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Chapter 10

Experimental Methods

10.1Materials preparation

10.2 Magnetic fields

10.3 Atomic-scale magnetism

10.4 Domain-scale measurements

10.5 Bulk magnetization measurement

10.6 Excitations

10.7 Numerical methods

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10.1 Materials Preparation

10.1.1 Bulk material

Metals: Melt in an arc furnaces or a rf induction furnace.

Heat treat in a resistance furnace (controlled temperature or atmosphere.

Amorphous metals are produced by rapid solidification - melt spinning

Insulators: Mill components e.g. CoO + Fe2O3 ! CoFe2O4 . Grind and fire nx

Mix ions in solutions. Precipitate gel as a precusror.

Crystals:

seed

temperature

Bridgeman method

seed

Czochralski method

Arc melter Glovebox X-ray Diffractometer SQUID magnetometer

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10.1.2 Thin films

Physical vapour deposition

source

Substrate 400 - 1000 C

Evaporation: Thermal

e-beam e.g. 10 kV, 1A

Mean-free path " = 6/P "in mm, P in Pa.

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cap

film

substrate

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Pulsed-laser deposition (PLD)

ns pulses of UV light

! 1 J cm2 on the target, ! 10 Hz.

directed plume cos11#

Growth rate ! 1 nm s-1

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Molecular-beam epitaxy (MBE)

Carried out in UHV 10-7 - 10-9 Pa Needed to avoid conamination of a slowly-growing film by residual gas.

Time for a monolayer

$t = (12MkBT/M)1/2/Pa2

e..g Oxygen a ! 0.2 nm, P= 10-5 Pa, $t ! 6 0s

Growth rate < 0.2 nm s-1

• Franck-van der Merwe

• Volmer-Weber

• Strannsky-Krastanov

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10.1.3 Small particles

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Sputtering

Use Ar gas, Ar+ ions are acceleratedtowards the cathode (target). A glow-discharge is formed.

Target-substrate distance ! 100 mm

To enhance the ionization of Ar, a magnetic field is applied with a ‘magnetron’’

Growth rate ! 10 nm s-1

DC sputtering for metals. P ! 0.05 - 1 Pa

RF sputtering for insulators. 13.56 MHz P ! 0.02 Pa

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Base pressure < 3 x 10-8 Torr

2 Target Facing Target guns (MgO)

Base pressure < 3 x 10-7 Torr

6 Series-III S Guns (DC& RF)

!!Chamber AChamber A!! Chamber B Chamber B

MgO

6 targets

2x3-clusters2 tfts

Multiple-target sputtering tool

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Seed Layer

AFFM

Tunnel Barrier

Bottom Contacts

Top Contacts

Tunnel Barrier

AAFM

Middle Free layer

DMTJ stack

Ta5

Ru50

Ta5

NiFe5

IrMn10

CoFe2

Ru0.85

CoFeB5

MgO2.5

CoFeB3.5

MgO2.5

CoFeB5

Ru0.85

CoFe2

IrMn10

Ta 5

Cu10 50

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Chemical methods

Electrodeposition.

Good for thick films of alloys of metals which are not too electronegative. e.g. Ni78Fe22

1 microamp mm-2 deposits a monolayer in 5s.

1 milliamp mm-2 deposits 40 nm s-2.

Chemical vapour deposition (CVD). Use organometallic precursors, decompose byheated substrates or laser light.

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Superconducting magnet 10 T

Electromagnet 1 T

Helmholtz coils 0.01 T

10.2 Magnetic fields

10.2.1 Generation Steady fields

Bitter magnet 33 T

Polyhelix

Hybrid magnet 42 T record

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54 T 75 ms pulsed magnet, Nijmegen

100 T pulsed magnet laboratory, Dresden

50 MJ capacitor bank

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10.2.2 Field Measurement

a) Search coil b) Rotating coil

b) Hall generator d) 77Rb vapour magnetometer

E = -Nd%/dt

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10.2.3 Shielding

Static: Soft magnetic shields. Permalloy µ > 10,000

Superconducting shields, exclude flux penetration

High-frequency:

Faraday cage.

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10.3 Atomic-scale magnetism

10.3.1 Diffraction

Elastic scattering; 2d sin# = n" & = ghkl

Ineastic scattering; & = ghkl + q

K’ - K = &; '’ - ' = (

Differential scattering cross section

)diff = d2)(&,(,T)/d&d(

K = 2*/" ghkl = 2*/dhkl

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Intensities of Bragg reflection are proportional to the square of the structure factor

Fhkl = +I fi exp (i&.ri) = +I fi exp (hxi + kli + mzi)

The sum is over the i atoms in the unit cell at (xi, yi, zi)

X-ray tube

Synchrotron

Cu Kedge 8.98 keV

1016 photons s-1

5 GeV ,mc2 ! 104 mc2

"c = 0.00714/B,2m

1017 photons s-1 in 0.1%bandwidth

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SmCo5. Sintered magnet c || & Powder

Magnetic scattering of X-rays is 106 times weaker than X-ray scattering.The effect can reach 1% near an absorption edge.A good method for Sm, Gd. (huge neutron scattering cross section)

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Magnetic neutron scattering

P = 1.91reS fS or if both spin and orbital moments are present 1.91re(S fS + (1/2) L fL )

fL,S = [J(J+1) ± S(S+!) - L(L+1)]/[2(J+1)]

Unpolarized neutrons: |Fhkl|2 = |+I bi exp (i&.ri)|2 + |+I pi µi exp (i&.ri)|2

polarized neutrons |Fhkl|2 = |+I (bi + ".p) exp (i&.ri)|2

Magnetic interaction vector µ = m - &(&.m)/&2

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The triple-axis spectrometer allows scan so be made at constant E or constant q.

The dispersion relation for any excitation can be mapped out.

q

E

Antiferromagnetic magnon

2*/a

Inelastic neutron scattering

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The triple-axis spectrometer

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10.3.2 Spectroscopy

Absorption and photoemissio nprocesses for a single photon

X-ray photoemission spectroscopy (XPS)

X-ray absorption spectroscopy (XAS);

X-ray absorption fine structure (EXAFS). Measure structure near the X-ray absorpftion edge - element specificlocal structure

X-ray magnetic circular dichroism (XMCD). Measure difference of absorption for left and right circular polarisedlight. Deduce <S> and <L> for the element

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Mossbauer spectroscopy of FeFe

111(1+cos2#)3,4 (±1/2 !-/+1/2 )

4024 sin2#2,4 (±1/2 !±1/2 )

3333(1+cos2#)1,6 (±3/2 !±1/2 )

k -, k || ,powderlines

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Mossbauer spectra of BaFe12O19 There are five different sites. The ferrimagnetic sublattices areseparated by an applied field.

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10.3.3 Electronic structure

Spin-polarized densities of states for SmCo5

Dispersion relations for spin-polarized electrons E(k)are acomplete description of theelectronic structure of a solid.

UV Photoemission spectroscopygives some information on thedispersion rlations and the densityof states N(E)

Computation Is now the mainsource of informations, especiallydensity functional theory (DFT)calculations in the local spin densityapproximation (LSDA)

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10.4 Domain-scale measurements

10.4.1 Stray field methodsy

Stray-field methods for observing domain structure, a) Bitter method (magnetic colloid)b) Magnetic force microscopy and c) scanning electron microscopy

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10.4.1 Radiation methods

Faraday effect and Kerr effect

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00

5

10

15

20

25

30

35

0.6nm

MOKE spectra Pt(2nm)/Co(t)/Pt(2nm)

RA

S u

nits

photon energy

0.5nm

0.8nm

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

Hysteresis Loops Pt(2nm)/Co(t)/Pt(2nm)

RA

S u

nits

Current Electromagnet [A]

0.5nm3.6eV

0.6nm3.6eV

0.6nm(4eV)

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Faraday effect spectrum of BaFe12O19

Kerr image of a polisher surface of Nd2Fe14B

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Imaging schemes in transmission electron microscopy. Fresnel and Foucoult

Samples are Nd2Fe14B

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A TEM image of a thin foil of melt-spun Nd2Fe14B showing domain walls oinned at grain boundaries.

Left Fresnel image, right Foucallt image. Top is a lattice image showing the planes in the structure.

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10.5 Magnetization

10.5.1 Open circuit

Force methods; a) Faraday balance, b)Torque magnetometer c)Alternating gradient force magnetometer

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Flux methods: a) Extraction b) Vibrating sample magnetometer (VSM) c) Superconducting quantum interference device (SQUID)

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Measurement of anisotropy field, Ha = 2K1/Ms H is the internal field.

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10.5.2 Closed circuit

Schematic illustration of a hysteresigraph for measuring B (or M) as a function of the internal field H in acylindrical sample. On the right are the compensated coils needed to measure M and the potential coil usedto measure H.

The compensated coil has n1A1 = n2A2. The emf is then proportional to (N1 - N2) Amµ0M

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Use of a potential coil to measure potential difference between two points of a magnetic circuit

The long coil has cross section a and n turns m-1. .% = µ0na(/x - /y).

Measure .% with an integrating voltmeter. E = -Nd%/dt.

The potential coil

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10.6 Excitations

10.6.1 Thermal analysis The methods of thermal analysis involve heating a small sample ata uniform rate (e.g. 10 K min-1), and recording some parameter.

Differential thermal analysis; differential scanning calorimetry thermogravimetry thermopiezic analysis

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10.6.2 Spin waves

Inelastic neutron scattering.

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10.7 Numerical methods

A grid used to obtain numerical solutions of differential equations using the finite difference method in two dimensions

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A triangular mesh used fro two-dimensional finite element calculations