Spettroscopie risonanti SILS06

Giacomo Ghiringhelli1

Spettroscopia risonante di stati elettronici: un approccio impossibile

senza i sincrotroni

XAS, XMCD, XES, RIXS, ResXPS:introduzione alle spettroscopie risonanti

Seminari sulla luce di sincrotrone - Università degli studi di Napoli “Federico II” - 5 e 6 luglio 2006(*) in sostituzione di Lucio Braicovich, Politecnico di Milano

Giacomo Ghiringhelli*Dipartimento di Fisica - Politecnico di Milano

Coherentia


Summary

Absorption edges and x-ray energies

XAS: x-ray absorption spectroscopy

Taking advantage of the polarisation of x-rays

XES: X-ray emission spectroscopy

RIXS: resonant inelastic x-ray scattering


Electromagnetic spectrum

UV andx-rays


Core levels

0 10 20 30 40 50 60 70 80 90 100

10

100

1000

10000

100000

O

4d5/24p3/23d5/2

3p3/22p3/21s

Fe Mo Th

Actinides

AuLuGdCe

RE

CdYZnSc

4dTM3dTMSiC

Har

d X

-Ray

sSo

ft X

-Ray

sU

V

Bin

ding

ene

rgy

(eV

)

Atomic number Z

K

L3

M3

M5


X-ray Absorption Cross Section

0.0

0.5

1.0

1.5

2.0

2.5

10 100 1000 10000

1E-4

1E-3

0.01

0.1

1

Cu K9000 eV

O K530 eV

Abs

orpt

ion

coef

ficie

nt (a

rb. u

.)

Photon Energy (eV)

CuOCu L2,3

930-950 eV

log scale

Linearscale


Resonances in the XAS

K edge 530 eV

3dEFermi

E

3p

2p

1s

1s

2sM2,3 edges (28-77 eV)

L2,3 edges (400-950 eV)

K edge (4.5-9.0 keV)

2p

3d TM Oxygen4sp

2p

Rare Earths

L2,3 edges (5.5-10 keV)

3d M4,5 edges (830-1580 eV)

5d4f

Strong resonances


3p: M2,3 edge XAS

Source: S. Nakai, et al PRB 9, 1870 (1974)

Spin-Orbitsplitting

Spin-Orbitsplitting


640 645 650 655 660

MnO

photon energy (eV)

Mn L2,3 XAS

La0.7Sr0.3MnO3

2p: L2,3 edge XAS

Spin-Orbitsplitting

Source: G. Ghiringhelli, N.B. Brookes et al unpublished Source: C. Aruta, G. Ghiringhelli et al unpublished

850 860 870 880

850 855 860

L2

Photon Energy (eV)

Ni metal

NiO

L3 L3

Ni metal

NiO

Spin-Orbitsplitting


Orbitals and XAS

2p

3p

3dThe radial integral is important!

( )( )Ω⋅=Φ⋅Φ ∫∫ dYYdrRRr irfifif uεrε **3


1s: Ni and Mn K edge XAS

Source: G. Subìas, et al PRB 56, 8183 (1997)Source: Z. Tan et al Phys. Rev. B 47, 12365 (1993)

NO Spin-Orbitsplitting

E0=8333eV


Cu K edge XAS

Source: Z. Tan et al Phys. Rev. B 47, 12365 (1993) Source: G. Liang, Phys. Rev. B 51, 1258 (1995)

E0=8980eV


EXAFS and NEXAFS


1s: Oxygen K edge XAS

Source: M. Abbate, et al Phys. Rev. B 46, 4511–4519 (1992)Source: P. Kuiper et al Phys. Rev. B 44, 4570–4575 (1991)

La2–xSrxNiO4+δ

NO Spin-Orbitsplitting


E

EF

Ev

Oxygen

1s

2p

Band model…

E

EF

Ev

3dTM

3p

2p

1s

4sp3d

hybridisation

XAS probes Density of Empty states

hνin hνin


and atomic model

Total E3dTM - O

|g>

2p53dn+2L2p53dn+1

3dn

3dn+1L

C.I. M.S.

M.S.: Multiplet Splitting

C.I.: Configuration Interaction

XAS probes orbital occupation


Crystal field

CubicOh

10Dq

eg

t2g

d states

xy, yz,zx

x2-y2, z2

SphericalO3

10Dq

eg

b2yz,zx

x2-y2

z2

xy

a1

b1

TetragonalD4h

x

y

z Cu: x -y orbital2 2


3d split states

xy

z

xy

z

xy

z

xy

z

xy

z

x2-y2 z2xy

yz

zx

b1 a1

b2

e

eeg states

t2g states


L3 XAS and multiplets

Ground state

EExcitation

hνin

2p3/2

3d

3d n 2p53d n+1

Excited states

NiO: 3d8 3d9

MnO: 3d5 3d6 Many peaks636 638 640 642 644 646

photon energy (eV)

MnO

CuO: 3d9 3d10 One single peak

928 930 932 934

Photon Energy (eV)

CuO


L3 XAS and valence

Cu metal: 3d104s1

L3

L2

Cu2O: Cu1+ is 3d10

CuO: Cu2+ is 3d9

Source: M. Grioni et al PRB 45, 3309 (1992)

930 935 940

Photon Energy (eV)

CuOCu2O

2.1 eV

Source: M. Finazzi et al PRB 61, 4629 (2000)


L3 XAS and cuprates doping

931 932 933 934 935 936 937

Cu L3 XAS

La2-xSrxCuO4

x=0.30 x=0.22 x=0.15 x=0.07 x=0.03 CuO

Photon energy (eV)

Source: G. Ghiringhelli, N.B. Brookes et al unpublished

Cu2+ 3d9

O2- : 2p6

Cu2+: 3d9

O1- : 2p5

Doped:Zhang-Rice singlet

3d9L

Source: Z. Hu et al Europhys. Lett. 59, 135 (2002)

3d9 3d9L

1.5 eV

By choosing the excitation on the main peak we select the 3d9 component

Undoped:3d9


Linear polarisation of x-rays

xy

z

xy

z

x2-y2 z2b1a1

E

hνin

Empty 3d stateE

High absorption

No absorption

E

hνin

E

No absorption

High absorption

Empty 3d state


3d hole symmetry in cuprates

hνθ

E

Result: the hole in Cu2+ has 100% x2-y2 symmetry

3d9 (2p3/2)33d10


Circular polarisation of x-rays

m=-1

z

RCP

m=1z

LCP

MXAS-MCD experimental geometry

sample

E

Fermi level3d

2p j=3/2j=1/2

z

M

LCP

RCP

m

XAS-MCD: x-ray absorption magnetic circular dichroism

number offree states

matrixelements

transitionrates

absorption

LCP RCP

3d

2p3/2

L3

M

L3: 2p3/2→3d

L2: 2p1/2→3d


XMCD

700 720 740 760 780 800 820 840 860 880 900-2

-1

0

1

2

3

4

5

6

7

8

Inte

nsity

(arb

. uni

ts)

Photon energy (eV)

-10

0

10

20

30

40

L2L3L2L3

Inte

grat

ed In

tens

ity (a

rb. u

nits

)

L2L3

Fe

∆(L3+L2)∆(L3)

Σ(L3+L2) Co

Σ(L3+L2)

∆(L3)∆(L3+L2)

Ni

∆(L3)∆(L3+L2)

Σ(L3+L2)

XAS-MCD: x-ray absorption magnetic circular dichroism


XES: emission after a resonant absorption

E

EF

Ev

3dTM

3p

2p

1s

4sp3d

XES probes Density of Occupied States

E

EF

Ev

3dTM

3p

2p

1s

4sp3d

hνin hνout


Resonant O K edge XES of cuprates

Source: L. Duda et al Phys. Rev. B 61, 4186 (2000)


RIXS: a resonant inelastic scattering

RIXS probes charge neutral local excitations

hνin

|g>

|i>

|f>

hνout

Etransferred=hνin-hνout

Charge Transfer

dd excitations3dn*

3dn+1L


RIXS (2)

hνin

polarisation

x

sample y

z

hνout e spin

out

Core level to Valence empty states transition

hνin = x-ray photon

Element selective

EExcitation

Groundstate

Intermediatestates

Final states

Time

De-excitations

hνin

hν

e

out

out

-7 -5 0-6 -4 -3 -2 -1 1

(C)

Relative emitted energy (eV)

Inte

nsity

(arb

. uni

ts)

elas

tic p

eak

excited states

Energy loss

It is a Raman measurement!

G, Ghiringhelli et al. PRB 73, 035111 (2006)


RIXS of Cuprates

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 20

10

20

30

40

50

60

70

80

NCCO

BSCCO

LSCO

SCOC

LCO

CuO

x2

x2

Inte

nsity

(pho

tons

/s/e

V)

Relative photon energy (eV)

0.0

0.5

1.0Cu L3

LSCO XAS

Source: G. Ghiringhelli, et al PRL 92, 117406 (2004)


dd excitations of cuprates

CubicOh

10Dq

eg

t2g

d states

xy, yz,zx

x2-y2, z2

SphericalO3

10Dq

eg

b2yz,zx

x2-y2

z2

xy

a1

b1

TetragonalD4h

“How much is the energy needed to move the hole from the x2-y2 to other orbitals?”

10Dq

eg

b2yz,zx

z2

xy

a1

b1x2-y2

eg

b2

a1

b1

eg

b2

a1

b1


Resonant Photoemission

E

3d

2p3/2

1/22p

E E E

hν

e e

Groundstate

Intermediatestate

Finalstates

singlet triplet

Final state: singlet or triplet?

3dn (2p3/2)33d10 3d8

3d9LZhang-Rice

singlet

An original ideaof L.Hao Tjeng(tested on CuO)

PRL 78, 1126 (1997)


Zhang-Rice singlets in cuprates

MIN

MIN

t2g

t2g

t2g

t2g

e

e

e

e

b1

b1

b1

b1

b2

b2

b2

b2

a1

a1

a1

a1

eg

eg

eg

eg

MAJ

MAJ

Free ion Cubic Oh Tetragonal D4h

3 : Fd8 3

3 : Fd8 3

3 : Ad8 32g

3 : Ad8 32g

3 : Ad8 11

3 : Bd8 31

J(e

xcha

nge)

J(e

xcha

nge)

10D

q(c

r. fie

ld)

10D

q(c

r. fie

ld)

10D

q(c

r. fie

ld)

10D

q(c

r. fie

ld)

•3d9L state in hole-doped materials•Lowest energy 2-hole state•Hubbard model (by Zhang and Rice)•Cluster model (Eskes and Sawatzky)

singlet

triplet

singlet


Measuring 1ZR in BSCCO with ResSCP

Bi2Sr2CaCu2O8+δ

0

100

200

300

400

500

Sum Sing Trip

BSCCO

103 Co

unts

15 10 5 0

0.0

0.4

0.8

Polar

isati

on

1 G 1ZR

Binding Energy (eV)

1 0 -1

0

100

200

300

103 Co

unts

Brookes, Ghiringhelli et al, Phys. Rev. Lett. 87, 237003 (3 Dec 2001)

Almost pure singletcharacter at Fermi level

ResSCP: resonant Spin resolved photoemission with Circularly Polarised x-ray


Bibliography

High-Resolution X-ray Emission and X-ray Absorption Spectroscopy, Frank de Groot, Chem. Rev. 101, 1779 (2001)XAS

XMCDMagnetic properties of transition-metal multilayers studied withX-ray magnetic circular dichroism spectroscopy, J. Stohr and R. Nakajima, IBM J. RES. DEVELOP. 42, 73 (1998)

RIXSResonant inelastic x-ray scattering spectra for electrons in solidsAkio Kotani and Shik Shin, REV. MODERN PHYS. 73, 203 (2001)

Resonant inelastic X-ray scattering in d and f electron systemsA. Kotani, Eur. Phys. J. B 47, 3–27 (2005)

Spettroscopie risonanti SILS06

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