Summary Introducing resonant x-ray inelastic scattering dd - PowerPoint PPT Presentation

School on Synchrotron and Free-Electron-Laser Based Methods: Multidisciplinary Applications and Perspectives | (smr 2812) | 4-15 April 2016 Giacomo Ghiringhelli Dipartimento di Fisica - Politecnico di Milano CNR - SPIN giacomo.ghiringhelli@polimi.it 8 April, 2016

Summary Introducing resonant x-ray inelastic scattering dd excitations Cu L 3 RIXS and spin excitations in cuprates Giacomo Ghiringhelli 2016

Transition metal oxides matwww.technion.ac.il Giacomo Ghiringhelli 2016 3

Introduction to Resonant X-ray Scattering X-ray Energy Loss Absorption Spectroscopy Spectroscopy XAS ELS RXS XRD X-Ray Diffraction Giacomo Ghiringhelli 2016

From XRD to X-ray Scattering X-Ray X-Ray Scattering Diffraction q | k'|= | k| | k'|= | k| q=G 2 q l = l ' l = l ' crystal Real space Reciprocal lattice Bragg law Laue condition: q=G (0,2) l ' l (1,1) (0,1) k k' q = k' - k (1,0) (0,0) Giacomo Ghiringhelli 2016

ELS: from Raman to Inelastic X-ray Scattering Energy Loss w ' w Spectroscopy Inelastic k k' X-ray Scattering Raman light scattering k  0, q  0, w ' w W=w-w ' W=w-w ' X-ray photons q = k' - k w ' w W W Giacomo Ghiringhelli 2016

Resonant X-ray Absorption 2.5 CuO O K Photoelectric 1 Cu L 2,3 530 eV 2.0 effect dominates 930-950 eV Absorption coefficient (arb. u.) x-ray absorption 0.1 1.5 below 100,000 eV 0.01 Cu K 1.0 9000 eV 1E-3 0.5 1E-4 0.0 10 100 1000 10000 Photon Energy (eV) Edges are univocally element specific And often are dressed with a strong resonance Giacomo Ghiringhelli 2016

Core level binding energies and edges O Sc Fe Zn Y Mo Cd Ce Gd Lu Th C Si Au 3dTM 4dTM RE Actinides 100000 Hard X-Rays 10000 Binding energy (eV) Soft X-Rays 1000 100 UV 2p 3/2 4p 3/2 3p 3/2 3d 5/2 4d 5/2 10 1s 0 10 20 30 40 50 60 70 80 90 100 Atomic number Z Giacomo Ghiringhelli 2016

XAS of 3d transition metals E Spin-Orbit 3 d TM splitting E v 4 sp Mn L 2,3 XAS 3 d E F w La 0.7 Sr 0.3 MnO 3 h n in 3 p 2 p MnO 640 645 650 655 660 1 s photon energy (eV) Giacomo Ghiringhelli 2016

Resonant Inelastic X-ray Scattering w, l w ' , l ' Resonant Inelastic X-ray X-ray k k' Absorption Scattering RIXS W=w-w ' X-Ray q = k' - k Scattering Giacomo Ghiringhelli 2016

The choice of the resonance: 2 p 3 d, L 3 edge 3 d Transition Metal oxides: a lucky coincidence for soft x-rays E Oxygen 3 d TM 4s p 3 d 2 p 2 s M 2,3 edges (28-77 eV) 3 p K edge 530 eV Soft x rays 1 s L 2,3 edges (400-950 eV) 2 p Hard x rays K edge (4.5-9.0 keV) 1 s Strong resonances Giacomo Ghiringhelli 2016

L 3 RIXS Phonons E dd Spin E F e-h 3 d h n out - h n in E loss 0 h n out h n in E (930 eV) n n h h out in 2 p 3/2 core-hole: high energy low energy Ground Intermediate Final state states states Giacomo Ghiringhelli 2016

L edge RIXS : energy and momentum transfer Resonant Inelastic X-ray Scattering: • an energy loss experiment k  E’, ’, ’ S am ple • made with photons of high energy • at a core absorption resonance k  E, , Energy Scattering plane w h = E - E’ k ’ Conservation laws: • Energy q = k-k’ • Momentum Momentum k • “Angular momentum” Giacomo Ghiringhelli 2016

Photon momentum and kinematics Photons vs Neutrons: energy and momentum Wavevector of particles used in inelastic scattering Thermal neutrons 10 Neutrons 1 1st Brillouin zone boundary -1 ) K edges k (Ang 0.1 L edges 0.01 s M edges n o t o 1E-3 h P 1m 10m 100m 1 10 100 1k 10k 100k energy (eV) Giacomo Ghiringhelli 2016

L 2,3 edge RIXS: intermediate and final states 3 d h n out h n in Excitation De-excitations e E out 2 p 3/2 h n out h n in Time Ground Intermediate Final states state states 3 d n 2 p 5 3 d n +1 3 d n Giacomo Ghiringhelli 2016

The potential of soft RIXS (for 3dTM systems) Site selective, q resolved probe of elementary excitations • charge excitations across the gap • dd excitations • magnetic excitations • phonons 3 d n : elastic, magnetic and phonons 3 d n 2p 5 3 d n+ 1 3 d n *: dd excitations 3 d n L: Charge Transfer excitations Giacomo Ghiringhelli 2016

Cuprates: the “easy” case In cuprates Cu is divalent: Cu 2+ 3 d 9 CuO This makes XAS almost trivial: 1 peak only 3 d 9 (2p 3/2 ) 3 3 d 10 928 930 932 934 Photon Energy (eV) RIXS can be calculated even by hand: 3 d 9 (2p 3/2 ) 3 3 d 10 (3 d 9 )* Even for magnetic excitations (spin waves), because fast collision approximation is a very good approximation Giacomo Ghiringhelli 2016

dd excitations in Cu 2+ systems z x 2 -y 2 b 1 x z x 2 -y 2 , z 2 e g y z 2 a 1 d states z 10 Dq x 10 Dq y xy b 2 x z z y yz,zx e g t 2g xy, yz,zx x x Spherical Cubic Tetragonal Interatomic y y O 3 O h D 4h exchange x 2 -y 2 b 1 z 2 a 1 10 Dq xy b 2 yz,zx e g 3 d 9 2 p 5 3 d 10 3 d 9 Giacomo Ghiringhelli 2016

Cu L 3 RIXS of cuprates: mainly dd excitations 3 d 9 : elastic, magnetic and phonons 3 d 9 2p 5 3 d 10 3 d 9 *: dd excitations 3 d 10 L: Charge Transfer excitations All final states 600 are reached via Sr 2 CuO 2 Cl 2 2 electric dipole 500 allowed transitions! 400 Photons get coupled to electrons spin 300 thanks to 2 p spin-orbit interaction 200 At L 3 edge elastic 100 peak is very small (not the case at K) 0 -8 -6 -4 -2 0 Energy loss (eV) Giacomo Ghiringhelli 2016

Cu L 3 edge: CuO, La 2 CuO 4 , Malachite SAXES Swiss Light Sourc e & Politec nic o di Milano Cu 2+ in square 21 approximately planar coordination 1 ) - Cu-O distances: CuO 1 eV CuO 1.7 – 2-2 Ang 14 - Intensity (ph. s LCO 1.9 – 2.4 Ang Malachite 1.9 – 2.6 Ang La 2 CuO x2 4 Different Cu 2+ 7 coordination, symmetry, Cu 2 (OH) 2 CO hybridization 3 0 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 Different dd excitations Energy loss (eV) G . Ghiringhelli, A. Piazzalunga, X. Wang, A. Bendounan, H. Berger, F. Bottegoni, N. Christensen, C. Dallera, M. Grioni, J.-C. Grivel, M. Moretti Sala, L. Patthey, J. Schlappa, T. Schmitt, V. Strocov , and L. Braicovich, Eur.Phys. J. Special topics 169 , 199 (2009) Giacomo Ghiringhelli 2016

This is a very direct way of measuring the dd -excitation energies M. Moretti Sala , et al New J. Phys. 13 , 043026 (2011) Giacomo Ghiringhelli 2016

dd -excitation energies from fitting using atomic cross sections Ground state: 3𝑒 ↓ 𝑦 2 −𝑧 2 Spin flip: 3𝑒 ↑ 𝑦 2 −𝑧 2 Spin along [001] Spin along [110] F ( q in , f in , q out , f out , q spin , f spin ,  in ,  out ) NdBCO M. Moretti Sala , et al New J. Phys. 13 , 043026 (2011) Giacomo Ghiringhelli 2016

Crystal field trends in cuprates M. Moretti Sala , et al New J. Phys. 13 , 043026 (2011) Giacomo Ghiringhelli 2016 23

Crystal field trends in cuprates: theory vs experiment CASSCF: complete-active-space self-consistent-field method NBCO (exp) Liviu Hozoi, Liudmila Siurakshina, Peter Fulde & Jeroen van den Brink , SCIENTIFIC REPORTS 1 : 65 (2011) [14] M. Moretti Sala , et al New J. Phys. 13 , 043026 (2011) Giacomo Ghiringhelli 2016 24

dd excitations: Cu L 3 vs M 2,3 edges L 3 M 2,3 Very weak signal with respect to No spin excitations the elastic peak at Gamma point J. Schlappa et al NATURE 485, 82 (2012) L.A. Wray et al arXiv:1203.2397v1 Giacomo Ghiringhelli 2016 25

Ni L 3 edge: NiO, NiCl 2 Ni 2+ (3 d 8 ) in octahedral coordination c 40 1 ) z - y 1 eV x b - Intensity (ph. s a NiO 20 z x y NiCl 2 0 a b -4 -3 -2 -1 0 Energy loss (eV) Giacomo Ghiringhelli 2016

dd and CT excitations in simple oxides G . Ghiringhelli, A. Piazzalunga, X. Wang, A. Bendounan, H. Berger, F. Bottegoni, N. Christensen, C. Dallera, M. Grioni, J.-C. Grivel, M. Moretti Sala, L. Patthey, J. Schlappa, T. Schmitt, V. Strocov , and L. Braicovich, Eur.Phys. J. Special topics 169 , 199 (2009) Giacomo Ghiringhelli 2016

RIXS of NiO: incident photon energy SAXES Swiss Light Sourc e & Politec nic o di Milano depencence ... 852 853 854 855 856 857 858 Intensity (arb.u.) NiO Ni L 3 XAS S P 852 853 854 855 856 857 858 NiO S P P -5 5 5 RIXS NiO NiCl 2 x5 -4 4 4 Energy loss (eV) Energy loss (eV) -3 3 3 -2 2 2 -1 1 1 0 0 0 852 853 854 855 856 857 858 0 25 50 75 100 -1 eV -1 ) RIXS Intensity (ph. s Incident photon energy (eV) G. Ghiringhelli A. Piazzalunga, C. Dallera, L. Braicovich, T. Schmitt, V.N. Strocov, J. Schlappa, L. Patthey, X. Wang, H. Berger, and M. Grioni, PRL 102 , 027401 (2009) Giacomo Ghiringhelli 2016

... and magnetic excitations in NiO Interatomic exchange splitting : ~115 meV Main peak Satellite S H pol 6 6 V pol -1 ) -1 eV RIXS intensity (ph. s 4 4 -1 ) -1 ) q (A q (A 0.36 0.36 2 2 0.61 0.61 0.78 0.78 0 0 -4 -3 -2 -1 0 0.4 0.3 0.2 0.1 0.0 -0.1 0.4 0.3 0.2 0.1 0.0 -0.1 Energy loss (eV) Energy loss (eV) Energy loss (eV) No evident dispersion of these magnetic excitations G. Ghiringhelli A. Piazzalunga, C. Dallera, L. Braicovich, T. Schmitt, V.N. Strocov, J. Schlappa, L. Patthey, X. Wang, H. Berger, and M. Grioni, PRL 102 , 027401 (2009) Giacomo Ghiringhelli 2016