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)

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

> < > < 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 <

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

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

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

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

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).

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

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

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.

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)

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

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)

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

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.

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.

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.

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 .

(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 .

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.

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