschweig,Germany

    O. Afanasiev

    B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciencesof Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine

    P. Ghigna and A. Loidl

    Dipartimento di Chimica Fisica, Universita di Pavia, 1-27100 Pavia, Italy

    A. Yeremenko

    B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciencesof Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine(Submitted December 15, 2011)

    Fiz. Nizk. Temp. 38, 538548 (May 2012)

    The Raman-active phonons and magnetic excitations in the orbitally ordered, quasi one-dimensional

    Heisenberg antiferromagnet KCuF3 are studied as a function of temperature in the range between 3

    and 290 K in different scattering configurations. The low-energy Eg and B1g phonon modes showan anomalous softening (25% and 13%, respectively) between room temperature and thecharacteristic temperature TS 50 K. In this temperature range, a freezing-in of F ion dynamicdisplacements is proposed to occur. In addition, the Eg mode at about 260 cm

    1 clearly splits below

    TS. The width of the phonon lines above TS follows an activated behavior with an activation energyof about 50 K. Our observations clearly evidence reduction of the lattice symmetry below TS andindicate strong coupling of lattice, spin, and orbital fluctuations for T > TS. A strongly polarizationdependent quasielastic scattering is observed at temperatures above TN 39 K due to magnetic-energy fluctuations. For temperatures below TN a rich spectrum of additional modes is observed,with different lineshape, polarization and temperature dependence. We attribute them to longitudinal

    and transverse magnetic modes as well as to a continuum of magnetic excitations. VC 2012 AmericanInstitute of Physics. [http://dx.doi.org/10.1063/1.4709772]

    1. Introduction

    KCuF3 has long been known as a paradigm for an orbi-

    tally ordered system where cooperative JahnTeller (JT)

    distortion is strongly competing with the electronic degrees

    of freedom as the driving force behind the orbital order.14

    Recently, realistic band structure calculations highlighted

    KCuF3 as a benchmark system for modeling structural relax-

    ation effects due to electronic correlations5,6 and for reveal-

    ing the effect of electronic superexchange on the orbital

    ordering (OO).7 The compound seems to be orbitally ordered

    throughout its solid phase, but shows long-range A-type anti-

    ferromagnetic (AFM) ordering only below TN 39 K. In lit-erature, an orbital ordering temperature of about 800 K is

    often evoked in this system, but astonishingly, experimental

    evidence for a transition at this temperature seems to be

    evasive. Earlier it was reported that between 670 and 720 K

    an irreversible transition takes place.8 The paramagnetic

    (PM) susceptibility is described by a BonnerFisher law with

    an exchange constant J 190 K (Ref. 1) indicating that thiscompound is a good realization of a one-dimensional (1D)

    spin chain in the PM regime. Inelastic neutron scattering

    (NS) studies reveal a spinon-excitation continuum, a clearly

    1D quantum phenomenon existing also below the Neel tem-

    perature.9,10 From a structural point of view, the relatively

    high tetragonal symmetry (D184h I4=mcm) (Refs. 1116)makes KCuF3 one of the simplest systems to study. There

    exists a second structural polytype (D54h) with a differentarrangement of F distortions within the c plane.14 This phase

    1063-777X/2012/38(5)/9/$32.00 VC 2012 American Institute of Physics419

    LOW TEMPERATURE PHYSICS VOLUME 38, NUMBER 5 MAY 2012

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    http://dx.doi.org/10.1063/1.4709772

  • that may exist up to a few % in every sample has different

    physical properties regarding magnetic anisotropies and

    ordering temperature (TN 22 K). Nevertheless, the estab-lished symmetry assignment of the D184h phase has beenquestioned by the X-ray diffraction investigation17 which

    suggests an existence of orthorhombic distortions in KCuF3at room temperature with D42 symmetry. A low-temperatureRaman scattering (RS) study18 reveals a difference of spectra

    measured in xz and yz polarization as well as anomalouslybroad linewidths of the stretching modes, which are inter-

    preted as evidence of symmetry lower than D184h also belowthe Neel temperature. Although the orthorhombic distortions

    are involved in explaining the electron spin resonance (ESR)

    properties of KCuF3,19 discrepancies remain in the analysis

    of recent NQR,20 AFM resonance,21 and further experimen-

    tal and theoretical findings.22,23 Besides, in x-ray resonant

    scattering experiments on KCuF3 (Refs. 24 and 25) indica-

    tions for a coupling of lattice and magnetic degrees of free-

    dom are found. Only recently, the ESR properties for T > TNcould be successfully explained within the tetragonal sym-

    metry by assuming a dynamical DzyaloshinskyMoriya

    (DM) interaction related to strong oscillations of the bridg-

    ing F ions perpendicular to the crystallographic c axis.26 Itis argued that these dynamic distortions freeze in at a tem-

    perature TS 50 K, leading to an effectively lower symmetryand the occurrence of excitonmagnon sidebands in optical

    absorption experiments.27

    Here, we report on a detailed study of:

    (i) the temperature dependence of the Raman-active

    phonons in a KCuF3 single crystal tracking the symmetry

    reduction during the anticipated freezing of the dynamic dis-

    tortion at TS 50 K and the Neel ordering at TN 39 K;(ii) a complete data set of the magnetic excitations in

    this compound collected for the first time using Raman

    scattering.

    We find large softening of the lowest lying Eg mode andthe B1g mode by 25% and 13% between room temperatureand TS, respectively. The linewidth and the integrated inten-sity of these modes also exhibit anomalies at TS and TN.Moreover, the Eg mode at about 260 cm

    1 clearly splits

    below TS evidencing the existence of an antiferrodistortivelattice instability in KCuF3 which leads to a symmetry

    reduction at TS 50 K prior to magnetic ordering.At low temperatures (below TN), magnetic excitations

    characteristic of 3D and 1D magnetic correlations are

    observed simultaneously in our Raman experiment. The

    energy ranges of these phases are separated by another

    region where the crossover from 1D to 3D behavior occurs.

    2. Experimental details

    The single crystal was oriented by Laue diffraction, cut

    along the (110) pseudocubic plane and mechanically pol-

    ished to optical quality. Details on crystal growth are

    described in Ref. 25. The sample has previously been inves-

    tigated by ESR and optical spectroscopy.26,27 The Raman

    spectra were obtained with two different experimental setups

    and in two geometries of experiment: (i) a DILOR XY triple

    spectrometer with a liquid nitrogen cooled CCD detector

    (quasi-backscattering geometry) and (ii) a U1000 high-

    resolution double spectrometer with RCA 31034 A photo-

    multiplier (right-angle scattering geometry). The 647 nm

    Ar/Kr ion (5 mW output power), the 532.1 nm solid-state

    (5 mW output power), and the 632.8 nm HeNe (25 mW

    output power) lasers were used for excitation in these two

    setups. Temperature dependencies were obtained in optical

    gas-flow cryostats and a closed-cycle cryostat by varying

    temperature from 3 K to room temperature.

    3. Experimental results and discussion

    3.1. Raman phonons

    The polarized phonon Raman spectra of single crystal-

    line KCuF3 were obtained in yy, zz, xy, xz, and yz scatteringconfigurations. The number of lines and the selection rules

    are fully consistent with the theoretically expected Raman-

    active normal modes18 of KCuF3 with tetragonal D184h,

    CRam A1gyy; zz B1gyy 2B2gxy 3Egxz; yz:(1)

    The three lines observed in Raman spectra at 290 K in both

    the xz and yz spectra correspond to the three Eg modes. Theline observed with different intensities in yy and zz spectra isidentified as the A1g mode. The intense line observed only inyy spectrum can be assigned to the B1g mode. Finally, thetwo lines in xy spectra are the two B2g modes. At room tem-perature all lines have a Lorentzian lineshape. The observed

    spectra and the mode assignments are in agreement with the

    previously reported data at 10 K.18 A direct comparison of

    our data at 4 K and 290 K with Ref. 18 and theoretical esti-

    mates28 is presented in Table I. In general, there is a good

    agreement between the corresponding values except for the

    B2g(l) mode with a frequency of 240.4 cm1 observed in our

    experiments in contrast to a somewhat higher frequency of

    265.8 cm1 reported in Ref. 18. The second discrepancy is

    that the lines assigned to the Eg(l,2) and B1g are almost twotimes broader in the low-temperature Raman spectra of Ref.

    18. We can relate these discrepancies to different quality of

    the studied samples.

    In the following we will focus on the temperature de-

    pendence of the phonon modes in KCuF3 and mostly Eg(1),Eg(2) and B1g. In Figs. 13 we show the temperature depend-ent parameters (frequency, linewidth, and integrated inten-

    sity, respectively) for the five phonon modes. The phonon

    TABLE I. Frequencies and linewidths of the observed Raman modes in

    cm1 in KCuF3 at 4 and 290 K compared to the experimental values

    reported in Ref. 18 at 10 K and calculations from Ref. 28.

    Frequency, cm1 Linewidth, cm1

    Mode 290 K 4 K

    10 K

    (Ref. 18)

    Calculated

    (Ref. 28) 290 K 4 K

    10 K

    (Ref. 18)

    A1g 367.3 373.5 374.8 398 23.1 4.9 9.2

    B1g 81.6 70.9 72.8 100 7.1 0.9 1.6

    B2g(1) 240.4 245.2 265.8 259 30.8 8.7 7.0

    B2g(2) 554.8 561.3 563.0 586 22.6 9.1 9.1

    Eg(1) 63.0 47.4 53.2 50 5.8 0.7 3.0

    Eg(2) 262.9 260.8 261.6 136 7.5 1.7 3.0

    Eg(3) 132.3 129.3 131.2 268 7.5 1.6 1.6

    420 Low Temp. Phys. 38 (5), May 2012 Gnezdilov et al.

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  • lines of A1g and B2g symmetry have a larger linewidthcompared to the other modes. Aside from their broadened

    lineshape, the frequency of these modes does not show

    anomalous temperature behavior. In the full temperature

    range they exhibit a hardening of 1%2%. The temperature

    dependence of the A1g phonon mode eigenfrequency (seeFig. 1) fits very well to the equation

    xiT x0i 1 ci

    exphcxav=kBT 1

    ; (2)

    including anharmonic effects.29 Here, x0i indicates theeigenfrequency of the phonon in the absence of spin-phonon

    coupling at 0 K, ci is a mode dependent scaling factor, andxav is the arithmetic average of the IR- and Raman phononfrequencies at room temperature.

    The A1g phonon mode linewidth is shown in Fig. 2together with the expected T dependence according to acubic anharmonicity in second order, i.e., Refs. 30 and 31

    CT C0 1 2

    exphcx0=2kBT 1

    ; (3)

    with C0 4.88 cm1 and x0 373.5 cm1. A large A1g pho-non peak broadening is observed for temperatures above

    50 K. This anomalous broadening of the hard A1g phononmode can be understood assuming structural fluctuations at

    T > 50 K. Such structural...

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