magnetic dichroism in xas and its...

Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 1Freie Universität Berlin

Klaus BaberschkeKlaus Baberschke

Institut für ExperimentalphysikInstitut für ExperimentalphysikFreie Universität BerlinFreie Universität Berlin

Arnimallee 14 DArnimallee 14 D--14195 Berlin14195 Berlin--Dahlem GermanyDahlem Germany

1. Introduction.

2. Element specific magnetizations in trilayers.

3. Determination of orbital- and spin- magnetic moments;XMCD sum rules.Magnetic Anisotropy Energy (MAE) and anisotropic µL.

4. Induced magnetism at interfaces.

5. New developments, outlook

Magnetic dichroism in XASMagnetic dichroism in XASand its applicationand its application

Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 2

1. Introduction: XAS

L3,2 edges of 3d elements

Note: the intensity of the 2p → 3d dipole transitions (E1) is proportional to the number of unoccupied final state (i.e. 3d- holes).

X-ray Absorption Spectroscopy is the most appropriate technique for element specific investigations.

Fe

Co

Ni

Cu

Photon energy (eV)

X-r

ay a

bsor

ptio

n cr

oss

sect

ion

(arb

. uni

ts)

0

100

650 700 750 800 850 900 950 1000

200

300

400


Appendices/References

• In this lecture we will not discuss the equipment/apparatus,but rather focus on application of XAS in magnetism.

• Concerning XAS-technique there exist many review articles e.g.J. Stöhr: NEXAFS Spectroscopy, Springer Series in SurfaceScience 25, 1992; H. Wende: Recent advances in the x-ray absorption spectroscopy, Rep. Prog. Physics 67, 2105 (2004).

• See also lectures A13 J. Vogel; A14 Y. Joly;A’15 (Trieste) F. Sirotti; A”15 (Saclay) M. Sacchi.

• In the soft X-ray regime (VUV) one needs to work in vacuum.For nanomagnetism one wants to prepare and work anyway inUHV (in situ experiments).


X-ray Magnetic Circular DichroismFaraday – effect in the X-ray regime (Gisela Schütz, 1987)

XMCD signal is a measure of the magnetization

Many Reviews, e.g. H. Ebert Rep. Prog. Phys. 59, 1665 (1996)

0

1

2

3

4

5

6

700 710 720 730 740-3

-2

-1

0

Photon Energy (eV)

Nor

m. X

MC

D (a

rb. u

nits

)N

orm

. XA

S (a

rb. u

nits

)

µ−+

µµ

0

(E)(E)(E)

L2

3L

=µ+ −−µ(E)∆µ

Fe

M

continuum

Spin “up” Spin “down”

EF

2p

2p

left right

L 2

L 3

3d

12

32

+h −h

kM

2p12

2p 32

3d 3 23d 5 2

1 2−3 2−5 2− 1 2+ 3 2+ 5 2+1 2−3 2− 1 2+ 3 2+

1 2−3 2− 1 2+ 3 2+1 2− 1 2+


The origin of MCD (after K. Fauth, Univ. Würzburg)

Reviews e.g.: Lecture Notes in Physics Vol. 466 by H. Ebert, G. Schütz


2. Element specific magnetizations in trilayers

A trilayer is a prototype to study magnetic coupling in multilayers.

What about element specific Curie-temperatures ?

Two trivial limits: (i) dCu = 0 ⇒ direct coupling like a Ni-Co alloy(ii) dCu = large ⇒ no coupling, like a mixed Ni/Co powder

BUT dCu ≈ 2 ML ⇒ ?

substrate

CoTC

Co CuNi

TCNi

M

M

J int

er

853 eV(L )3 e -e-778 eV(L )3


Ferromagnetic trilayers

U. Bovensiepen et al.,PRL 81, 2368 (1998)

760 780 800 820 840 860 880 900

-40

-20

0

336K

336K

290K

290K

x 2

Ni L3,2

Co L3,2

XM

CD

(ar

b.uu

nits

)

Photon energy (eV)

Cu (001)

2.0ML Co

2.8ML Cu

4.3ML Ni

MCo

MNi

290 300 310 320 3300.0

0.1

0.4

0.8

TC

Co = 340 K

T*C

Ni = 308 K

T (K)

M (a

rb. u

nits

)

0

200

400 Ni L3,2Co L3,2

x 1.72

norm

. abso

rptio

n (

a.u

)

760 800 840 880-100

-80

-60

-40

-20

0

20

T = 140K

2.2 ML Co3.4 ML Cu3.6 ML NiCu(001)

Cu(001)

XM

CD

(arb

.uun

its)

h (eV)ν


P. Poulopoulos, K. B., Lecture Notes in Physics 580, 283 (2001)

a) J. Lindner, K. B., J. Phys. Condens. Matter 15, S465 (2003)b) A. Ney et al., Phys. Rev. B 59, R3938 (1999)c) J. Lindner et al., Phys. Rev. B 63, 094413 (2001)d) P. Bruno, Phys. Rev. B 52, 441 (1995)

Theory d)

2 3 4 5 6 7 8 9-20

-15

-10

-5

0

5

10

15

20

25

J inte

r (µe

V/a

tom

)d (ML)Cu

FMR / / / /

/ / /

→

→XMCD / / /→

Cu Cu Cu(001)

Cu Cu(001)Cu Cu(001)

FMR

Ni Ni

NiNiCoCo

a)b)c)

Interlayer exchange coupling

T*Ni

M (a

rb. u

nits

)

TCNi = 275K

2.8 ML Cu4.8 ML Ni

Cu(001)

150 200 250 300 350

2.8 ML Co2.8 ML Cu4.8 ML NiCu(001)

T (K)

0

0.25

0.50

0.75

1.75

2.00

37K


C. Sorg et al.,XAFS XII, June 2003Physica ScriptaT115, 638 (2005)

e_

IP

+HV

hνHstatisch

-0.2

-0.1

0.0

0.1

0.2

Mag

net

izat

ion (

arb. units)

Magnetic Field (Oe)-40 -20 0 20 40

281 K

265 K184 K

5 ML Cu

6 ML NiCu (100)

0 50 100 150 200 250 3000.0

0.1

0.2

0.3

0.4

0.5

Temperature (K)

Mag

net

izat

ion (

arb. units)

Remanence and saturation magnetization

M (

kA/m

)

0 30 60 90 120 150 180 210 2400

100

200

300

1200

1600

T (K)

Cu (100)

2.8 ML Ni

3.0 ML Cu

2.0 ML Co

Cu (100)

2.8 ML Ni

3.0 ML Cu

TC,Ni

T*C,Ni

38 KC,Ni∆T

2D

3D0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

T / TC,Ni

2.1 2.6 3.1 4.2 4.0

d (ML)Ni

1 2 3 4 5 6

Theory / Experiment

C,N

iM

C,N

iM

/(T

= 0

)


J.H. Wu et al. J. Phys.: Condens. Matter 12 (2000) 2847

-0.02

0.00

0.02

EFM2

ENM

EFM1

ETOT

0 1 2 3 4 5 6 7d NM

60

30

0

30

60 T1/ max

FM coupled

AFM coupled

1/m

ax (

arbi

trary

uni

t)

-0.010

-0.005

0.000

0.005

T=0oK

T=250oK

(c)

(a)

(b)

χ

χ

T (

o K)

∆

∆

∆∆∆∆

E=E

AFM

EFM

(eV

/ML)

∆-

+

+

Single band Hubbard model: Simple Hartree-Fock (Stoner) ansatz is insufficientHigher order correlations are needed to explain TC-shift

Enhanced spin fluctuations in 2D (theory)

∆T

/ T

CN

i

3 K

1 K

1 2

Co/Cu/Nitrilayer

d (ML)Ni

J =3 Kinter

MF

0 3 4 5 60.0

0.3

0.6

0.9 Tyablikov (or RPA)decoupling

, mean field ansatz (Stoner model) is insufficientto describe spin dynamics at interfaces of nanostructures S S ⟨ ⟩i j

+z

⟨⟨ ⟩⟩S Si j + −∂

∂t →Spin-Spin correlation function

S i S S S S S S S j i i j i j i≈ − ⟨ ⟩ − ⟨ ⟩ +⟨ ⟩S S i j+ + + + ++− −z z

RPA…

P. Jensen et al. PRB 60, R14994 (1999)


FM1 (Ni)

FM2 (Co)

NM (Cu)

IEC ~ 1dNM

2

dNM

dFM1

Jinter

2D sp

in

fluctu

ation

s

∆TC, Ni

Evidence for giant spin fluctuations PRB 72, 054447, (2005)


3. Determination of orbital- and spin- magnetic moments

Which technique measures what?

µL , µS in UHV-XMCD

µL + µS in UHV-SQUID

µL / µS in UHV-FMR

per definition:

1) spin moments are isotropic

2) also exchange coupling J S1·S2 is isotropic

3) so called anisotropic exchange is a (hidden)projection of the orbital momentum intospin space

For FMR see: J. Lindner and K. BaberschkeIn situ Ferromagnetic Resonance:An ultimate tool to investigate the coupling in ultrathin magnetic filmsJ. Phys.: Condens. Matter 15, R193 (2003)


−≡−−≡ −− 222)2( 2/1

2ψ

Orbital magnetism in second order perturbation theory

The orbital moment is quenched in cubic symmetry

⟨2- LZ 2-⟩ = 0,

but not for tetragonal symmetry

effective Spin Hamiltonian

L± • S

LZ • SZ

+λL • S +_

d1

W.D. Brewer, A. Scherz, C. Sorg, H. Wende, K. Baberschke, P. Bencok, and S. Frota-PessoaDirect observation of orbital magnetism in cubic solidsPhys. Rev. Lett. 93, 077205 (2004)andW.D. Brewer et al. ESRF – Highlights, p. 96 (2004)


Orbital and spin magnetic moments deduced from XMCD

H. Ebert Rep. Prog. Phys. 59, 1665 (1996)

860 880 900

L2 edgeL

µLµS

3 e dge

Ninorm

.XM

CD

(arb

.uni

ts)

Photon Energy (eV)

µLµS

dELL )2( 23 µµ ∆−∆∫

dELL )( 23 µµ ∆+∆∫

?

??

/µ

µL

S

Fe40 Fenm Fe 4 /V4 Fe2/V54 / V2

bulk Fe

0

0.06

0.12/FMR: (Fe+V)

XMCD: (Fe)µ µL / S

XMCD(V)µ µL / S

µSµ L

510 520 530 700 720 740-1

0

1

2

FeV

x5

prop. µL

prop. µS

Photon Energy (eV)

g<2 g>2

µS µL µS µ L

L3 L2

XM

CD

Inte

gral

(ar

b. u

nits

)( ) ( )( ) d

Zdh

2L3L

dZ

dZd

h2L3L

L2NN

dE

T7S23N

NdE2

∫

∫

=+

+=⋅−

? µ? µ

? µ? µ


Enhancement of Orbital Magnetism at Surfaces: Co on Cu(100)

λ

λλ

/10

/)2(3

/)1(

expnDd

n

nDdn

dD

S

L

eCeBAe

MM

−−=

−−=

−−

Σ+Σ+

=

M. Tischer et al., Phys. Rev. Lett. 75, 1602 (1995)


Giant Magn. Anisotropy of SingleCo Atoms and Nanoparticles

P. Gambardella et al., Science 300, 1130 (2003)

Induced magnetism in molecules

n = number of atoms

T. Yokoyama et al., PRB 62, 14191 (2000)

XMCD

XMCD

CO

~531 eV e-

∼10ML NiCu

µ

µL


1. Magnetic anisotropy energy = f(T)

2. Anisotropic magnetic moment ≠ f(T)

≈ 1µeV/atom is very small compared to≈ 10 eV/atom total energy but all important

B (G)

100

100 20000

500

300

300

M (G

)

[111]

[100]

Ni[100]

[111]

0.1 G∆µL ~~

Characteristic energies of metallic ferromagnets

binding energy 1 - 10 eV/atom

exchange energy 10 - 103 meV/atom

cubic MAE (Ni) 0.2 µeV/atom

uniaxial MAE (Co) 70 µeV/atom

K. Baberschke, Lecture Notes in Physics, Springer 580, 27 (2001)

anisotropic µL ↔ MAE

ξLSMAE ∝ ∆µL4µB

Bruno (‘89)

g|| - g⊥ = geλ(Λ⊥-Λ||)

D= ∆gλge

MAE = ?M·dB ˜ ½ ?M·?B ˜ ½ 200 · 200 G2

MAE ˜ 2·104 erg / cm3 ˜ 0.2 µeV / atom

Magnetic Anisotropy Energy (MAE) and anisotropic µL


O. Hjortstam, K. B. et al. PRB 55, 15026 (’97)

-0.005 0.000 0.005 0.010

-100

0

100

200

α =1α =0.05

Ni

c/a=1.08

c/a=0.69c/a=0.79

K (µ

eV)

V

∆ Orbital moment (µ )B

K(µ

eV

/ato

m)

VO

rbita

l mo

me

nt

B(

/ato

m)

µ

0.75 0.85 0.95 1.05

0.05

0.06

0.07

SO (001] SO+OP [110] SO+OP [001]

SO[110]

bcc fcc

-100

0

100

200

300

400

500

exp.

c/a

Magnetic Anisotropy Energy MAE and anisotropic µL


Ni and Pt carry a magnetic moment

No ‘dead’ Ni layers F. Wilhelm et al. PRL 85, 413 (2000) and ESRF Highlights 2000

Magnetic momentprofile for a Ni6/Pt5 ML

Ni

Pt

4. Induced magnetism at interfaces

1 2 3 4 5 6 7 8 9 10 110.0

0.2

0.4

0.6

theory

(b)bulk Ni TB-LMTO

Monolayers

0.0

0.2

0.4

0.6

experiment

(a)bulk Ni

Ni Pt

Mag

net

ic M

om

ent

(µ /

ato

m)

B

Ni

Ni

NiPt

Pt

Pt

Unitcell

PtNi

N

825 850 875 900

-2

0

2

4

(b)

x2 XANES XMCD

Energy (eV)

L 2

L3

Inte

nsi

ty (a

.u.)

Ni L-edgesNi2/Pt2

11.5 11.6 13.2 13.3

-0.4

0.0

0.4

0.8

(a)

x10

x10

L2

L3

XANES

XMCD

Energy (keV)

Inte

nsi

ty (a

.u.)

Pt L-edges

Ni2/Pt2


Induced magnetism in 5d-transition metals breakdown of 3rd Hund’s rule ?

F. Wilhelm et al.,Phys. Rev. Lett. 87, 207202 (2001)

alternatively: details of SP-DOS; hybridization

Fe

WλinterSZ LZ

.. Fe WJinterSZ SZ

.. Fe W

µS

µS λintra SZ LZ.. W W µL

Jinter SZ SZ.. Fe W λ interSZ LZ

.. Fe Wλintra SZ LZ

.. W W> >

10.16 10.20 10.24 11.52 11.56 11.60-5

0

5

10

15

mS

Sm Lm

Lm

W

x 2

x 50

L2

x 50

L3

XA

S,X

MC

D(a

rb.u

nits

)

Photon Energy (keV)

XMCD-Integral

Experiment

Expected from3 Hund’s rulerdFe/W interface


Fe/V/Fe(110)Trilayer

L 3,2

x 15

V FeL 3,2

µ+

µ

µ - µ (highlighted)+

520 540 700 720 740-2

0

2

4

norm

.XA

S,X

MC

D(a

rb.u

nits

)

Photon Energy (eV)

Advantages:controlable growth

• annealing to reduce surface roughness• preparation at 300 K

In-situ experiment, i.e. no capping layers

XMCD measurements:• BESSY II, third generation

synchrotron source inBerlin

• Newly developed ‘gapscan’mode: High degree ofcircularly polarized lightand high photon flux

5 MLFe

Fe

1< <8 MLn

~50ML

Cu(001)

µS

µS

µL

µL


510 520 530 540

-0.1

0.0

0.1

0.2

0.3

x2.23

C

B

A

norm

. XM

CD

(arb

. uni

ts)

Photon Energy (eV)

0

2

4

6

norm

. XA

S (a

rb. u

nits

)

V L3,2 edges

Fe/V3/Fe trilayer Fe90V10 alloy

D

E

E

a)

b)

Energy (eV)

V L3,2 edges

XA

S (a

rb. u

nits

)X

MC

D (

arb.

uni

ts) Fe 90V10 alloy: L 3,2 edge

a)

b)-10 0 10 20 30

-0.2

0.0

0.2

0.40

2

4

6

8

L2 edge Fe/V3/Fe trilayer

x6

A

B

C

D

525 530 5351.0

1.2

1.4

1.6

1.8

2.0 no oxygen !

exp.

theory

ExperimentA. Scherz et al.

TheoryJ. Minar, D. Benea, H. Ebert, LMU

PRB 66, 184401 (2002)

5. Full calculation of µ(E)


Sum rules and beyond* Gerrit van der Laan

Daresbury Laboratory ,Warrington WA 4 4AD ,UKAbstractSum rules relate the integrated signals of the spin-orbit split core levels to ground state properties, such as the spin-orbit coupling, magnetic moments and charge distribution. These rules give the zeroth moments of the spectral distribution. It is shown how this can be generalized to higher-moment statistical analysis … .Journal of Electron Spectroscopy and Related Phenomena 101–103 (1999) 859–868

Beyond sum rules: full calculation of µ(E)

Photon Energy (eV)

Nor

mal

ized

XM

CD

(arb

. uni

ts)

510 515 520 525 530-0.25

0.00

0.25

0.50 Fe/V/Fe

experiment

multipole-momentanalysis

SPR-KKR


single pole double pole

double pole approximation (time-dependent DFT)

Petersilka et al. PRL (1996) 1212 Atoms ( S )

761 →1P

PhD thesis A. ScherzL edges metals3,2

-5 0 5 10 15 20 25

Relative Photon Energy (eV)

Abs

orpt

ion

(arb

. uni

ts)

-5 0 5 10 15 20 25

L

XA

S (

arb.

uni

ts)

Relative Photon Energy (eV)

2,3

L2L3

0

unperturbed

unperturbed

perturbed perturbed

ground-state density

frequency-dependent perturbation

linear response theory

M11 M22

↓

⇓

•

•

perturbed resonances shift to higher energies

spectral weight is shifted L L branching ratio3 2→ ⇒

Ti

• energy shift of perturbed resonances• shift of spectral weight L3 → L2(branching ratio)

),,(|'|

),,(2

ωω r'rr'r xcfrr

eK +

−=

⇓

double pole approximation (time-dependent DFT)

determinematrix elements


6

8

10

12

14

16

6 8 10 12 14 16unperturbed (eV) ∆ω

Ti

V

Cr

Fe

Co

Ni

statistical branching ratio

Ti V Cr Mn Fe Co Ni

Bra

nchi

ng R

atio

0.4

0.5

0.6

0.7

0.8

L2L3

perturbed

∆ω

∆Ω

pert

urbe

d (

)∆

Ω e

V

experiment: L XAS 3,2••

→ ∆Ω binding energies* → ∆ω

∆ω−∆Ω

∆ω−∆ΩnH

≈ 0.125 eV/hole

⇒ double pole model describes branching ratio quite well

⇒ regime where sum rules fail

Ti: M =1.70 eV, M =0.8 eV11 22

experiment

DPA

experiment

DPA

*Fuggle and Mårtensson, J. Electr. Spectr. Relat. Phenom. (1980) 27521

Ti: M11=3.07 eV, M22=-0.56 eV, M12=0.54 eV

double pole model describesbranching ratio for light 3d’sKohn Sham energies → ∆ω

A. Scherz, et al. Measuring the kernel of time-dependent density functionaltheory with X-ray absorption spectroscopy of 3dtransition metalsPhys. Rev. Lett. 95, 253006 (2005)


1) intergral SR 2) MMA 3) calculation of full µ(E)

• gap-scan technique ⇒ systematic investigation of XAS, XMCD fine structure• development double pole approximation

⇒ correlation energies (Ti: M11=3.07 eV, M22=-0.56 eV, M12=0.54 eV)

• experiment ⇒ failure of spin sum rule ↔ core-hole interaction • theory ⇒ correlation energies as input for theory

⇒ future ab initio calculations must includecore-hole correlation effects

H. Wende, Rep. Prog. Phys. 67 (2004) 2105-2181

ü

Summary

see: Recent advances in x-ray absorption spectroscopy


• All spectroscopic techniques do not restrict themselves tomeasure the intensity (area under the resonance) only. i.e.: integral sum rules.

• A resonance signal contains a resonance position, a width,an asymmetry profile, etc.

• The optimum is given if theory can calculate the full profileof the resonance, in our case µ(E) i.e. the spectral density.

Recent advances in x-ray absorption spectroscopy H. Wende , Rep. Prog. Phys. 67, 2105 (2004)


A. Scherz et al., XAFS XII June 2003 Sweden, Physica Scripta T115, 586 (2005)A. Scherz et al., BESSY Highlights p. 8 (2002)

L2,3 XAS and XMCD of 3d TM‘s

450 46 0 470 48 0

-2

0

2

4

510 520 530 540 570 580 590 600

-2

0

2

4

700 720 740

-2

0

2

4

780 800 82 0

norm

aliz

ed X

AS,

XM

CD

(arb

. uni

ts)

840 86 0 880

-2

0

2

4

Ti

Photon Energy (eV)

V Cr

Fe Co Ni

x10 x5x15

Ti V Cr Fe Co NiSc Mn Cu Zn


Conclusion, Future

During last few years: enormous progress in

• calculate µ(E), spin dependent spectral distribution

• full relativistic calculations

• real (not ideal) crystallographic structures

• higher ∆E/E, detailed dichroic fine structure

• undulator, gap-scan technique, constant high PC

• element-selective microscopy, probe of “non-magnetic” constituents

• core hole effects:

→ change of branching ratio for early 3d elements

→ effect on XMCD unknown!

• correct determination of ∆ µL and MAE with XMCD (x30)

• correction for spin- and energy-dependence of matrix elements

Theory:

Experiment:

Future:

magnetic dichroism in xas and its...

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