size- and site-dependence of xmcd spectra of iron clusters...

26
Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations O. ˇ Sipr 1 and H. Ebert 2 1 Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnick ´ a 10, 162 53 Prague, Czech Republic 2 Universit ¨ at M ¨ unchen, Department Chemie, Butenandtstr. 5-13, D-81377 M ¨ unchen, Germany – p.1/18

Upload: others

Post on 19-Jun-2020

1 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Size- and site-dependenceof XMCD spectra of iron clusters

from ab-initio calculationsO. Sipr1 and H. Ebert2

1 Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnicka 10,

162 53 Prague, Czech Republic2 Universitat Munchen, Department Chemie, Butenandtstr. 5-13, D-81377 Munchen,

Germany

– p.1/18

Page 2: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

What are the clusters about?

Clusters mark the transition between atoms, surfaces and bulksystems

Interesting phenomena (and a lot of fun) can be expected

We concentrate on their magnetic properties and on how do theyget revealed through XMCD

– p.2/18

Page 3: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Magnetic properties of iron

atom surface bulk

mspin = 4 µB mspin = 2.5–3.0 µB mspin = 2.2 µB

morb = 2 µB morb = 0.07–0.12 µB morb = 0.05 µB

(clusters go in between)

Clusters contain a high portion of surface atoms⇒ ought to have larger magnetic moments.

– p.3/18

Page 4: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Magnetic properties of iron

atom surface bulk

mspin = 4 µB mspin = 2.5–3.0 µB mspin = 2.2 µB

morb = 2 µB morb = 0.07–0.12 µB morb = 0.05 µB

(clusters go in between)

Clusters contain a high portion of surface atoms⇒ ought to have larger magnetic moments.

– p.3/18

Page 5: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Magnetism of iron clusters (1)

Selected knowledge about iron clusters containing 25–700 atoms:

Stern-Gerlach-type experiments [Billas et al. PRL 71, 4067 (1993)]−→ average total magnetic moment per atom is larger in clustersthan in bulk,

mtot = mspin + morb ≈ 2.2 –3.1µB ,

and approaches the bulk limit in an oscillatory way.

– p.4/18

Page 6: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Magnetism of iron clusters (2)

Theoretical results on the site-dependence of magnetic momentsof atoms in clusters (“magnetic profile”) differ quite a lot one fromanother.

2.9 µB

2.2 µB

2.5 µB

2.5 µB2.5 µB

2.5 µB

2.9 µB

2.9 µB

2.9 µB

2.9 µBCh.Y. Yang et al. Phys. Rev. B 24,5673 (1981)

G.M. Pastor et al. Phys. Rev. B 40,7642 (1989)

A. Vega et al. Phys. Rev. B 47, 4742(1993)

J.A. Franco et al. Phys. Rev. B 60, 434(1999)

– p.5/18

Page 7: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Can XMCD help?

Is there a way to learn more about cluster magnetism through XMCDspectra?

Through the sum rules, XMCD can inform about mspin and morb

separately. Even more reliably, about the ratio morb/mspin.

Experiments on supported clusters suggest an essentialenhancement of morb and of morb/mspin in comparison with bulk(mspin remains unchanged or even decreases).

[K.W. Edmonds et al. Phys. Rev. B 60, 472 (1999); P. Ohresser et al.Phys. Rev. B 62, 5803 (2000).]

– p.6/18

Page 8: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Our aim

The task we subscribed to:

Calculate the magnetic structure and Fe L2,3 edge XMCD spectraof free iron clusters

Compare calculated spectra for different cluster sizes one withanother and with the bulk

Search for “markers of clusterization”

– p.7/18

Page 9: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

System we study

free spherical-like clusters with geometry taken as if they were cutfrom a bcc Fe crystal

cluster size range between 9 atoms (one coordination shell) and89 atoms (seven coordinations shells)

helicity of the incoming photons parallel or antiparallel with thecluster magnetization (coincides with the [001] direction in theparental crystal)

magnetization

photon helicity

parallel

antiparallel [001]

x-rays

we focus on iron only [visit the Thursday 11:45 talk in the Materialssection to learn more about other systems]

– p.8/18

Page 10: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Theoretical formalism

magnetic moments and XMCD spectra calculated in real space viaa fully-relativistic spin-polarized multiple-scattering technique asimplemented in the SPRKKR code[H. Ebert: in “Electronic structure and physical properties of solids”(Springer, Berlin 2000), vol. 535, p. 191]

spherical ASA approximation, clusters surrounded by emptyspheres

scattering potential obtained from SCF-Xα calculations applied tomolecular clusters

total XMCD of a cluster obtained by superposing calculated XMCDsignals from all the constituting atoms

details in Šipr and Ebert, Czech. J. Phys. 53, 55 (2003)

– p.9/18

Page 11: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Magnetic moments of clusters (1)

• Average spin magneticmoments do not approachbulk limit for clustersof . 100 atoms.

Different calculations by differ-ent authors provide different os-cillatory structure

0 20 40 60 80 100number of atoms in cluster

2.0

2.2

2.4

2.6

2.8

3.0

spin

mag

netic

mom

entp

erat

om[

B]

average mspin

bulk limit

– p.10/18

Page 12: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Magnetic moments of clusters (2)

• Average orbital magneticmoments have hot con-verged to bulk values ei-ther . . .

0 20 40 60 80 100number of atoms in cluster

0.0

0.05

0.1

0.15

0.2

0.25

orbi

talm

agne

ticm

omen

tper

atom

[B]

average morb

bulk limit

– p.11/18

Page 13: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Magnetic moments of clusters (3)

[ ] / [ ]

• The ratio morb/mspin

attains bulk values forclusters larger than≈60 atoms !

0 20 40 60 80 100number of atoms in cluster

0.0

0.02

0.04

0.06

0.08

ratio

betw

een

mor

ban

dm

spin

morb /mspin

bulk limit

– p.12/18

Page 14: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Conflict with experiment ?

Theory: Ratio morb/mspin converges to bulk forN ≈ 60 atoms.

Experiment: For clusters of few hundreds ofatoms the ratio morb/mspin as deduced via sumrules is about twice as high as in the bulk![K.W. Edmonds et al. Phys. Rev. B 60, 472(1999); P. Ohresser et al. Phys. Rev. B 62, 5803(2000).]

0 20 40 60 80 100number of atoms in cluster

0.0

0.02

0.04

0.06

0.08

ratio

betw

een

mor

ban

dm

spin

morb /mspin

bulk limit

???

There is no need for a contradiction!

→ Experiment investigated supported clusters — rather flat thanspherical, large portion of edge atoms.

→ Our calculations deal with free clusters.

– p.13/18

Page 15: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

No real conflict with experiment. . .

Theory: Ratio morb/mspin converges to bulk forN ≈ 60 atoms.

Experiment: For clusters of few hundreds ofatoms the ratio morb/mspin as deduced via sumrules is about twice as high as in the bulk![K.W. Edmonds et al. Phys. Rev. B 60, 472(1999); P. Ohresser et al. Phys. Rev. B 62, 5803(2000).]

0 20 40 60 80 100number of atoms in cluster

0.0

0.02

0.04

0.06

0.08

ratio

betw

een

mor

ban

dm

spin

morb /mspin

bulk limit

???

There is no need for a contradiction!

→ Experiment investigated supported clusters — rather flat thanspherical, large portion of edge atoms.

→ Our calculations deal with free clusters.

– p.13/18

Page 16: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

XMCD of iron clusters

• Splitting of the bulk L3

peak not seen inexperiment (but present infull-potential calculations).Energy resolution?

• Narrowing andenhancement of mainpeaks (more apparent atL3 than at L2).

• Peaks tilted towards thelow-energy side.

• Small positive peak just af-ter the main L3 minimum.

0 5 10 15energy [eV]

Fe

L 2,3

edge

XM

CD

(per

atom

)

bulk

– p.14/18

Page 17: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

XMCD of iron clusters

• Splitting of the bulk L3

peak not seen inexperiment (but present infull-potential calculations).Energy resolution?

• Narrowing andenhancement of mainpeaks (more apparent atL3 than at L2).

• Peaks tilted towards thelow-energy side.

• Small positive peak just af-ter the main L3 minimum.

0 5 10 15energy [eV]

Fe

L 2,3

edge

XM

CD

(per

atom

)

bulkclusters

15 atoms[2 shells]

27 atoms[3 shells]

89 atoms[7 shells]

– p.14/18

Page 18: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

XMCD of iron clusters

• Splitting of the bulk L3

peak not seen inexperiment (but present infull-potential calculations).Energy resolution?

• Narrowing andenhancement of mainpeaks (more apparent atL3 than at L2).

• Peaks tilted towards thelow-energy side.

• Small positive peak just af-ter the main L3 minimum.

0 5 10 15energy [eV]

Fe

L 2,3

edge

XM

CD

(per

atom

)

bulkclusters

15 atoms[2 shells]

27 atoms[3 shells]

89 atoms[7 shells]

– p.14/18

Page 19: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Where have all the structures gone?

Fe(001) surface Fe2Cu6 (001) multilayer

[Wu et al. PRL 71, 3581 (1993)] [Guo et al PRB 50, 3861 (1994)]

0 5 10 15energy [eV]

Fe

L 2,3

edge

XM

CD

(per

atom

)

bulkclusters

15 atoms[2 shells]

27 atoms[3 shells]

89 atoms[7 shells]

Calculated XMCD of surface or multilayers exhibit quite a pronouncedfine structure at the Fe L3 and L2 edges.

Calculated XMCD of clusters display no such fine structure.

– p.15/18

Page 20: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Where have all the structures gone?

Fe(001) surface Fe2Cu6 (001) multilayer

[Wu et al. PRL 71, 3581 (1993)] [Guo et al PRB 50, 3861 (1994)]

0 5 10 15energy [eV]

Fe

L 2,3

edge

XM

CD

(per

atom

)

bulkclusters

15 atoms[2 shells]

27 atoms[3 shells]

89 atoms[7 shells]

Calculated XMCD of surface or multilayers exhibit quite a pronouncedfine structure at the Fe L3 and L2 edges.

Calculated XMCD of clusters display no such fine structure.

– p.15/18

Page 21: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Where have all the structures gone?

Fe(001) surface Fe2Cu6 (001) multilayer

[Wu et al. PRL 71, 3581 (1993)] [Guo et al PRB 50, 3861 (1994)]

0 5 10 15energy [eV]

Fe

L 2,3

edge

XM

CD

(per

atom

)

bulkclusters

15 atoms[2 shells]

27 atoms[3 shells]

89 atoms[7 shells]

Calculated XMCD of surface or multilayers exhibit quite a pronouncedfine structure at the Fe L3 and L2 edges.

Calculated XMCD of clusters display no such fine structure.

– p.15/18

Page 22: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

The wiggles cancel each other!

center

1st shell

2nd shell

3rd shell

Fe cluster 27 atoms

view in Z direction

Spectrum of the whole clusteris a superposition of signalsfrom all individual atoms

Magnetization decreases thesymmetry → more inequiva-lent atomic sites in a singleshell

0 5 10 15energy [eV]

Fe

L 2,3

edge

XM

CD

ofin

divi

dual

atom

s

27-atoms cluster

central

1st shell

2nd shell

3rd shell

– p.16/18

Page 23: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

The wiggles cancel each other!

center

1st shell

2nd shell

3rd shell

Fe cluster 27 atoms

view in Z direction

Spectrum of the whole clusteris a superposition of signalsfrom all individual atoms

Magnetization decreases thesymmetry → more inequiva-lent atomic sites in a singleshell

0 5 10 15energy [eV]

Fe

L 2,3

edge

XM

CD

ofin

divi

dual

atom

s

27-atoms cluster

central

1st shell

2nd shell

3rd shell

– p.16/18

Page 24: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Yet another look at XMCD profiles

outermost atom (min symm)outermost atom (maj symm)central atomwhole cluster

Individual spectra of thecentral atoms and of theatoms of the outermostshell

Pronounced features mu-tually cancel and/or getsmeared if they are super-posed

No unique pattern, no gen-eral rule

energy [eV]

norm

aliz

edF

eL 2

,3ed

geX

MC

D

L3 L2

-2 0 2

15 atoms

27 atoms

89 atoms

12 14

– p.17/18

Page 25: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Yet another look at XMCD profiles

outermost atom (min symm)outermost atom (maj symm)central atomwhole cluster

Individual spectra of thecentral atoms and of theatoms of the outermostshell

Pronounced features mu-tually cancel and/or getsmeared if they are super-posed

No unique pattern, no gen-eral rule

energy [eV]

norm

aliz

edF

eL 2

,3ed

geX

MC

D

L3 L2

-2 0 2

15 atoms

27 atoms

89 atoms

12 14

– p.17/18

Page 26: Size- and site-dependence of XMCD spectra of iron clusters ...sipr/posters/xafs12_clusters_03.pdf · Size- and site-dependence of XMCD spectra of iron clusters from ab-initio calculations

Conclusions

The ratio morb/mspin converges in clusters quickly towards bulkvalues

XMCD spectra of clusters distinguish from XMCD of bulk throughleaner and enhanced peaks

Bold fine structure in XMCD of individual atoms gets smeared inthe combined spectrum of whole cluster

Small yet distinct positive hump just after the L3 peak — a generalmarker of clusterization ?

– p.18/18