Spettroscopia risonante di stati elettronici: un approccio impossibile senza i sincrotroni XAS, XMCD, XES, RIXS, ResXPS: introduzione alle spettroscopie risonanti * Dipartimento di Fisica - Politecnico di Milano Coherentia 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 1
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 2
Electromagnetic spectrum UV and x-rays 3
Core levels C O Si Sc Fe Zn Y Mo Cd Ce Gd Lu Au Th 3dTM 4dTM RE Actinides 100000 K Binding energy (ev) 10000 1000 100 L 3 M 3 M 5 Hard X-Rays UV Soft X-Rays 10 1s 2p 3/2 3p 3/2 3d 5/2 4p 3/2 4d 5/2 4 0 10 20 30 40 50 60 70 80 90 100 Atomic number Z
X-ray Absorption Cross Section Absorption coefficient (arb. u.) 1 0.1 0.01 1E-3 log scale Linear scale O K 530 ev Cu L 2,3 930-950 ev CuO Cu K 9000 ev 2.5 2.0 1.5 1.0 0.5 1E-4 10 100 1000 10000 Photon Energy (ev) 0.0 5
Resonances in the XAS 3d TM 4sp 3d E 2p Oxygen Rare Earths 5d 4f E Fermi M 2,3 edges (28-77 ev) 3p 2s K edge 530 ev L 2,3 edges (400-950 ev) 2p 1s 3d M 4,5 edges (830-1580 ev) K edge (4.5-9.0 kev) 1s 2p L 2,3 edges (5.5-10 kev) Strong resonances 6
Spin-Orbit splitting 3p: M 2,3 edge XAS Spin-Orbit splitting Source: S. Nakai, et al PRB 9, 1870 (1974) 7
2p: L 2,3 edge XAS Spin-Orbit splitting Spin-Orbit splitting Mn L 2,3 XAS L 3 L 3 NiO La 0.7 Sr 0.3 MnO 3 Ni metal 850 855 860 NiO Ni metal L 2 MnO 850 860 870 880 Photon Energy (ev) Source: G. Ghiringhelli, N.B. Brookes et al unpublished 640 645 650 655 660 photon energy (ev) Source: C. Aruta, G. Ghiringhelli et al unpublished 8
Orbitals and XAS 2p 3p The radial integral is important! 3d Φ f ε r Φ i = ( r R R dr)( Y ε u Y dω) 3 * * f i f r i 9
1s: Ni and Mn K edge XAS NO Spin-Orbit splitting E 0 =8333eV Source: Z. Tan et al Phys. Rev. B 47, 12365 (1993) Source: G. Subìas, et al PRB 56, 8183 (1997) 10
Cu K edge XAS E 0 =8980eV Source: Z. Tan et al Phys. Rev. B 47, 12365 (1993) Source: G. Liang, Phys. Rev. B 51, 1258 (1995) 11
EXAFS and NEXAFS 12
1s: Oxygen K edge XAS NO Spin-Orbit splitting La 2 x Sr x NiO 4+δ Source: P. Kuiper et al Phys. Rev. B 44, 4570 4575 (1991) Source: M. Abbate, et al Phys. Rev. B 46, 4511 4519 (1992) 13
Band model E 3dTM E Oxygen E v E v 4sp E F 3d hybridisation E F hν in 3p hν in 2p 2p 1s 1s XAS probes Density of Empty states 14
and atomic model Total E 3dTM - O 2p 5 3d n+2 L 2p 5 3d n+1 M.S.: Multiplet Splitting 3d n+1 L C.I.: Configuration Interaction 3d n C.I. M.S. g> XAS probes orbital occupation 15
Crystal field z 2 2 Cu: x -y orbital x y d states x 2 -y 2, z 2 10Dq xy, yz,zx e g t 2g x 2 -y 2 z 2 10Dq xy yz,zx b 1 a 1 b 2 e g Spherical O 3 Cubic O h Tetragonal D 4h 16
3d split states t 2g states e g states e zx z z z x x x y y z x y x b 2 xy b x 2 -y 2 z 2 1 a 1 e yz z y y 17
L 3 XAS and multiplets E Excitation CuO 3d hν in 2p 3/2 Ground state Excited states 928 930 932 934 Photon Energy (ev) MnO 3d n 2p 5 3d n+1 CuO: 3d 9 3d 10 NiO: 3d 8 3d 9 MnO: 3d 5 3d 6 One single peak Many peaks 636 638 640 642 644 646 photon energy (ev) 18
L 3 XAS and valence L 3 L 2 CuO: Cu 2+ is 3d 9 2.1 ev Cu 2 O: Cu 1+ is 3d 10 Cu metal: 3d 10 4s 1 CuO Cu 2 O 930 935 940 Photon Energy (ev) Source: M. Grioni et al PRB 45, 3309 (1992) Source: M. Finazzi et al PRB 61, 4629 (2000) 19
L 3 XAS and cuprates doping La 2-x Sr x CuO 4 Cu L 3 XAS x=0.30 x=0.22 x=0.15 x=0.07 x=0.03 CuO Doped: Zhang-Rice singlet 3d 9 L Cu 2+ : 3d 9 O 1- : 2p 5 Undoped: 3d 9 Cu 2+ 3d 9 O 2- : 2p 6 931 932 933 934 935 936 937 Photon energy (ev) 3d 9 1.5 ev 3d 9 L By choosing the excitation on the main peak we select the 3d 9 component Source: G. Ghiringhelli, N.B. Brookes et al unpublished Source: Z. Hu et al Europhys. Lett. 59, 135 (2002) 20
Linear polarisation of x-rays Empty 3d state z E hν in Empty 3d state z E hν in E E x y x y x 2 -y 2 z 2 b 1 a 1 High absorption No absorption No absorption High absorption 21
3d hole symmetry in cuprates 3d 9 (2p 3/2 ) 3 3d 10 hν θ E Result: the hole in Cu 2+ has 100% x 2 -y 2 symmetry 22
Circular polarisation of x-rays XAS-MCD: x-ray absorption magnetic circular dichroism E Fermi level 3d 2p j=3/2 j=1/2 z LCP m RCP M L 3 : 2p 3/2 3d L 2 : 2p 1/2 3d M 3d 2p 3/2 m=-1 RCP sample number of free states matrix elements z transition rates m=1 LCP z absorption XAS-MCD experimental geometry M L 3 LCP RCP 23
Intensity (arb. units) 8 7 6 5 4 3 2 1 0-1 XMCD XAS-MCD: x-ray absorption magnetic circular dichroism L 3 Fe Σ(L 3 +L 2 ) Co Ni L 2 L 3 L 2 L 3 L 2 Σ(L 3 +L 2 ) Σ(L 3 +L 2 ) (L 3 +L 2 ) (L 3 +L 2 ) (L (L 3 ) (L 3 ) 3 ) (L 3 +L 2 ) 40 30 20 10 0 Integrated Intensity (arb. units) -2 700 720 740 760 780 800 820 840 860 880 900 Photon energy (ev) -10 24
XES: emission after a resonant absorption E 3dTM E 3dTM E v E v E F 4sp 3d E F 4sp 3d hν in 3p 3p hν out 2p 2p 1s 1s XES probes Density of Occupied States 25
Resonant O K edge XES of cuprates Source: L. Duda et al Phys. Rev. B 61, 4186 (2000) 26
RIXS: a resonant inelastic scattering i> E transferred =hν in -hν out hν in hν out 3d n+1 L Charge Transfer g> f> 3d n * dd excitations RIXS probes charge neutral local excitations 27
RIXS (2) x hν out e out spin E Excitation De- excitations e out hν out sample y hν in z hν in polarisation Ground state Intermediate states Final states Ti me hν in = x-ray photon It is a Raman measurement! excited states elastic peak 28 Core level to Valence empty states transition Element selective G, Ghiringhelli et al. PRB 73, 035111 (2006) Intensity (arb. units) (C) -7-6 -5-4 -3-2 -1 0 1 Relative emitted energy (ev) Energy loss
RIXS of Cuprates Intensity (photons/s/ev) 1.0 80 Cu L 3 70 0.5 60 LSCO XAS 0.0 CuO 50 LCO 40 SCOC 30 NCCO 20 LSCO 10 x2 BSCCO x2 0-9 -8-7 -6-5 -4-3 -2-1 0 1 2 Relative photon energy (ev) Source: G. Ghiringhelli, et al PRL 92, 117406 (2004) 29
dd excitations of cuprates d states x 2 -y 2, z 2 10Dq xy, yz,zx e g t 2g x 2 -y 2 z 2 10Dq xy yz,zx b 1 a 1 b 2 e g Spherical O 3 Cubic O h Tetragonal D 4h How much is the energy needed to move the hole from the x 2 -y 2 to other orbitals? x 2 -y 2 z 2 10Dq xy yz,zx b 1 a 1 b 2 e g b 1 a 1 b 2 e g b 1 a 1 b 2 e g 30
Resonant Photoemission 3d E E E e E e An original idea of L.Hao Tjeng (tested on CuO) PRL 78, 1126 (1997) hν Final state: singlet or triplet? 2p 3/2 2p 1/2 singlet triplet 31 Ground state Intermediate state Final states 3d n (2p 3/2 ) 3 3d 10 3d 8 3d 9 L Zhang-Rice singlet
Zhang-Rice singlets in cuprates Free ion Cubic O h Tetragonal D 4h 3 : d 8 3 F MIN 3 d 8 : 3 A2g 10Dq (cr. field) e g 3 d 8 : 1 A1 b 1 b 1 b 2 singlet 3d 9 L state in hole-doped materials Lowest energy 2-hole state Hubbard model (by Zhang and Rice) Cluster model (Eskes and Sawatzky) t 2g a 1 J (exchange) e g e MAJ 10Dq (cr. field) b 2 t 2g a 1 e 3 d 8 : 3 F 3 d 8 : 3 A2g 3 d 8 : 3 B1 b 1 J (exchange) MIN 10Dq (cr. field) e g t 2g e g a 1 b 2 b 1 e triplet singlet MAJ 10Dq (cr. field) a 1 b 2 t 2g e 32
Measuring 1 ZR in BSCCO with ResSCP ResSCP: resonant Spin resolved photoemission with Circularly Polarised x-ray 1 0-1 Bi 2 Sr 2 CaCu 2 O 8+δ 500 BSCCO 300 10 3 Counts 400 300 Sum Sing Trip 200 100 10 3 Counts 200 0 100 0 0.8 Almost pure singlet character at Fermi level Polari sation 0.4 0.0 1 G 1 ZR 15 10 5 0 Binding Energy ( ev) 33 Brookes, Ghiringhelli et al, Phys. Rev. Lett. 87, 237003 (3 Dec 2001)
Bibliography XAS High-Resolution X-ray Emission and X-ray Absorption Spectroscopy, Frank de Groot, Chem. Rev. 101, 1779 (2001) XMCD Magnetic properties of transition-metal multilayers studied with X-ray magnetic circular dichroism spectroscopy, J. Stohr and R. Nakajima, IBM J. RES. DEVELOP. 42, 73 (1998) RIXS Resonant inelastic x-ray scattering spectra for electrons in solids Akio Kotani and Shik Shin, REV. MODERN PHYS. 73, 203 (2001) Resonant inelastic X-ray scattering in d and f electron systems A. Kotani, Eur. Phys. J. B 47, 3 27 (2005) 34