Lecture 5: X-ray Absorption Spectroscopy:Introductionusers.physik.fu-berlin.de/~bab/teaching/Fudan2005/Fudan2005-5.pdf · Lecture 5: X-ray Absorption Spectroscopy:Introduction L 3,2

1K. Baberschke FU Berlin „Lectures on magnetism“ #5, Fudan Univ. Shanghai, Oct. 2005

Lecture 5: X-ray Absorption Spectroscopy: Introduction

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


References

• 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 magnetizationMany 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

2p 1 22p 3 2

3d 32

3d 52

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)

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

NiNiCoCo

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

izat

ion (

arb. units)

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

281 K

265 K184 K

5 ML Cu6 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 (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 60.0

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 (PRB 72, 054447 (2005)


Crossover of MCo(T) and MNi(T)

Two order parameter of TCNi and TC

Co

A further reduction in symmetry happens at TClow

760 800 840 880-60

-40

-20

0

20

x2

Nor

m.X

MC

DD

iffer

ence

(arb

.uni

ts)

Photon Energy (eV)

Cu(001)

2.1ML Cu

4ML Ni

Cu(001)

2.1ML Cu

4ML Ni

1.3ML Co

-edgesL3,2Co Ni -edgesL3,2

45K

0 40 80 120 160 200 2400

100

200

300

500

750

1000

Mag

netiz

atio

nM

(Gau

ss)

Temperature (K)

MNieasy

MCoeasy

H ,ext k

MNiAFM

[110]

[100]

Msat

M sat

2√

[110

]


Periodic alternation of ferro and non-magnetic layers

F Focus on the 5d induced magnetic moments

A large fraction of atoms are located at the interface

5d

5d

5d3d

3d

3dSoft and hard XMCD

Systematics: the induced magnetism in 5d Series (orbital magnetism) -Magnetic moments of W, Ir and Pt in multilayers

Comparison with 5d impurities in Fe matrix

F Full layer resolved magnetic profile in Ni/Pt multilayers

Probe the Interface MagnetismFe/V A. Scherz et al., Phys. Rev. B66, 184401 (2002)

2 Dimensional systems

Element specific XMCD, induced magnetism


Magnetization per NiMagnetization per Ni--volume: SQUID volume: SQUID -- XMCDXMCD

No 1/n dependence for Ni/Pt multilayer (predicted by MOKE) !

Group A (n > 4ML Ni)

Group B (n < 4ML Ni)

Bulk-like behaviour

Depends on Pt thickness

0.0 0.1 0.2 0.3 0.4 0.50

200

400

600

10K

4

5

2

5

2

10

4

2

Incr

easi

ng P

t thi

ckne

ss m

SQUID XMCD

group B

group A

3

n (ML-Ni)210 5

bulk Ni

Mag

netiz

atio

n (G

)

1/n

Ni

Ni

Ni

Pt

Pt

Pt


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 ∆+∆∫

?

??

( ) ( )( ) d

Zdh

2L3L

dZ

dZd

h2L3L

L2N

NdE

T7S23N

NdE2

∫

∫

=+

+=⋅−

? µ? µ

? µ? µ


NiNi22 / Pt/ Pt22 multilayermultilayer

Low Temperature Measurements10K

TC ~ 300K

• No ‘dead Ni layers’ at the interfaceµS

Ni=0.35 µB/atom µL

Ni=0.038 µB/atom• Strong induced magnetic moments in Pt

µSPt=0.14 µB/atom

µLPt=0.03µB/atom

Contrary to Kim et al.:Sputtering methods

(1-2 ML Ni ‘dead’ layers atthe interfaces)11.55 11.60 13.25 13.30

0.0

0.5

1.0

1.5 Pt L2

L3

µ (+) µ (-)N

orm

. XA

S (

a.u.

)

Photon Energy (keV)

-0.04

-0.02

0.00

0.02

0.04

XM

CD

(a.u.)

xmcd

840 860 880 900-4

-2

0

2

4 Ni

µ (+) µ (-)

Photon Energy (eV)

L2

L3

Nor

m. X

AS

(a.u

.)

-1.0

-0.5

0.0

0.5

1.0

1.5

XMCD

XM

CD

(a.u.)

ESRF ID12


11.55 11.60 13.25 13.30-0.08

-0.06

-0.04

-0.02

0.00

0.02 3T15K Pt

Ni6 / Pt

2

Ni2 / Pt

2

Ni2 / Pt

5

L2

L3

XM

CD

(arb

. uni

ts)

Photon Energy (keV)

Pt XMCD as a function of Ni and Pt thicknessPt XMCD as a function of Ni and Pt thickness

µµ

SNiL

Ni

µµ

SNiL

Ni

µPtL µS

Pt

<L z> = 0.056(3) µ

<Sz>=0.24(1) µ

(per Pt atom)To compare with

0.49 per Ni atomµ

B

B

B

Via the magneto-optical sum-rules

for Ni6/Pt2


Results for Results for NiNinn / / PtPtmm multilayersmultilayers

Ni n (ML) Pt m (ML) µ Ni

(µ B /atom)µ Pt

(µB /atom)

µ tot

per Ni-volume(µ B/atom)

2 2 0.39 0.17 0.56

2 5 0.24 0.09 0.47

6 2 0.49 0.29 0.59

6 5 0.47 0.17 0.61

13 5 0.54 0.21 0.62

bulk Ni 0.61 (Kittel)

Even samples with 2 ML of Ni separated by thicker Pt layers are magnetic. They would not be magnetic if alloyed (onset of ferromagnetism :>40 at. % Ni).

No magnetically ‘dead’ Ni layers at the interfaces.

Strong polarization of the Pt 5d electrons.(contributes of about 10-50% to the magnetization)

From Sum-Rules:

Ni

Ni

Ni

Pt

Pt

Pt


Ni

Ni

NiPt

Pt

Pt

Unitcell

PtNi

N

Magnetic profile of a NiMagnetic profile of a Ni66 /Pt/Pt55 multilayermultilayer

F. Wilhelm et al., Phys. Rev. Lett. 85, 413 (2000).P. Poulopoulos et al., J. Appl. Phys. 89, 3874 (2001).

1 2 3 4 5 6 7 8 9 10 110.0

0.2

0.4

0.6

theory

bulk Ni TB-LMTO

Monolayers

0.0

0.2

0.4

0.6

experiment

bulk Ni

Ni Pt

Mag

netic

Mom

ent

(µ /

atom

)B

Tota

l S

pin

Exp.

• Atomic Interface exchange processes between Pt and Ni (could leads to alloyed region at the interface)

• Reduction of Ni moment, Pt unaffected

Theory

• Lattice distortions neglected(1-5% in volume change 10% moment)

• Spin-only calculations(20% of orbital for Pt)

H. EbertMünchen

• S. Frota-Pessôa et al., Phy. Rev. B66, 132416(2002)Ni and Pt profile well reproducedassuming only 25% interface intermixing


Ebert group, 1990impurity

Ebert group, 1997impurity

Tyer et al., 2002layer

Wilhelm et al., 2001layer

calc

ulat

ion

expe

rimen

t Schütz group, 1993alloys

Hf Ta W Re Os Ir Pt Au

∗

µ L

“Breaking” alloys / impurity vs. layer Ni/Pt*

Fe/5dµ S

Calculation versus ExperimentCalculation versus Experiment


5c XMCD beyond integral sum rules

standard XMCD analysis fails (sum rules, MMA)for important elements:

• rare earth metals

• light 3d transition metals


rare earth L2,3 edge XMCD: Tb

• E1 (2p → 5d) and E2 (2p → 4f) contributions• spin-dependence of matrix elements

⇒ sum rules: wrong sign of 5d moment!

sum rule:

magnetometry:

4f 5d

4f 5d

10 K7 T

ESRF: ID12


3d transition elements

effect of core-hole correlations

→ on isotropic spectra:

• Zaanen et al., PRB 32 (1985) 4905• Schwitalla, Ebert, PRL 80 (1998) 4586• Ankudinov, Nesvizhskii, Rehr

PRB 67 (2003) 115120• Teramura, Tanaka, Jo, J. Phys. Soc. Jap. 65(1996) 1053: Mn, Fe, Co, Ni

But:

→ unknown on dichroic spectra of light 3d’s (Ti, V, Cr)

influence of core-hole interaction on early 3d L-edge spectra

Ti V Cr Fe Co NiSc Mn Cu Zn3d:

2p-3d core-hole interaction

e−

E

hν

2p3/2

2p1/2}∆E

early 3d: ∆E ≈ core-hole correlation energy

⇒ identification of pure 2p3/2 ↔ 2p1/2 states not possible

⇒ mixing


gap-scan technique at BESSY II → XMCD spectra with detailed fine structure

• A. Scherz PhD thesis FUB 2003

• A. Scherz, H. Wende, C. Sorg et al., BESSY-Highlights 2002, p. 8• A. Scherz, H. Wende, K. Baberschke, Appl. Phys. A 78 (2004) 843


standard XMCD analysis fails for early 3d elements

A. Scherz, H. Wende, K. Baberschke, J. Minár, D. Benea, H. Ebert, PRB 66 (2002) 184401

multipole-moment analysis failsintegral sum rule analysis fails

Cr: E. Goering et al PRL 88 (2002) 207203V: M. Sacchi et al PRB 60 (1999) R12569


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)


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


0 10 20 300

2

4

Nor

mal

ized

XA

S (a

rb. u

nits

)


Ti

V

Cr

FeCo

Ni

continuum

Bra

nchi

ng r

atio

statistical branching ratio

0.4

0.5

0.6

0.7

0.8

Ti V Cr Mn Fe Co Ni

experimental determination of branching ratio

core-holeinteraction

relativistic effectsin final states

branching ratio = Area L3

Area L3 + Area L2⇒

branching ratio independent of: lifetime broadening experimental broadening

••

experimental determination of branching ratio


A. Scherz, H. Wende, C. Sorg, K. Baberschke, J. Minar, D. Benea, H. EbertLimitations of integral sum rules for early 3d elementsXAFS12 proceedings Physica Scripta T115, 586 (2005)

Ti V Cr Mn Fe Co Ni0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

branching ratio DPA

/ (2/3)ratio

(

appa

rent

) /

(th

eo)

µµ

SS

• theory Ebert, Minar → µS(theo)• experiment + sum rule → µS(apparent)

• spin sum rule breaks down forstrong correlation effects

⇓


1) integral 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 include

core-hole correlation effects

Conclusion

see review article: H. Wende, Rep. Prog. Phys. 67 (2004) 2105-2181

ü

Lecture 5: X-ray Absorption Spectroscopy:Introductionusers.physik.fu-berlin.de/~bab/teaching/Fudan2005/Fudan2005-5.pdf · Lecture 5: X-ray Absorption Spectroscopy:Introduction L 3,2

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