1

K.E.

P1/2

B.E.

hf

s

Transition Metals

L-edge Absorption

L2 Core level

Valance Band

L2 Edges

Re d 5

Ir d 7

Pt d 8

Au d 10

40 40 800

0.1

0.5

0.9

1.3

1.7

2.1

Energy (eV)

No

rmal

ized

Ab

sorp

tio

n C

oef

fici

ent

00

2

20

00

2

20

00

2

20

4

40

00

2

20 40

00

2

20 40

00

1

20 40

Ca d 0

Ti d 2

Cr d 4

Co d 7

Ni d 8

Cu d 9

Energy (eV)

LII,

III-Ed

ges

Ab

sorp

tio

n C

oef

fici

ent

(10

5 cm

1)

2

Hamiltonian of A Many Electron Atom

n

1i i

22

i

20

r

Ze

2mH

n

1iji ij ji

2

ee K(ij)J(ij)r

eH

CFTslee0 HHHHH

2S+1L 2S+1LJDq

ijr

1ijJ(ij)*

ij

Coulomb integral

jir

1ijK(ij)*

ij

Exchange integral

CFTCFT VH

n

1iiisl SξLH

dr

dV

r

1

c2m

1)ξ(r *

2e

i

2p X-ray Absorption Spectra of Transition Metal Compounds (L-Edge Absorption )

3

ψ1SS1LL1JJ2

1ψSL

)SL(J2

1SL

S2LSLS)S)(L(LJJ

2

222

22

(b) Considering CF:

CFTV Strong fieldij

2

r

e>

CFTV Weak field<ij

2

r

e

(a) Without considering CF:

ij

2

r

eLS coupling

iii SξL>

JJ couplingij

2

r

e i

ii SξL<

2S1LJ

J

4

f

fλi

2

fiλ )EEδ(EφXφ~)σ(E

)E(Eρφ(3d)X2pφ~)(Eσ 2pλ3d

2

λ2p

X-ray absorption cross section:

E： Photon Energy X： The perturbation acting on the system

Dipole allowed transition： p d ; s p ; d f

3d(E) is the unoccupied 3d-projected density of state

以 2p 3d 為例 :

5

In the atomic approach, the 2p XAS cross section for 3dn transition metal ions:

(2p63dn 2p53dn+1)

)EEδ(E)3d(2pφX3dφ~)(Eσ fλGj

21n5

jfn

Gλ2p

G(3dn)is the ground state of the 3dn multiplet

The important correlation effects are : 　　　　　　　　　　 (1) multiplet (2) charge transfer satellites

6

Figure: LS jj transition for 2p53d1. In LS-c

oupling only the 1P1-state can be reached, but in intermediate coupling there is admixture of the 1P1-state with the 3P1-state and the 3D1-state

For Ti4 : 2p6d0 2p5d1

1S 2P 2D 1P1 1D2 1F3 3P0,1,2 3D1,2,3 3F2,3,4

A1

J = 0 A1

1 T1

2 ET2

3 A2T1T2

4 A1ET1T2

For dipole transition (x,y,z) in Oh T1u

只有 T1 與 T1 作用，可產生 A1 的 term 。 含有 T1 為 J = 1 , 3 , 4

J = 1 1P1 , 3P1 , 3D1

J = 3 1F3 , 3D3 , 3F3

J = 4 3F4

4

3

2

1

0

1F

1D

1P

3F

3D

3P

LS Intermediate

J

In Oh:

7

7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

462 464 466 468 470 472 474

Energy (eV)

Inte

nsi

ty

(10

1)

1 2 3 4 5 6 7

Ti4 (d 0)

☆ 10Dq 1.5

8

452 462

Oh

D4h

D3d

Td

Ti3

Octahedral

Tetragonal

Trigonal

Tetrahedral

Trivalent

Energy (eV)

SrTiO3

Figure:Crystal field multiplet calculations. In all spectra the cubic crystal field strength (10Dq) is 2.1 eV. From bottom to top : a calculation in octahedral symmetry, tetragonal (D4h) symmetry, trigonal (D3d) symmetry, tetrahedral symmetry (10Dq = 2.1eV) and a calculation for Ti3 (3d1 2p53d2).

Ti4

：

Ti3

：

2p6 2p53d1

2p53d1 2p53d2

10Dq = 2.1 eV (Oh and Td )

Effect on Symmetry

9

Energy (eV)

Inte

nsi

ty

(10

1) 0eV

Energy (eV)

Inte

nsi

ty

(10

1) 0.3eV

Energy (eV)

Inte

nsi

ty

(10

1) 0.6eV

Energy (eV)

Inte

nsi

ty

(10

1) 0.9eV

Energy (eV)

Inte

nsi

ty

(10

1) 1.2eV

Energy (eV)

Inte

nsi

ty

(10

1) 1.5eV

Energy (eV)

Inte

nsi

ty

(10

1) 1.8eV

Energy (eV)

Inte

nsi

ty

(10

1) 2.1eV

Energy (eV)

Inte

nsi

ty

(10

1) 2.4eV

Energy (eV)

Inte

nsi

ty

(10

1) 2.7eV

Energy (eV)

Inte

nsi

ty

(10

1) 3.0eV

Energy (eV)

Inte

nsi

ty

(10

1) 3.3eV

Energy (eV)

Inte

nsi

ty

(10

1) 3.6eV

Energy (eV)

Inte

nsi

ty

(10

1) 3.9eV

Energy (eV)

Inte

nsi

ty

(10

1) 4.2eV

Energy (eV)

Inte

nsi

ty

(10

1) 4.5eV

Ti4 (d 0)2p6d 0 → 2p5d 1

Effect on Dq

10

650 660Energy (eV)

Inte

nsi

ty

Mn2

635 645 655

00

03

06

09

12

15

18

Mn2 in Oh

Energy (eV)

Inte

nsi

ty

Exp

Cal

638 648Energy (eV)

Inte

nsi

ty

MnF2

☆10Dq 0.75 eV

518 528

Exp

Cal

Energy (eV)

Inte

nsi

ty

VF3

☆10Dq 1.5 eV

510 520 530

00

03

06

09

12

15

18

21

24

Energy (eV)

Inte

nsi

ty

V3 in Oh

Effect on the crystal field strength (Dq)

Dq(eV)

Dq(eV)

11

705 715 725

00

03

06

09

12

15

18

Energy (eV)

Inte

nsi

tyFe2 in Oh

700 705 710 715 720 725 730

Experiment

Calculation

Energy (eV)

Ab

sorb

ance

Figure:Comparison between experimental and calculated (3d6 to 2p53d7 multiplet ) L2,3 edge spectra for the high-spin Fe(phen)2(NCS)2 isomer. Calculation is made considering Oh symmetry with a 10Dq cubic crystal field parameter equal to 0.5eV.

Experiment

Calculation

AB C

700 705 710 715 720 725 730

Energy (eV)

Ab

sorb

ance

Figure:Comparison between experimental and calculated (3d6 to 2p53d7 multiplet ) L2,3 edge spectra for the low-spin Fe(phen)2(NCS)2 isomer. Calculation is made considering Oh symmetry with a 10Dq cubic crystal field parameter equal to 2.2eV.

Dq(eV)

12

Energy (eV)

0eV

Inte

nsi

ty(

101)

Energy (eV)

0.3eV

Inte

nsi

ty(

101)

Energy (eV)

0.6eV

Inte

nsi

ty(

101)

Energy (eV)

0.9eV

Inte

nsi

ty(

101)

Energy (eV)

1.2eV

Inte

nsi

ty(

101)

Energy (eV)

1.5eV

Inte

nsi

ty(

101)

Energy (eV)

1.8eV

Inte

nsi

ty(

101)

Energy (eV)

2.1eV

Inte

nsi

ty(

101)

Energy (eV)

2.4eV

Inte

nsi

ty(

101)

Energy (eV)

2.7eV

Inte

nsi

ty(

101)

Energy (eV)

3.0eV

Inte

nsi

ty(

101)

Energy (eV)

3.3eV

Inte

nsi

ty(

101)

Energy (eV)

3.6eV

Inte

nsi

ty(

101)

Energy (eV)

3.9eV

Inte

nsi

ty(

101)

Energy (eV)

4.2eV

Inte

nsi

ty(

101)

Energy (eV)

4.5eV

Inte

nsi

ty(

101)

Fe2 (d 6)2p6d 6 → 2p5d 7

t6

1 t g

6

2

A11

t1

1 e1

13

Multiplet with Charge transfer

　 2p63dn 2p53dn1

<A> (2p63dn) (2p63dn1) (2p53dn1) (2p53dn)

<B> (2p63dn) (2p63dn1) (2p53dn1) (2p53dn2)

Charge transfer

<A> MLCT

<B> LMCT

2p6dn 2p5dn1

2p6dn1Lm1 2p5dnLm1

2p6dn 2p5dn1

2p6dn1Lm1 2p5dn2Lm1

For 3d-TM

14

707 714 721 728 735 742

0.0

1.0

2.0

Energy (eV)

Inte

nsi

ty(

101)

0.0

1.0

2.0

Inte

nsi

ty(

101)

707 714 721 728 735 742

Energy (eV)

Fe2+ in High Spin , Dq=0.9eV with CT Fe2+ in Low Spin , Dq=2.2eV with CT

15

HS

LS

LIII

LII

HS-1, 298K

HS-1, multiplet calculated with charge transfer

HS-1, multiplet calculated without charge transfer

LS-1, 15K

LS-1, multiplet calculated with charge transfer

LS-1, multiplet calculated without charge transfer

695 700 705 710 720715 725 730 735

Photon Energy (eV)

Arb

itra

ry S

cale

Multiplet Calculation

HS： 10Dq 0.91eV

LS： 10Dq 2.13eV

Experimental and Calculated LII,III-absorption edge of Fe(phen)2(NCS)2 on 298K, 15K

JACS 2000, 122,5742-7

16

LiCoO2

Li0.2Co0.8O

Li0.2Co0.9O

CoO

770 775 780 785 790 795Energy (eV)

Inte

nsi

tyCo

3

2

Figure:The Co L2,3 x-ray absorption spectra of CoO 、Li0.2Co0.9O、 Li0.2Co0.8O and LiCoO2.

Li2MnO3

LiMn2O4

LiMnO2

MnO

632 637 642 647 652

Energy (eV)

Inte

nsi

ty

Mn

4

3.5

3

2

Figure:

The Mn L2,3 x-ray absorption spectra of Mn

O、 LiMnO2、 LiMn2O4 and Li2MnO3.

L2,3 absorption of TM with various oxidation states

17

La1-xSrxTiO3 Ti L2,3 XAS

Photon Energy (eV)450 455 460 465 470

No

rmal

ized

Inte

nsi

ty[Sr]

1.0

0.9

0.8

0.5

0.4

0.2

0.0

Figure:The 2p x-ray absorption spectra of the La1-xSrxTiO3-system. The solids lines are the results of crystal field multiplet calculations: At the bottom the 3d1 [2T2] 2p53d2 transition is given and the solid line simulating the SrTiO3 spectrum relates to the 3d0 [1A1] 2p53d1

La1-xSrxFeO3 Fe L2,3 XAS

0.0

0.1

0.3

0.5

0.7

1.0

700 710 720 730

[Sr]

Photon Energy (eV)N

orm

aliz

ed In

ten

sity

Figure:The 2p x-ray absorption spectra of the

La1-xSrxFeO3 system.

SrTiO3

LaTiO3

LaFeO3

SrFeO3

18

Figure:(a) and (b) Oxygen 1s x-ray-absorption spectra : the shaded area is assigned to oxygen p character in the transition metal 3d band . The broader structure above is assigned to oxygen p character in the metal 4s and 4p bands . The vanadium edges are distorted by the tail of the vanadium L2 edge.

530 540 550

Energy (eV)

No

rmal

ized

Inte

nsi

ty

Sc2O3

TiO2

Ti2O3

VO2

V2O3

Cr2O3

O K-edge(a)

530 540 550

Energy (eV)

No

rmal

ized

Inte

nsi

ty

MnO2

Fe2O3

Fe3O4

NiO

CuO

(b)

19

Figure:Dipole transition from a core p level to a continuum s state with left and right circularly polarized light, and the resulting circular dichioism in the photoemission .

Continuum State

Core State

j mj

1/2

3/2

1/2

1/21/2

1/21/2

3/2

3/2

1/2

m 1

Lm 1

R L-RB

uil

din

g E

ne

rgy

mj 1

120

80

40

(a) L2,3 Photoabsorption of Nickel

850 870 890

L3 L2A A’

Ab

sorp

tio

n In

ten

sity

Photon Energy (eV)

(b) Magnetic Circular Dichroism4

4

0

8

850 870 890

L3

L2

B

B’

Inte

nsi

ty D

iffe

ren

ce

Photon Energy (eV)

Magnetic Circular Dichroism (MCD)

20

Figure (a):A normalized soft-x-ray absorption spectrum of sample (Co40Å / Cr5Å)10/ Mo/MgO(100) under different magnetized directions .

Figure (b):The net difference of the spectrum in Fig. (a) , which is the MCD intensity .

760 780 800 8200.05

0.00

0.05

(Co40/Cr5)20/Mo/MgO

Photon Energy (eV)

(b)(a)

760 770 780 790 800 810 820

0.2

0.4

0.6

0.8

Photon Energy (eV)

Inte

nsi

ty

Co LIII

Co LII

21

700 720 740 760

0.0

0.4

0.8

700 720 740 760

0.0

0.4

0.6

0.2

IRON

Photon Energy (eV)

4S1/2 3d3/2 3d5/2

1/2 1/2 1/23/2 3/25/21/2

1/2 1/2 1/2 1/2

1/2 1/23/2 3/2 5/2

3/2 3/2

2P1/2 2P3/2

Left circularly polarized light： mj 1

Right circularly polarized light： mj 11. C.T. Chen, Y.U. Idzerda,H.-J. Lin, N.V. Smith, G. Meigs, E. Chaban,

G. H. Ho, E. Pellegrin, Sette, Phys Rev. Lett. 75, 152(1994).

2. H. Ebert, G. Schutz, Spin-Orbit Influenced Spectroscopies of magnetic Solids, 1996, p161.

22

Figure :L2,3-edge XAS and MCD spectrum of iron ：(a) Transmission spectra of Fe/parylene thin films, and of the parylene substrates alone, taken at two opposite saturation magnetizations. (b) The XAS absorption spectra calculated from the transmission data shows in (a). (c) and (d) are the MCD and summed XAS spectra and their integrations calculated from the spectra shown in (b). The dotted line shown in (d) is the two-step like function for edge-jump removal before the integration. The p and q shown in (c) and the r shown in (d) are the three integrals needed in the sum-rule analysis.

0.8

1.0

1.2 (a)

IIIs

L3

L2

Tra

nsm

iss

ion

Ab

sorp

tio

n

0.0

0.2

0.4

0.6 (b)

IRON

0.2

0.4

0.6

0.0

0.2

0.2

0.1

0.0

0.1(c)

MC

D

MC

D In

tegra

tion

p

q

4.0

2.0

0.00.0700 720 740 760

Photon Energy (eV)

0.4

0.8

(d)

XA

S

XA

S In

tegratio

n

r XMCDReference: Coord. Chem. Rev. 249(2005) 3-30