Magnetic dichroism in XAS and its...

Freie Universität Berlin Hercules A15 / Trieste / 17.3.05 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 µorb.

4. Induced magnetism at interfaces.

Magnetic Magnetic dichroismdichroism in XASin XASand its applicationand its application

Freie Universität Berlin Hercules A15 / Trieste / 17.3.05 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.

• 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 (

arb.

uni

ts)

Nor

m. X

AS

(arb

. uni

ts)

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

1 2

32

+h −h

kM

2p12

2p 32

3d 32

3d 52

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

12−3

2− 12+ 3

2+12− 1

2+


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

There are many 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

(arb

.uun

its)

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

(arb

. uni

ts)

0

200

400 Ni L3,2Co L3,2

x 1.72

no

rm.

ab

sorp

tion

(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 (µ

eV/a

tom

)

d (ML)Cu

FMR / / / /

/ / /

→

→XMCD / / /→

Cu Cu Cu(001)

Cu Cu(001)Cu Cu(001)

FMR

Ni Ni

NiNiCo

Co

a)b)c)

Interlayer exchange coupling

T*Ni

M (

arb.

uni

ts)

TCNi = 275K

2.8 ML Cu4.8 ML NiCu(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 Scripta 2005

e_

IP

+HV

hνHstatisch

-0.2

-0.1

0.0

0.1

0.2

Mag

net

ization (

arb.

unit

s)

Magneti c Field (Oe)-40 -20 0 20 40

281 K

265 K184 K

5 ML Cu6 ML Ni

Cu (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 (k

A/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 /

TC

Ni

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 (to be published)


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)


−≡−−≡ −− 2}22{)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


Orbital and spin magnetic moments deduced from XMCD

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

860 880 900

L2 edgeL

µLµS

3 e dg e

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

µSµL

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 µL

L3 L2

XM

CD

Inte

gral

(ar

b. u

nits

)( ) ( )( ) d

Zdh

2L3L

dZ

dZd

h2L3L

L2N

NdE

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


anisotropic µL ↔ MAE

ξLSMAE ∝ ∆µL4µBBruno (‘89)

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

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

B (G)

100

100 20000

500

300

300

M (G

)

[111]

[100]

Ni[100]

[111]

0.1 G∆µL ~~

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 µorb


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(

/a

tom

)

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

500ex

p.

c/a

Magnetic Anisotropy Energy MAE and anisotropic µorb


Quadrupolar effects (E2)

Rare earth metals:

(5d)

• highly localized 4f states • ordering by exchange interaction via magnetized conduction band

XMCD at L edges:3,2 electric dipolar transitions E1: 2p ( l=1) ( l=2)

∆∆

5d4fand electric quadrupolar transitions E2: 2p

Literature: rare earth compounds (3d,4f) Bartolomé, Tonnerre et al., Phys. Rev. Lett. , 3775 (1997) Giorgetti, Dartyge et al., Appl. Phys. A, , 703 (2001)• •

7973

µ ρ(E) |M (E)| (E)fi2

∝

Tb foil: G. Schütz et al: Z. Phys. B: Condens. Matter (1988) 6773

but: E2 contributions neglectedTheory: • H. Ebert et al., Solid State Comm. (1990) 475

• Xindong Wang, P. Carra et al., Phys. Rev. B (1993) 9087

76 47

⇒”simple model for interpretation in terms of spin-polarization of the d-band - in contrast to transition metals - ”is not justified

5d

4f

2p3/2

2p1/2

7512.5

7517.5

8249.0

8254.0~5 eV

~736.5 eV

L3 L2

{

{


Tb XMCD at L3,2-edges

7500 7520 7540 8240 8260 8280

-0.01

0.00

E2

E2

XMC

D(a

rb.u

nits

)

Photon Energy ( eV )

0.0

0.5

1.0 µ+

µ-

Abso

rptio

n(a

rb.u

nits

)

10 K, 7 T

L3

L2

µ

µ

C

0/

E (eV)

0

0.02

0.04

-0.0 4

-0.02

Abs

orpt

ion

• XMCD of single element magnetTb single crystal

• High resolution at ESRF (ID 12A):

fine structurefree of noise

Pioneer experiment:G. Schütz et al.Z. Phys. B:Condens Matter73 (1988) 67


Separation E1 ↔ E2 contributions

• FEFF8*: - self-consistent- full multiple scattering in real-space

details of5d spin polarized DOS

H. Wende et al., and J.J. Rehr et al., J. Appl. Phys. 91, 7361 (2002)and Highlights ESRF p. 84 (2003)

• Separation of E1 and E2 contributionsby switching on/off the E1,2 contributionin the calculation

7500 7520 7540 8240 8260 8280

-0,01

0,00

0,01

Experiment Theory E1 Theory E2

Nor

mal

ized

XMC

D(a

rb.u

nits

)

Photon Energy ( eV )


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 /a

tom

)B

Ni

Ni

NiPt

Pt

Pt

Unitcell

PtNi

N

825 850 875 900

-2

0

2

4

(b)

x2 XANES XMCD

Energy (eV)

L2

L3

Inte

nsity

(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 WJi nterSZ SZ

.. Fe W

µS

µS λintra SZ LZ.. W W µL

JinterSZ SZ.. Fe W λ interSZ LZ

.. Fe W λint ra 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 al loy: 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 !

ex p.

theory

ExperimentA. Scherz et al.

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

PRB 66, 184401 (2002)

Beyond sum rules: 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


• 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;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 59 0 600

-2

0

2

4

700 720 740

-2

0

2

4

780 800 82 0

norm

aliz

ed X

AS,

XM

CD

(ar

b. u

nits

)

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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