Experimental Techniques for the Study of

(1)

School on Pulsed Neutrons - October 2007 - ICTP Trieste

Experimental Techniques for the Study of

Magnetism

Prof. Dr. Thomas Brückel

Institute for Scattering Methods Institute for Solid State Research Forschungszentrum Jülich GmbH

first compass

History: Loadstone Fe

3

O

4

( ^≈ 800 BC)

100 A.D.

Chinese "south pointer"

"perpetual motion machine"

1269 Europe: Petrus Perigrinus

"Epostolia de Magnete"

what’what’s new ?s new ?

magnetic nanostructures correlated electron systems ...

The “Founding Fathers”

Albert FertUniv. Paris Sud Peter Grünberg IFF / FZ Jülich

• 2006 “European Inventor”

• 2007 “Stern-Gerlach-Medaille”

of the German Physical Society

• 2007 Japan-Prizeof the Science and Technology Foundation (JSTF)

• 2007 Wolf-Foundation-Prizein Physics, Israel

• 2004 Member of the

“Académie des Sciences”

Spintronics

"Spintronics“ / “Magnetoelectronics”:

Information transport, storage and processing using the spin of the electron (not just the charge!)

2007: Nobelprize in Physics

Outline

• What's new in magnetism ?

• Experimental techniques

• Elastic magnetic neutron scattering

• Example: Thin film magnetism

• X-ray techniques for magnetism

• Nonresonant magnetic x-ray scattering

• Resonant magnetic x-ray scattering

•Example: Resonance exchange scattering from mixed crystals

• Summary

Magnetic Nanostructures

Thin Film Multilayer:

Fe₅₀Pt₅₀Nanoparticle Network by colloidal self organisation

Sun et al; Science 287 (2000), 1989

⇒Surfaces,

⇒Interfaces,

⇒Proximity effects

Interlayer Exchange Coupling

Peter Grünberg:

Interlayer Exchange Coupling in Fe/Cr Multilayers Phys. Rev. Lett. 57 (1986), 2442

Oscillatory coupling as function of interlayer thickness:

Co Cu Co

Ferromagnetic Antiferromagnetic

(2)

Giant Magnetoresistance (GMR)

P. Grünberg et al.

Phys. Rev. B 39 (1989), 4828 (and independently: A. Fert, Paris)

GMR-effect

Fe/Cr/Fe 1.5 %

Artificial Nano-Structures

→purpose designed properties

Applications: Hard Disks

GMR effect:

< 10 years from discovery in curiosity-driven fundamental research to application in computer storage, ABS sensors, …: multi billion $ !

Areal density

(Hitachi Global Storage Technologies) Terabits!

Applications: MRAM

MRAMMRAM

•100 Million storage elements per mm²

•1 /100 Million gram mass per cm² Magnetic Random Access Memory:

independently 1988 A. Fert

"Spintronics":

Information transport, storage and processing with the spin of the electron (not the charge!)

Complex transition metal oxides:

High T

_C

Superconductors; CMR-Manganates; …

New phenomena appear from the New phenomena appear from the bottom of the Fermi sea due to bottom of the Fermi sea due to electronic correlations:

electronic correlations:

• Magnetism

• Superconductivity

• Metal-insulator transition (CMR)

• Charge- & orbital order

• Multiferroica

Highly correlated electron systems

Materials

Combination in layered systems:

Magnetic Metals:

Combined with: - "non magnetic" metals: Cu, Cr, Mn - oxides as tunnel barriers: Al2O3

- semiconductors: Si

3d itinerant magnetism 4f localized moments

New materials

Dilute magnetic semiconductors: (Ga,Mn)As, Ge(Fe,Mn) Half-metals: La0.7Sr0.3MnO3, CrO2, Fe2O3

Colossal magnetoresistance effect: La0.7Ca0.3MnO3

Multiferroica: TbMnO₃, LuFe₂O₄ Highly correlated electron systems!

Dimensionality

multilayer

surface

chains self-organized nano-

particle networks lithographic

stripes

clusters

crystal

10²⁰macroscopic 10¹⁰ mesoscopic

10³ nanoscopic 10 molecular magnet number of spins

number of spins

complex systems:

• interaction

• domains

• magnetization dynamics

single molecule magnet:

• “giant spin”

• quantum tunneling

• quantum interference

(3)

Outline

• Example: Resonance exchange scattering from mixed crystals

• Summary

Susceptibility and Magnetisation

M H

H M =χ⋅ linear response theory

→Internal structure? (atom positions, moment arrangement)

→Microscopic dynamics? (atom movements, spin dynamics)

⇒ Macroscopic properties (conductivity, susceptibility, ...) Scattering:

interaction sample ↔radiation weak

⇒ non-invasive, non destructive probe for structure & dynamics

Scattering

v N

μ

_N

Generalised Susceptibility

linear response theory:

Fourier transform:

( ,) ( ,) 0

= ld _H=

ldt M R t

R

M^β ^β ( ^,^') ( ^'^'^, ^')^'

' '

'

' t R R t tdt

R

t H

d l ld d

l d

∫ ∑∑−∞ l − −

+ ^αβ

α

α χ

(^, ^') ⁽ ⁾ ( 0'^, ^')

1 '

'

0 R R t t

e t t

Q ⁱ^Q^R ^R _ld _d

dd

d

ld − −

=

−

∑

^⋅ ⁻ ^αβ

αβ χ

χ

( )^Q ^e dd( )^Q^t^dt

t i

dd , _' ,

' 0

αβ ω

αβ ω χ

χ ⁼∫^{∞ −}

perturbation of magnetic system described by spacial and temporal varying magnetic field H (r, t)

system reaction:

local magnetisation M (r,t)

linear response theory→susceptibility )

, ( tr χ

Outline

• Summary

Magnetic Structures

Mn²⁺

b=a a=4.873 Å

c=3.31 Å

Collinear Antiferromagnets:

F -

MnF2:

Modulated Structures:

Cr:

MnO:

Complex Structures:

Er6Mn23:

Rare Earth:

General description in Fourier representation:

∑ ^⋅ ⁻ ^⋅

=

k l k

e m ikR

m_ij _ijexp( )

(4)

Neutron-Matter-Interaction

First Born Approximation: 2 2

|

|' 2 ⎟ |< >

⎠

⎜ ⎞

⎝

=⎛

Ω m k V k

d d

π σ

•strong interaction n ↔nucleus

•magnetic dipole-interaction with B-field of unpaired e^- major

?

r d e r V

r d e r V e

r Q i

r k i r k i

3 3 '

) (

⋅

−

∫

⋅

=

Magnetic Interaction Potential

e^-

ve

μe

R

B μn

n

magnetic moment of the neutron:

σ

⋅ γμ

−

=

μn N

magnetic field of the electron:

L

S B

B

B= +

dipolar field of the spin moment: ; 2 S

R R x

B_S ^e₃ μ_e=−μ_B⋅

⎟⎟⎠⎞

⎜⎜⎝

×⎛μ

∇

=

field due to the movement of the electron (Biot-Savart): L ^e₃ R

R v c

B =−e ×

n B m=−μ ⋅ V

Zeeman energy:

Magnetic Scattering Cross Section

σz Vm k

σz‘ k‘

2 z m z 2 2

n k' ' k

2 m d

d ⎟⎟⎠ σ σ

⎜⎜ ⎞

⎝

⎛

= π Ω

σ V

( ) z ( ) z ²

B

02 ' M Q

2 r 1 d

d σ ⋅ σ

− μ γ Ω= σ

σ ⊥ cm 10 539 . 0 r0= ⋅ −¹² γ

→"equivalent scattering length" for 1 µB(S=

2

1): 2.696 fm ≈b_co

( )^Q ^Q^ˆ ^M( )^Q ^Q^ˆ

M_⊥ = × ×

( )Q=∫M( )re ^⋅dr

M ⁱ^Q^r³

( )^r ^M( )^r ^M ( )^r

M = _S + _L

( )=−μ ⋅ ( )=−μ ∑δ(− )

i i i

B B

Sr 2 Sr 2 r r S

M

1. Born approximation

Directional Dependence

Q k‘

M k

M⊥

( )^Q ^Q^ˆ ^M ^Q^ˆ

M_⊥ = × ×

Illustration: scattering from the dipolar field Only the component of the magnetisation perpendicular to the scattering vector gives rise to magnetic scattering!

M || Q M

Q

Planes with equal phase factor

M⊥Q M

Q

Pure Spin Scattering

Ri rik

tik Sik

Si

Atom i

Separation of intra-atomic quantities for localised moments:

( )=−μ ∑δ(− )⋅ +

=

ik ik ik

B ik S

i

ik R t ; M r 2 r r s

r

( )Q =∫M ( )re ^⋅dr

M _S ⁱ^Q^r³

∑ ∑ ⋅

∑ =

= ^⋅ ^⋅ ^⋅

i iQR k iQt ik ik

ik r Q

i s e e s

e ⁱ ⁱ ^ik

Expectation value of the operator for the thermodynamic state of the sample:

( )=−μ ⋅ ( )⋅∑ iQ^⋅R ⋅ i m

B f Q e S

2 Q

M ⁱ

( )= ∫ρ( ) ^⋅

Atom r3 Q i s

mQ re dr

f

( ) ( ) ²

i R Q i i 2 m

0 f Q S e i

d r

dΩ=γ ∑

σ ⊥

0.0 0.2 0.4 0.6 0.8 1.0

normalized form factor

sin(Θ/λ) nuclear scattering

orbital

x-ray spin Chromium

0.0 0.2 0.4 0.6 0.8 1.0

sin(Θ/λ) Q || b Q || a

a b

form factor

Form Factor: Spin, Orbit, Anisotropy

M(r)

λ

F

i. a. anisotrop:

in general anisotropic:

⇒ information on anisotropic magnetization density distribution!

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Magnetic Bragg Diffraction from a Type I Antiferromagnet on a tetragonal body-centered lattice

nuclear structure factor (ignore F^-):

magnetic structure factor Mn²⁺

F-

b=a a=4.873 Å

c=3.31 Å

MnF2

( ) ( )

2

0 ,

( , , ) ( , , )

i

i i Q r

nucl i

i

iQ r

mag i i

i

I h k l S h k l

S b e

S γr f Q S e

⋅

⊥

= ⋅

∑

∼

v N

μ

N

Magnetic Neutron Scattering

inelastic / quasielastic scattering:

directly related to generalized suszeptibility:

) ' , ' ( ) ' , , ' , ( ) ,

(rt rr tt Hr t

M =χ ⋅

magnetic excitations:

spinwaves, crystal field etc.

( 0)² 1 ' () ² z z B n mag

Q M d r

dωσ ₌γ ₋μ σ σ_⋅ _⊥ σ elastic scattering:

directly related to magnetization:

spin structures, magnetization densities

Molecular Magnets

Polyoxometalates (30 Fe³⁺spins) Mn 12 - acetate

(12 Mn spins)

Spin-Density Distribution

J. Luzón et al Physica B335 (2003),1

Crystal structure &

possible exchange pathways

Pure organic ferromagnet below T_C=1.3K

Magnetization density from pol. neutron diffraction

in Molecular Magnet p-O2N·C6F4·CNSSN

Spin Excitations

I. Mirebeau et al PRL 83 (1999), 628

Low E excitations: neutron data and fit

Energy level diagram:

splitting of lowest S multiplett (S=10 ground state)

in Mn12-acetate Spin Cluster

Outline

• Summary

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Reflectometry

αi αf

Substrate Ferromagnet Diamagnet Ferromagnet

M1

M2

specular reflectivity αi=αf

incident beam

specular reflectivity: vertical scattering length profile

Scattering Under Grazing Incidence

roughness

domains off-specular diffuse scattering αi≠αf

vertical correlations:

from 0.1 nm to 100 nm

lateral correlations: from 1 nm to 100 μm off-specular diffuse scattering:

Remagnetization Process

substrate Gd 450 Å

100 bilayers

TiNx

FeCoV TiN_x FeCoV

H Magnetic gradient multilayer with 100 bilayers (“supermirror”):

remagnetization process

E. Kentzinger et al 2007

µ

0

H = 0.5 mT after saturation in -y direction (μ

0

H = -50 mT)

++ --

+- -+

Remagnetization Process

α

i

α

f

specular αi= αf

H B║ P

B⊥P

µ

0

H = 1.0 mT

µ

0

H = 2.0 mT

(7)

µ

0

H = 2.6 mT

µ

0

H = 3.1 mT

µ

0

H = 3.6 mT

µ

0

H = 4.0 mT

H

µ

0

H = 4.6 mT

µ

0

H = 5.0 mT

(8)

µ

0

H = 5.5 mT

µ

0

H = 6.0 mT

µ

0

H = 6.5 mT

µ

0

H = 7.0 mT

µ

0

H = 10 mT

µ

0

H = 15 mT

(9)

µ

0

H = 20 mT

µ

0

H = 25 mT

µ

0

H = 50 mT

µ

0

H = 100 mT

µ

0

H = 151 mT

µ

0

H = 200 mT

(10)

µ

0

H = 422 mT

H

µ₀H = 1 mT:

µ₀H = 3.8 mT:

µ₀H = 5.6 mT:

Data

(HADAS @ FRJ-2)

µ₀H = 1 mT:

µ₀H = 3.8 mT:

µ₀H = 5.6 mT:

Simulations within DWBA

E. Kentzinger et al

Importance of Polarization Analysis

with polarization analysis

Roughness of interfaces Magnetization of thin layers Magnetization of thick layers

lateral magnetic correlations parallel H (longitudinal)

lateral magnetic correlations perpendicular H (transverse)

unpolarized

Diffuse scattering from a supermirror→ lateral correlations

Summary: Supermirror

• increasing interface roughness from substrate to air: 7 Ǻ→14 Ǻ

• scattering length density ≈15% smaller than nominal (voids)

• thicknesses ≈5% lower than nominal

• no true remanence: magnetization fluctuations

• layers flip sequentially: thin bottom layers flip first!

• random anisotropy model for soft magn. nanocrystalline alloys

reversed layers as function of field coercive field and grain size vs layer thickness

U.Rücker, E.Kentzinger, B.Toperverg, F.Ott, Th. Brückel; Appl. Phys. A74 (2002), 607 E. Kentzinger et al; PRB submitted

Outline

• Summary

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Powder Diffraction

Chemical structure, but not

Magnetic Structure RT

10 K

E. Gorelik (2004)

Neutrons: La_0.5Sr_0.5MnO₃ X-rays:

La

7/8

Sr

1/8

MnO

3

-Kristall

< 112>

T = 120 K

Perßon, Li, Mattauch, Kaiser, Roth, Heger (2004)

ESRF @ Grenoble, France 6 GeV

APS @ Argonne/Chicago, USA 7 GeV SPRING8, Japan, 8 GeV

Synchrotron Sources

X-Ray Probes of Magnetism

- Kerr-microscopy - Faraday effect

- Linear x-ray magnetic dichroism - Circular x-ray magnetic dichroism

- Spin resolved x-ray absorption fine structure SEXAFS - Magnetic x-ray diffraction (non-resonant scattering) - Resonant magnetic x-ray scattering (X-ray resonance

exchange scattering XRES) - Nuclear resonant scattering - Magnetic x-ray reflectivity - Magnetic Compton scattering

- Angular- and spin resolved photoemission

Outline

• Example: Non-resonant scattering from transition metal di-flourides

• Summary

E

H E

H

H H E

E

interaction re-radiation

-e

-e μ μ force

-eE

grad(μH)

torque Hxμ

E-dipole

H-quadr.

E-dipole

H-dipole σ

σ

π,σ

π

π μ

De Bergevin & Brunel 1981

Nonresonant Scattering: Classical

Thomson scattering from charges

⇒ Structure

But: X-rays are electromagnetic radiation ⇒ non resonant magnetic x-ray

scattering

⇒ Magnetism

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Cross Section for Magnetic X-Ray Scattering Non-relativistic treatment in second order perturbation theory (Blume 1985, Blume & Gibbs 1988)

•Hamiltonian for e^-in e-m field:

))2 ( 2 (

1 Arj

c j e P j m

H=∑ −

∑ +jiV(rij)

∑ ⋅∇×

− jsj Arj mc

e ( )

)) ( ( ) 2 ( ) (

2 Arj

c j e P jsj Erj mc

e ∑ ⋅ × −

−

2) ) 1 ( ) (

∑ (+ +

+ λω λ λ

k kc k ck

kinetic energy Coulomb interaction Zeeman energy -µ · H spin-orbit coupling -μ·H~s·(E×v) self energy of e-m-field

•Vector potential in plane wave expansion:

21

q Vq

c2 ) 2 r ( A =∑σ πω

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

r] q ei ) q ( c ) q ( r * q ei ) q ( c ) q (

[ε σ σ ⋅+ε σ + σ −⋅

×

H = Ho+ Hr+ Hint

e^--system e-m-wave interaction

→ perturbation theory (Fermi's "golden rule")

first order for terms quadratic in A second order for terms linear in A

2 int ,, , ' ,

' fH k i

d k

dσ_∝ ε ε

Ω

Cross Section for Magnetic X-Ray Scattering

2 ' 2

2 2

' εε

ε ε

σ

fC

mc e d

d ⎥ ⋅

⎦

⎢ ⎤

⎣

=⎡

Ω →

2

' '

2

2 2

' εε εε

ε ε

λ σ

M C

C f

i d mc f

e d

d ⎥ ⋅ +

⎦

⎢ ⎤

⎣

=⎡

Ω →

non-resonant elastic scattering cross section:

re= 2.818 fm π/2 phase shift

interference~ fC· fM

Intensity ratio: ~106

2 f S NfM NM dc

~ IMC

I −

⋅

⋅ ⋅ λ

charge ~ |fC|² magnetic~ |fM|²

h/mc = 2.426 pm

incident and final polarization

Cross Section: Nonresonant

cross section:

scattering geometry:

Polarization Dependence

2

' '

2

2 2

' εε εε

ε ε

λ σ

M C

C f

id mc f

e d

d ⎥ ⋅ +

⎦

⎢ ⎤

⎣

=⎡

Ω →

Q=k’-k

Charge scattering: "NSF"

Magnetic scattering: "NSF" (S2, L2) –_┴scattering plane + "SF" (S₁, S₃, L₁) – in scattering plane

⇒ Separation S↔L

Amplitude-matrices:

to\^from σ π

σ' ρ( Q) 0 π' 0 ρ(Q) cos2( θ)

<fC> for charge scattering: ^e^-

E Hertz

Dipole Radiation

⇒ charge density ρ(Q)

to\^from σ π

σ' S₂⋅cosθ [(L₁+S₁)⋅cosθ +S₃⋅sinθ]⋅sinθ π' [−(L1+S₁)⋅cosθ +S₃⋅sinθ]^⋅sinθ

[

^{2 L}2⋅sin²θ +S2

]

^⋅cosθ

<fM> for the magnetic part:

⇒ spin density S(Q) and orbital angular momentum density L(Q)

50 m

5 mm properties calculable

small source size

wiggler clean ultra-high vacuum source

time structure

intense continuous spectrum highly collimated

undulators

. .

polarised

Synchrotron X-Ray Source

(13)

Outline

• Summary

Resonant Magnetic X-Ray Scattering

resonance exchange scattering

neutron scattering

resonant x-ray scattering

( )

2

0 M

mag E E i /2

E / d

d

Γ

−

∝ α Ω

σ Hannon, Trammell, Blume & Gibbs

PRL 61 (1988), 1245 γ_L

III ε_F

2s 2p 2p

1s 1/2 3/2 4f↑ 4f↓

s-p-d

up E down

exchange splitting

E1: 2p3/2→5d5/2 E2: 2p3/2→4f7/2

7942 eV 7938 eV 7935 eV 7933 eV

ω 0 1000 2000 3000

5 5.2 5.4 5.6 5.8

counts / sec

energy

7924 eV 7930 eV

0 20 40 60 80 100 120 140

0 50 100 150 200 250

7920 7925 7930 7935 7940 7945 7950

peak intensity [a.u.] flourescence yield [a.u.]

energy [eV]

GdS 9/2 1/2 1/2

L_II edge

GdS: L

II

Edge Resonance

Brückel, Hupfeld, Strempfer, Caliebe, Mattenberger, Stunault, Bernhoeft, McIntyre; Eur. Phys. J B19 (2001); 475

) ( ) ( ) ( ) 1(

linE f circE f o E f E E

fres = + +

Dipole Approximation:

⎥⎦

⎢ ⎤

⎣

⎟⎡

⎠⎞

⎜⎝

⎛εε⋅ ++−

= 1

F1 11 F ' ) E 0( f

⎥⎦

⎢ ⎤

⎣

⎟ ⎡

⎠⎞

⎜⎝

⎛ε×ε⋅ −−+

= 1

F1 11 F m ' i ) E circ( f

( ) ⎥⎦

⎢ ⎤

⎣

⎟ ⎡

⎠⎞

⎜⎝

⎛ε⋅ ε⋅ −+−−

= 1

F1 11 1 F F0 2 m m ' ) E lin( f Amplitudes:

Oscillator Strengths:

i 2 res 1 M

FM ω−ω −Γ

= α

⎟⎠

⎜ ⎞

⎝⎛

( ) ^...²

' 1 ' '

2 2 2

'= ⋅ + + +

Ω → ⎟

⎠

⎜ ⎞

⎝

⎛

ε ε ε

λ ε ε ε ε

ε

σ E _E

fres fM d i c fc mc

e d

d

Anomalous Scattering: Cross Section

XRES: Resonance Enhancements

thin films thin films

elements edge transition energy range [keV]

resonance strength

comment

3d K 1s → 4p 5 - 9 weak small overlap

3d ^LI 2s → 3d 0.5 - 1.2 weak small overlap

3d LII, LIII 2p → 3d 0.4 - 1.0 strong dipolar, large overlap, high spin polarisation of 3d

4f ^K 1s → 5p 40 - 63 weak small overlap

4f LI 2s → 5d 6.5 - 11 weak small overlap

4f ^LII, L_III 2p → 5d 2p → 4f

6 - 10 medium dipolar

quadrupolar

4f MI 3s → 5p 1.4 - 2.5 weak small overlap

4f ^MII, MIII 3p → 5d 3p → 4f

1.3 - 2.2 medium to strong

dipolar quadrupolar 4f ^MIV, M_V 3d → 4f 0.9 - 1.6 strong dipolar, large overlap,

high spin polarisation of 4f 5f MIV, MII 3d → 5f 3.3 - 3.9 strong dipolar, large overlap,

high spin polarisation of 5f

Outline

• Summary

(14)

Gd

x

Eu

1-x

S-Phase-Diagram

0 10 20 30 40 50 60 70

0 0.2 0.4 0.6 0.8 1

T [K]

x GdxEu

1-xS

P AF FM

SG

insulator

metal

EuSEuS GdSGdS

Gd S

Gd

0.73

Eu

0.27

S: Resonances

→

→dominant dipolar transitions 2p →dominant dipolar transitions 2p →5d5d

Gd

0.8

Eu

0.2

S: Temperature Dependence

0 0.2 0.4 0.6 0.8 1

0 10 20 30 40 50 60

M/Ms

T [K]

Eu0.2Gd 0.8S 9/2 1/2 1/2 Eu L_II

Gd LII non resonant

Gd-resonance

Eu-resonance

Hupfeld, Schweika, Strempfer, Mattenberger, McIntyre, Brückel Europhys. Lett. 49 (2000), 92

Frustration Model Gd

1-x

Eu

x

S

JEE>O

Eu-spin triple (4.9 % for x = 0.8)

JEG<O JEE>O

Eu-spin pair (7.9 % for x = 0.8) JGE<O

single Eu-spin (5.2 % for x = 0.8) JGG<O

?

? ?

?

H = H_Gd-Gd+ H_Gd-Eu+ H_Eu-Eu

⇒ Perturbation Theory:

H‘: molecular field approximation ΔH = HEu-Eu: exact diagonalization for Eu- pairs, triples,... in the molecular field

H‘ ΔH

Sj Si Jij

H=−∑ ⋅

Heisenberg:

T-Dependence

"Frustration Model" Monte Carlo Simulation

Gd-Gd Gd-Eu Eu-Eu J1 -1.27 K -0.85 K +1.21 K J2 -2.82 K -1.86 K 0

Hupfeld, Schweika, Strempfer, Caliebe, Köbler, Mattenberger, McIntyre, Yakhou, Brückel

Eur. Phys. J. B 26 (2002), 273

Canted Versus Collinear States

GdS Gd0.8Eu0.2S Gd0.73Eu0.27S T/T_N

∞ 0.25 0.02

collinear canted canted

(15)

Success!

Wolfgang Caliebe

&

Dirk Hupfeld

@

W1 – DORIS - HASYLAB

Outline

• Summary

Scattering Methods for Orbital and Spin Physics Neutrons

☺powder samples

☺complex magnetic structures (spherical PA)

☺excitations

☺spin densities

☺complementarity (probes 4f moments directly, L- determination with “x-n technique”, …) XRES: element and band sensitive probe!

☺soft x-rays (magnetisation density profile, magnetic domain structure^≈1 keV) for thin film magnetism (3d & 4f):

☺hard x-rays (spin polarisation in conduction band (dipole transitions)^≈10 keV) for thin films and bulk 4f magnets:

HEX: High energy (^≈100 keV) non resonant magnetic x-ray scattering

☺absolute determination of spin form factors (in part. 3d) Anomalous X-ray scattering:

☺Local distortions and orbital ordering

Experimental Techniques for the Study of