The Muppet’s Guide to:The Structure and Dynamics of Solids

Magnetic Reflectivity

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Electronic resonancesA core electron is excited and creates a spin polarised photoelectronExchange split final states act as a filter of the spin

Magnetic sensitivity comes through the spin-orbit coupling and exchange and has strong polarisation dependence (MOKE)

Courtesy W. Kuch, Freie Universität Berlin

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XMCD Examples at Resonant Edges

From Magnetism by J. Stöhr and H.C. Siegmann, Springer

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Circular Polarised LightA photon is a spin-one particle which carries ±1 unit of L

along its direction of motion. This angular momentum is transferred to the absorbing material.

.Right Circular, +Pc, s=+1

Left Circular, -Pc, s=-1

s=HelicityM

Faraday Effect

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Detecting XMCDTransmission Thin Samples

Drain CurrentField Sensitive, AnisotropicEscape Depth ~3nm

FluorescenceEscape Depth ~1mm, AnisotropicSecondary processes

PEEM – ESG group at the ALShttp://xraysweb.lbl.gov/peem2/webpage/Home.shtml

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Element Specific M-H loops

-1

0

1

-10 -5 0 5 10

IronCobalt

Field (mT)

Mag

netis

atio

n (M

/MS)

-1

0

1

2

3

630 640 650 660 670

Energy (eV)

XMC

D -

Diff

/Sum

(flip

ping

ratio

%)

-1.0

-0.5

0

0.5

1.0

-400 -200 0 200 400

Field (Oe)

Flip

ping

Rat

io (

FR/F

RM

AX)

MnSb

-10

0

10

680 720 760 800 840

Energy (eV)

Diff

eren

ce (%

)

FeCoZr

Mn

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Resonant X-ray ‘Magnetic’ Scattering

Im.E f Em

Absorption spectroscopy sensitive to the exchange split final state and the split core levels (spin-orbit). Basis behind XMCD.

2

Re ImScattering f E f E

Resonant elastic scattering is sensitive to the same terms but contains both the real and imaginary terms to the scattering factor.

2p

3d

Circular polarised x-rays. Element specific.

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On Resonance – Scattering Factor

Resonant processes enter the scattering factor through f’ and f’’ and must describe the initial and final state.

0, Magmf iq mq f ff f i

From XAS obtain f’’ From XMCD obtain m’’

Use Kramers-Kronig transforms to obtain the real parts of the scattering factors and thereby f(q,).

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Scattering amplitude

Scattering is sensitive to both the real and imaginary components which are related via the Kramers-Kronig transforms.....

0, , ,f q f q f m if m

The magnetic dependent absorption (XMCD) gives a magnetic dependence on the real part of the scattering factorFe

From Magnetism by J. Stöhr and H.C. Siegmann, Springer

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Electric Dipole Transition 0 1 2

0ˆ ˆ ˆˆ ˆ ˆ ˆ ˆ ˆf i f i f if r Z F i mF m m F

Resonant and non-resonant charge scattering

Circular Dichroism and Kerr Effect

Linear Dichroism and the Voigt Effect

F0, F1, F2 are all complex numbers containing the scattering factors and depend on the incident energy, and therefore resonance.

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q-space

0

2

4

6

8

10

-10 -8 -6 -4 -2 0 2 4 6 8 10

10 keV0.707 keV

2>180°

>180°<0°

Si (004)d=1.358Å

d=10Å

qx(Å-1)

q z(Å-1

)

Diffraction

Small AngleScattering & Reflectivity

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Reflections from Surfaces

http://www.glenspectra.co.uk

jj j

jo

A fA

rN Re2

2

m

4Im

22 f

ArN

j j

jo

A

j

jjfrn

21

2

1n i

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Reflectivity from layered systems

Intensity is proportional to layer thickness and the refractive index of the layers (electron density).Roughness modifies the reflection and transmission coefficients - interface roughness

Sensitivity <1Å. Max. thickness - 1000Å. Max Roughness - 35 Å

Based on Simple Optical Theorems:Snell’s LawFresnel’s Law

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[FeCoZr/AlZr]x20

• Periodicities in the sample give rise to different beat frequencies in spectra. Profile proportional to FT{electron density profile)• Roughness modifies the Fresnel reflection and transmission coefficients and hence the overall fall-off.

Phys. Rev. B 80 (13) 134402 (2009),

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Amorphous Multilayer Example

Averaged:Layer thicknessInterface widthRefractive index - Density

TPA Hase et al. Phys. Rev. B 80(13) 134402 (2009)

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Anomalous Dispersion

Enhance the scattering factor difference between the layers.

0.001

0.1

10

1000

100000

0 0.02 0.04 0.06 0.08

=1.3803Å=1.4800Å

qz(Å-1)

Nor

mal

ised

Inte

nsity

(a.u

.)

-10

-5

0

5

1.0 1.2 1.4 1.6 1.8 2.0

f'

f"

CoCu

Wavelength (Å)

Sca

tterin

g F

acto

r C

orre

ctio

ns, e

lect

rons

0

50

100

150

200

1.0 1.2 1.4 1.6 1.8 2.0

2CoCoCuCuBragg nfnfI

2CoCu ff

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Grazing IncidenceScattering

M. Wormington et al. Phil. Mag, Lett. 74(3) 211 (1996)

In-plane q

Out-of-plane q

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Resonant magnetic reflectivity

n2

n3

Refractive index now depends on the moment

direction:

1n i

002

2cosen r

f m Ef Ek

02

2cosen r

f E m Ek

On resonance the scattering becomes sensitive to both the structural and magnetic profiles of the element under consideration. Extract magnetic signal through the flipping ratio:

. . I IF RI I

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Alloy – Pd resonant Scattering

Sum (left) and flipping ratio (right) determined by reversing the applied field for the alloy sample at 200 K . The flipping ratio shows the same periodicity as seen in the sum signal and changes sign when the incident helicity (±Pc) is reversed.

∂

T=20K

0.05 0.10 0.15 0.20 0.25 0.30

1E-5

1E-4

1E-3

0.01

0.1

1N

orm

alis

ed S

truct

ural

Ref

lect

ivity

qz(Å)-1

0 50 450 500

-1.6

-1.2

-0.8

-0.4

0.0

Stru

ctur

al P

rofil

e (s

catte

ring

leng

th)

qz(Å)-1

Structural

∂

0.05 0.10 0.15 0.20 0.25 0.30-20

-10

0

10

20

Flip

ping

Rat

io (%

)

qz(Å)-1

0 50 450 500

0.00

0.01

0.02

0.03

0.04

Mag

netic

Pro

file

qz(Å)-1

Magnetic dead-layer at interface with buffer and an enhanced moment at the surface

T=20K

Magnetic

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Compositional and Magnetic Profiles (Pd)

0 100 200 300 400 5000.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ised

Com

posi

tion

Depth (Å)

Si Fe Pd

0 100 200 300 400 5000.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ised

Pro

file

Depth (Å)

Structural Magnetic

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PNR from a single layer

10-6

10-4

10-2

100

0 0.05 0.10 0.15

Qz[Å-1]

RE

FLE

CTI

VIT

Y

Courtesy Sean Langridge, ISIS

Directly proportional to mB.

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Fe/Pd Example

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Comparison of Profiles

• 1.4 and 0.5 ML profiles have the magnitude of the moments fixed by PNR.

• The spatial extent of the Fe moment increases with increasing δ-layer thickness but the induced moment extent remains approximately constant.

• Samples close to half integer coverage appear to induce a higher moment.

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-8 -6 -4 -2 0 2 4 6 8

-15

-10

-5

0

5

10

15 165 K 215 K 252 K 272 K 296 K

F.R

(%)

Applied Field (mT)

-4 -3 -2 -1 0 1 2 3 4

-4

-2

0

2

4

6 205 K 218 K 235 K 252 K 283 K

F.R

(%)

Applied Field (mT)

Fe edge Pd edge

The remanent magnetisation is extracted by fitting each hysteresis loop to a pair of arctan functions:

Hysteresis Loops – 1.4ML Fe in Pd