Spettroscopia risonante di stati elettronici: un approccio impossibile senza i sincrotroni

Size: px

Start display at page:

Download "Spettroscopia risonante di stati elettronici: un approccio impossibile senza i sincrotroni"

Shona Francis
5 years ago
Views:

Politecnico di Milano Coherentia Seminari sulla luce di sincrotrone - Università degli studi di

1 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

2 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

3 Electromagnetic spectrum UV and x-rays 3

4 Core levels C O Si Sc Fe Zn Y Mo Cd Ce Gd Lu Au Th 3dTM 4dTM RE Actinides K Binding energy (ev) 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/ Atomic number Z

5 X-ray Absorption Cross Section Absorption coefficient (arb. u.) E-3 log scale Linear scale O K 530 ev Cu L 2, ev CuO Cu K 9000 ev E Photon Energy (ev) 0.0 5

6 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 ( ev) 2p 1s 3d M 4,5 edges ( ev) K edge ( kev) 1s 2p L 2,3 edges ( kev) Strong resonances 6

7 Spin-Orbit splitting 3p: M 2,3 edge XAS Spin-Orbit splitting Source: S. Nakai, et al PRB 9, 1870 (1974) 7

8 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3 NiO La 0.7 Sr 0.3 MnO 3 Ni metal NiO Ni metal L 2 MnO Photon Energy (ev) Source: G. Ghiringhelli, N.B. Brookes et al unpublished photon energy (ev) Source: C. Aruta, G. Ghiringhelli et al unpublished 8

9 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

10 1s: Ni and Mn K edge XAS NO Spin-Orbit splitting E 0 =8333eV Source: Z. Tan et al Phys. Rev. B 47, (1993) Source: G. Subìas, et al PRB 56, 8183 (1997) 10

11 Cu K edge XAS E 0 =8980eV Source: Z. Tan et al Phys. Rev. B 47, (1993) Source: G. Liang, Phys. Rev. B 51, 1258 (1995) 11

12 EXAFS and NEXAFS 12

13 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, (1991) Source: M. Abbate, et al Phys. Rev. B 46, (1992) 13

14 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

15 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

16 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

17 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

18 L 3 XAS and multiplets E Excitation CuO 3d hν in 2p 3/2 Ground state Excited states 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 photon energy (ev) 18

19 L 3 XAS and valence L 3 L 2 CuO: Cu 2+ is 3d ev Cu 2 O: Cu 1+ is 3d 10 Cu metal: 3d 10 4s 1 CuO Cu 2 O Photon Energy (ev) Source: M. Grioni et al PRB 45, 3309 (1992) Source: M. Finazzi et al PRB 61, 4629 (2000) 19

20 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 Photon energy (ev) 3d 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

21 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

22 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

23 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

24 Intensity (arb. units) 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 ) Integrated Intensity (arb. units) Photon energy (ev)

25 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

26 Resonant O K edge XES of cuprates Source: L. Duda et al Phys. Rev. B 61, 4186 (2000) 26

27 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

28 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, (2006) Intensity (arb. units) (C) Relative emitted energy (ev) Energy loss

RIXS of Cuprates Intensity (photons/s/ev) 1.0 80 Cu L 3 70 0.

0 CuO 50 LCO 40 SCOC 30 NCCO 20 LSCO 10 x2 BSCCO x2 0-9 -8-7

29 RIXS of Cuprates Intensity (photons/s/ev) Cu L LSCO XAS 0.0 CuO 50 LCO 40 SCOC 30 NCCO 20 LSCO 10 x2 BSCCO x Relative photon energy (ev) Source: G. Ghiringhelli, et al PRL 92, (2004) 29

30 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

31 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

32 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

33 Measuring 1 ZR in BSCCO with ResSCP ResSCP: resonant Spin resolved photoemission with Circularly Polarised x-ray Bi 2 Sr 2 CaCu 2 O 8+δ 500 BSCCO Counts Sum Sing Trip Counts Almost pure singlet character at Fermi level Polari sation G 1 ZR Binding Energy ( ev) 33 Brookes, Ghiringhelli et al, Phys. Rev. Lett. 87, (3 Dec 2001)

34 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

Probing Matter: Diffraction, Spectroscopy and Photoemission

$Probing Matter: Diffraction, Spectroscopy and Photoemission$ Probing Matter: Diffraction, Spectroscopy and Photoemission Anders Nilsson Stanford Synchrotron Radiation Laboratory Why X-rays? VUV? What can we hope to learn? 1 Photon Interaction Incident photon interacts