1. LII,III-Edges Absorption Coefficient
L-edge Absorption 2 20 4 40 1
Ca d 0
Ti d 2
Cr d 4
Co d 7
Ni d 8
Cu d 9
Energy (eV)
LII,III-Edges Absorption Coefficient
(105cm1)
Transition Metals L2
Core level
Valance Band h
K.E. f  s
B.E.
P1/2
Normalized Absorption Coefficient
L2 Edges
2.1
Re d 5
Ir d 7
Pt d 8
Au d 10
1.7
1.3
0.9
0.5
0.1
40 40 80
Energy (eV)

2. 2p X-ray Absorption Spectra of Transition Metal Compounds
(L-Edge Absorption )
Hamiltonian of A Many Electron Atom
2S+1L
2S+1LJ Dq
Coulomb integral
Exchange integral

3. > < > < LS coupling 2S1LJ JJ coupling J Strong field
(a) Without considering CF:
LS coupling
>
JJ coupling
<
2S1LJ J
(b) Considering CF:
Strong field
>
Weak field
<

4. X-ray absorption cross section:
E：Photon Energy
X：The perturbation acting on the system
Dipole allowed transition：p  d ; s  p ; d  f
以2p  3d為例:
3d(E) is the unoccupied 3d-projected density of state

5. The important correlation effects are :
In the atomic approach, the 2p XAS cross section for 3dn transition metal ions:
(2p63dn  2p53dn+1)
G(3dn)is the ground state of the 3dn multiplet
The important correlation effects are :
　　　　　　　　　　(1) multiplet (2) charge transfer satellites

6. 4 3 2 1 1F 1D 1P 3F 3D 3P LS
Intermediate J
Figure:
LS  jj transition for 2p53d1. In LS-coupling 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
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
In Oh:
J = 0  A1
1  T1
2  ET2
3  A2T1T2
4  A1ET1T2

7. Ti4 (d 0) ☆ 10Dq  1.5 (101) Intensity Energy (eV) 1 2 3 4 5 6 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)
Intensity
(101) 1 2 3 4 5 6 7
☆ 10Dq  1.5

8. Effect on Symmetry SrTiO3 Ti4： 2p6  2p53d1 Ti3： 2p53d1  2p53d2
452
462 Oh
D4h
D3d Td
Ti3
Octahedral
Tetragonal
Trigonal
Tetrahedral
Trivalent
Energy (eV)
Ti4：
2p6  2p53d1
10Dq = 2.1 eV (Oh and Td )
Ti3：
2p53d1  2p53d2
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).

9. Effect on Dq Ti4 (d 0) 2p6d 0 → 2p5d 1 0eV 0.3eV 0.6eV 0.9eV 1.2eV
Energy (eV)
Intensity
(101)
0eV
Energy (eV)
Intensity
(101)
0.3eV
Energy (eV)
Intensity
(101)
0.6eV
Energy (eV)
Intensity
(101)
0.9eV
Effect on Dq
Ti4 (d 0)
2p6d 0 → 2p5d 1
Energy (eV)
Intensity
(101)
1.2eV
Energy (eV)
Intensity
(101)
1.5eV
Energy (eV)
Intensity
(101)
1.8eV
Energy (eV)
Intensity
(101)
2.1eV
Energy (eV)
Intensity
(101)
2.4eV
Energy (eV)
Intensity
(101)
2.7eV
Energy (eV)
Intensity
(101)
3.0eV
Energy (eV)
Intensity
(101)
3.3eV
Energy (eV)
Intensity
(101)
3.6eV
Energy (eV)
Intensity
(101)
3.9eV
Energy (eV)
Intensity
(101)
4.2eV
Energy (eV)
Intensity
(101)
4.5eV

10. Effect on the crystal field strength (Dq)
650
660
Energy (eV)
Intensity
Mn2
Exp
Cal
638
648
Energy (eV)
Intensity
MnF2
☆10Dq  0.75 eV
510
520
530 00 03 06 09 12 15 18 21 24
Energy (eV)
Intensity
V3 in Oh
Dq(eV)
635
645
655 00 03 06 09 12 15 18
Mn2 in Oh
Energy (eV)
Intensity
Dq(eV)
518
528
Exp
Cal
Energy (eV)
Intensity
VF3
☆10Dq  1.5 eV

11. Fe2 in Oh Dq(eV) B C A Absorbance Experiment Calculation Energy (eV)
700
705
710
715
720
725
730
Experiment
Calculation
Energy (eV)
Absorbance
705
715
725 00 03 06 09 12 15 18
Energy (eV)
Intensity
Fe2 in Oh
Dq(eV)
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 A B C
700
705
710
715
720
725
730
Energy (eV)
Absorbance
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.

12. Fe2 (d 6) 2p6d 6 → 2p5d 7 0eV 0.3eV 0.6eV 0.9eV 1.2eV 1.5eV 1.8eV
Energy (eV)
0eV
Intensity
(101)
Energy (eV)
0.3eV
Intensity
(101)
Energy (eV)
0.6eV
Intensity
(101)
Energy (eV)
0.9eV
Intensity
(101)
Energy (eV)
1.2eV
Intensity
(101)
Energy (eV)
1.5eV
Intensity
(101)
Energy (eV)
1.8eV
Intensity
(101)
Energy (eV)
2.1eV
Intensity
(101)
Energy (eV)
2.4eV
Intensity
(101)
Energy (eV)
2.7eV
Intensity
(101)
Energy (eV)
3.0eV
Intensity
(101)
Energy (eV)
3.3eV
Intensity
(101)
Energy (eV)
3.6eV
Intensity
(101)
Energy (eV)
3.9eV
Intensity
(101)
Energy (eV)
4.2eV
Intensity
(101)
Energy (eV)
4.5eV
Intensity
(101)

13. Multiplet with Charge transfer
For 3d-TM
2p63dn  2p53dn1
<A> (2p63dn)  (2p63dn1)  (2p53dn1)  (2p53dn)
<B> (2p63dn)  (2p63dn1)  (2p53dn1)  (2p53dn2)
Charge transfer
<A> MLCT
2p6dn  2p5dn1
2p6dn1Lm1  2p5dnLm1
<B> LMCT
2p6dn  2p5dn1
2p6dn1Lm1  2p5dn2Lm1

14. Fe2+ in High Spin , Dq=0.9eV with CT
Fe2+ in Low Spin , Dq=2.2eV with CT
707
714
721
728
735
742
0.0
1.0
2.0
Energy (eV)
Intensity
(101)
0.0
1.0
2.0
Intensity
(101)
707
714
721
728
735
742
Energy (eV)

15. HS LS Multiplet Calculation
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
720
715
725
730
735
Photon Energy (eV)
Arbitrary Scale
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. various oxidation states
LiCoO2
Li0.2Co0.8O
Li0.2Co0.9O
CoO
770
775
780
785
790
795
Energy (eV)
Intensity Co 3 2
L2,3 absorption of TM with
various oxidation states
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)
Intensity Mn 4
3.5 3 2
Figure:
The Mn L2,3 x-ray absorption spectra of MnO、LiMnO2、LiMn2O4 and Li2MnO3.

17. La1-xSrxTiO3 Ti L2,3 XAS La1-xSrxFeO3 Fe L2,3 XAS
Photon Energy (eV)
450
455
460
465
470
Normalized Intensity
[Sr]
1.0
0.9
0.8
0.5
0.4
0.2
0.0
0.0
0.1
0.3
0.5
0.7
1.0
700
710
720
730
[Sr]
Photon Energy (eV)
Normalized Intensity
SrTiO3
SrFeO3
LaFeO3
LaTiO3
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
Figure:
The 2p x-ray absorption spectra of the
La1-xSrxFeO3 system.

18. O K-edge (a) (b) Sc2O3 MnO2 TiO2 Fe2O3 Ti2O3 Fe3O4 VO2 NiO V2O3 CuO
530
540
550
Energy (eV)
Normalized Intensity
Sc2O3
TiO2
Ti2O3
VO2
V2O3
Cr2O3
530
540
550
Energy (eV)
Normalized Intensity
MnO2
Fe2O3
Fe3O4
NiO
CuO
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.

19. Magnetic Circular Dichroism (MCD)
120 80 40
(a) L2,3 Photoabsorption of Nickel
850
870
890 L3 L2 A A’
Absorption Intensity
Photon Energy (eV)
Continuum State
Core State j mj
1/2
3/2
1/2
1/2
3/2
3/2
1/2
m  1 L
m  1 R
L-R
Building Energy
 mj  1
(b) Magnetic Circular Dichroism 4 4 8
850
870
890 L3 L2 B B’
Intensity Difference
Photon Energy (eV)
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 .

20. (a) (b) Co LIII (Co40/Cr5)20/Mo/MgO  Intensity Co LII
760
770
780
790
800
810
820
0.2
0.4
0.6
0.8
Photon Energy (eV)
Intensity
Co LIII
Co LII  
760
780
800
820
0.05
0.00
0.05
(Co40/Cr5)20/Mo/MgO
Photon Energy (eV)

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 .

21. Left circularly polarized light：mj  1
  
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
3/2
5/2
1/2
3/2
5/2
2P1/2
2P3/2
Left circularly polarized light：mj  1
Right circularly polarized light：mj  1
1. 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 : XMCD L2,3-edge XAS and MCD spectrum of iron：
0.8
1.0
1.2
(a) I I Is L3 L2
Transmission
Absorption
0.0
0.2
0.4
0.6
(b)
 
 
IRON
0.2
0.4
0.6
0.1
0.1
(c)
MCD
  
   
MCD Integration p q
4.0
2.0
700
720
740
760
Photon Energy (eV)
(d)
XAS
XAS Integration
  
    r
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.
XMCD
Reference: Coord. Chem. Rev. 249(2005) 3-30