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X-Ray Absorption Spectroscopy

1. The document discusses using synchrotron radiation for x-ray spectroscopy techniques to study 3d transition metal oxides. 2. It introduces x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS) as two techniques that can probe core electron excitations and provide information about materials' electronic and magnetic properties. 3. Synchrotron radiation facilities provide tunable x-ray energies, polarization control, and high photon fluxes needed for these resonant spectroscopy techniques to study transitions in transition metal oxides.

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MAX-PLANCK-UBC CENTRE FOR QUANTUM MATERIALS International Summer School on Surfaces and Interfaces in Correlated Oxides 30th August, 2011 Giacomo Ghiringhelli Dipartimento di Fisica Politecnico di Milano Italy giacomo.ghiringhelli@fisi.polimi.it
Introducing myself... Picture of POLIMI Keywords: • Synchrotron radiation • Soft x-rays • Resonant spectroscopy • 3d transition metal oxides 2 Giacomo Ghiringhelli
Summary 1. Why synchrotron radiation? • Main properties • Absorption edges and x-ray energies 2. XAS: x-ray absorption spectroscopy • Basic process and the choice of absorption edges • XLD and XMCD: polarization dependent XAS • Some examples on oxide interfaces 3. RIXS: resonant inelastic x-,ray scattering • A second order process • dd excitations • Magnetic excitations 3 Giacomo Ghiringhelli
Synchrotron radiation, summary 4 Giacomo Ghiringhelli
Undulators: many photons 5 Giacomo Ghiringhelli
Undulators: polarization control Elettroni Campo Luce polarizzata magnetico linearmente Lu ce po lar izz ata circolarmente Elettroni Campo magnetico Full control of the polarization at the source: • Linear horizontal or vertical or any orientation (more difficult) • Circular Right or Left handed 6 Giacomo Ghiringhelli
Beam line High quality mirrors, gratings and crystals are needed to make the beam monochromatic (bandas narrow as possible) and to focalize it onto the sample State of the art beam lines for resonant spectroscopy Parameter Typical figures Flux at the sample 1010 - 1013 photons/s Beam size at sample (hoz x ver) 50 m x 5 m - 1 mm x 1 mm Energy bandpass: UV (20 – 50 eV) 10 - 50 meV soft x rays (300 – 1000 eV) 50 – 500 meV hard x rays (2 - 10 keV) 50 – 500 meV 7 Giacomo Ghiringhelli
X-ray spectroscopy for 3d Transition Metal systems E 3dTM oxides X-ray resonant spectroscopies Ev • XAS: x-ray absorption 4sp spectroscopy EF 3d • XLD and XMCD: polarization dependent XAS Ox 2p • RIXS: resonant inelastic x-ray 3p scattering • Resonant reflectivity • Resonant Elastic X-ray 2p Scattering • Resonant Photoemission 1s 8 Giacomo Ghiringhelli
X-ray Absorption measurements X rays Tunable or X rays Monochromator “white” source e nA Detection: • transmission (only hard x-rays) • fluorescence yield • electron yield (including drain current) 9 Giacomo Ghiringhelli
X-ray Absorption Cross Section log scale 2.5 OK 1 530 eV Cu L2,3 CuO 930-950 eV 2.0 Absorption coefficient (arb. u.) Cu 0.1 M edges 1.5 0.01 Cu K 9000 eV 1.0 1E-3 Linear 0.5 scale 1E-4 0.0 10 100 1000 10000 Photon Energy (eV) 10 Giacomo Ghiringhelli
Resonances in the XAS 3d TM E Oxygen Rare Earths 4sp 6s,5d EFermi 3d 2p 4f 2s M2,3 edges (28-77 eV) 3p K edge 530 eV 1s L2,3 edges (400-950 eV) 2p M4,5 edges 3d (830-1580 eV) K edge (4.5-9.0 keV) 1s L2,3 edges 2p (5.5-10 keV) Strong resonances 11 Giacomo Ghiringhelli
Core levels C O Si Sc Fe Zn Y Mo Cd Ce Gd Lu Au Th 3dTM 4dTM RE Actinides 100000 K Hard X-Rays L3 10000 Binding energy (eV) M3 M5 Soft X-Rays 1000 100 UV 2p3/2 3p 10 1s 3/2 3d5/2 4p3/2 4d5/2 0 10 20 30 40 50 60 70 80 90 100 Atomic number Z Giacomo Ghiringhelli 12 - Politecnico di Milano; Source: X-ray data booklet, Lawrence Berkeley National Laboratory GG 25/03/02 18:29:59
3p: M2,3 edge XAS Spin-Orbit splitting Spin-Orbit splitting Source: S. Nakai, et al PRB 9, 1870 (1974) 13 Giacomo Ghiringhelli
2p: L2,3 edge XAS Spin-Orbit Spin-Orbit splitting splitting Mn L2,3 XAS L3 L3 La0.7Sr0.3MnO3 NiO Ni metal 850 855 860 L2 NiO MnO Ni metal 850 860 870 880 640 645 650 655 660 Photon Energy (eV) photon energy (eV) Source: G. Ghiringhelli, N.B. Brookes et al unpublished Source: C. Aruta, G. Ghiringhelli et al unpublished 14 Giacomo Ghiringhelli
Atomic model Total E 3dTM - O 2p53dn+2L 2p53dn+1 M.S.: Multiplet Splitting C.I.: Configuration 3dn+1L Interaction 3dn |g> XAS probes orbital occupation C.I. M.S. 15 Giacomo Ghiringhelli
L3 XAS and multiplets Excit ation De- excitation s eout E CuO h ou t 3d h in 2p3/2 928 930 932 934 Photon Energy (eV) Excited Ti me Ground Ground states Intermediate Fin al MnO state stat es stat es state Resonant scattering without relaxation of intermediate state 3d n 2p53d n+1 CuO: 3d9  3d10 One single peak NiO: 3d8  3d9 Many peaks MnO: 3d5  3d6 636 638 640 642 644 646 photon energy (eV) 16 Giacomo Ghiringhelli
L3 XAS and valence L3 L2 2.1 eV CuO: Cu2+ is 3d9 Cu2O: Cu1+ is 3d10 CuO Cu2O Cu metal: 3d104s1 930 935 940 Photon Energy (eV) Source: M. Grioni et al PRB 45, 3309 (1992) Source: M. Finazzi et al PRB 61, 4629 (2000) 17 Giacomo Ghiringhelli
X-ray absorption intensity Fermi golden rule Joint density Matrix element of states, separated by energy h Electric dipole perturbation associated to a photon 18 Giacomo Ghiringhelli
Electric dipole selection rules f ε r i 3 * r R Ri dr f Y ε u rYi d * f Radial integral Angular integral Mind the nodes of R! 4 0 NB what matters is Rf , ε ur Y1 3 in the presence of the core hole! Selection rules (via Wigner- Eckart) l=0 Transitions pd l=1 Y2m '* Y1 p Y1m m=-1,0,+1 p=-1,0,+1 l=2 m’=m-1,m,m+1 19 Giacomo Ghiringhelli
Crystal field z Cu: x2-y2 orbital x2-y2, z2 x2-y2 eg b1 z2 a1 x d states 10Dq 10Dq xy b2 yz,zx xy, yz,zx t2g eg y Spherical Cubic Tetragonal O3 Oh D4h 20 Giacomo Ghiringhelli
3d split states t2g states z eg states e zx z z z x y z x x y x y y b2 xy x b1 x2-y2 a1 z2 e yz y 21 Giacomo Ghiringhelli
2p states all occupied: Spherical harmonics and orbitals anisotropy in final states spherical distribution 3d states partly empty: |Y1-1|2 = |Y11|2 |Y10|2 2 |Y2-2|2 = |Y22|2 |Y2-1|2 = |Y22|2 |Y20| Y1-1= Y11= Y10= 22
2p to 3d transitions 2p3/2 photon 3d • Spherical distribution • Anisotropic occupation • No well defined spin due to crystal field state • Possible spin polarization • Spin “parallel” to (FM or AF) orbital moment • Spin-orbit interaction not always negligible RCP = Y11 LCP = Y1-1 z-linear = Y10 x-linear = (Y1-1+Y11)/sqrt(2) 23 Giacomo Ghiringhelli
Transition of a hole from 3d to 2p 3d photon 2p3/2 Example: transition to a 3d(x2-y2) orbital RCP = Y11 Initial state 3d hole is 100% spin down Final state 2p hole has main spin up character 24 Giacomo Ghiringhelli
Linear polarization of x-rays: orbital occupation Empty 3d state Empty 3d state E E z h in h in z E E x x y y b1 x2-y2 (Y2-2+Y22) a1 z2 Y20 High absorption (Y1-1+Y11) Weak absorption No absorption Y10 High absorption 25 Giacomo Ghiringhelli
3d hole symmetry in cuprates 3d9 (2p3/2)33d10 h E Result: the hole in Cu2+ has 100% x2-y2 symmetry 26 Giacomo Ghiringhelli
Linear polarization of x-rays: magnetization orientation Atomic spin Atomic spin orientation orientation E E h in h in E E M M Different absorption Same absorption MAGNETIC LINEAR DICHROISM: Works for Ferro and AntiFerro 27 Giacomo Ghiringhelli
Circular polarization of x-rays and ferromagnetic materials XAS-MCD: x-ray absorption magnetic circular dichroism E z M Fermi level LCP 3d m L3: 2p3/2 3d 3d RCP M L2: 2p1/2 3d j=3/2 2p j=1/2 2p 3/2 sample number of matrix free states elements RCP m=-1 z transition rates z m=1 LCP absorption XAS-MCD LCP RCP experimental geometry M L3 28 Giacomo Ghiringhelli
XMCD: sum rules For late 3dTM sum rules allow to extract spin and orbital magnetic moments directly from spectra without the need of theoretical simulations of spectra 8 40 Fe (L3+L2) Co Ni 7 6 L3 L2 L3 L2 L3 L2 30 Integrated Intensity (arb. units) 5 (L3+L2) Intensity (arb. units) 4 20 3 (L3+L2) 2 10 1 0 0 (L3+L2) (L3+L2) (L3) (L3+L2) -1 (L3) (L3) -2 -10 700 720 740 760 780 800 820 840 860 880 900 Photon energy (eV) 29 Giacomo Ghiringhelli
XAS: some examples Manganite thin films • Strain and orbital occupation • Magnetic anisotropy (FM and AF) STO/LAO interface Cuprates: ferromagnetism 30 Giacomo Ghiringhelli
Films of La2/3Sr1/3MnO3: strain and phase separation Manganites: Mn3+: 3d4 → Mn3+/Mn4+ Mn4+: 3d3 → CMR LaMnO3 Mott Hubbard Insulator: → Phase separation Mn – Mn fluctuations → Orbital ordering more likely than O - Mn 31 Giacomo Ghiringhelli
Manganites XAS: strain and orbital occupation 8 100 u.c. V (E//ab) XAS (V, H) [a.u.] 6 H (E//c) SrTiO3 substrate c/a=0.98 z2 4 x2- y2 z2 eg 2 z-in x2-y2 LSMO 0 Doct 0.3 STO t2g yz xz V-H [a.u.] 0.0 yz xz xy -0.3 xy -0.6 Linear Dichroism=IXAS//ab-IXAS//c 637 644 651 658 Preferential occupation of in-plane 3dx2-y2 orbitals Photon Energy [eV] 8 100 u.c. V (E//ab) LaAlO3 substrate c/a=1.04 XAS (V, H) [a.u.] 6 H (E//c) 4 x2- y2 x2- y2 z2 2 eg 0 0.3 LSMO z-out z2 Doct 0.0 xy V-H [a.u.] -0.3 t2g yz xz xy -0.6 LAO yz xz 637 644 651 658 Photon Energy [eV] Preferential occupation of the out-of-plane 3dz2–r2 orbitals 32 Giacomo Ghiringhelli
Manganites XAS: strain and dimensionality How strain and reduced dimensionality influence magnetic and orbital anisotropies 33 Giacomo Ghiringhelli
Manganites XAS: ferromagnetic behavior XMCD: FM hysteresis loops 34 Giacomo Ghiringhelli
Manganites XAS: linear dichroism LD: magnetic and orbital anisotropy 35 Giacomo Ghiringhelli
Manganites XAS: magnetic linear dichroism MLD: ferromagnetic and antiferromagnetic anisotropy 36 Giacomo Ghiringhelli
Manganite superlattices (SrMnO3)n/(LaMnO3)2n LaMnO3 : Mott insulator, Mn3+, 3d4, AFM SrMnO3 : band insulator, Mn4+, 3d3, AFM Koida et al, PRB 66 144418 (2002) 37 Bhattacharya et al, PRL 100 257003 (2008) Giacomo Ghiringhelli
Manganite superlattices: the effect of layer thickness n = 1, 5, 8 SMO film LMO film MnO2 La LaO Sr MnO2 O Mn LaO MnO2 SrO MnO2 C. Adamo et al, App. Phys. Lett. 92, 112508 (2008) 38 Giacomo Ghiringhelli
LMO/SMO: linear dichroism XLD at room T, no magnetic order, the dichroism is given only by the orbital occupation C. Aruta, C. Adamo, A. Galdi, P. Orgiani, V. Bisogni, N. B. Brookes, J. C. Cezar, P. Thakur, C. A. Perroni, G. De Filippis, V. Cataudella, D. G. Schlom, L. Maritato, and G. Ghiringhelli, Phys. Rev. B 80, 140405(R) (2009), 39 Giacomo Ghiringhelli
LMO/SMO: linear dichroism XLD at low T,magnetic+orbital signal, we take out the room T XLD to remain with the magnetic dichroism only C. Aruta, C. Adamo, A. Galdi, P. Orgiani, V. Bisogni, N. B. Brookes, J. C. Cezar, P. Thakur, C. A. Perroni, G. De Filippis, V. Cataudella, D. G. Schlom, L. Maritato, and G. Ghiringhelli, Phys. Rev. B 80, 140405(R) (2009), 40 Giacomo Ghiringhelli
LMO/SMO: linear dichroism What do we learn about magnetic (AFM+FM) ordering? C. Aruta, C. Adamo, A. Galdi, P. Orgiani, V. Bisogni, N. B. Brookes, J. C. Cezar, P. Thakur, C. A. Perroni, G. De Filippis, V. Cataudella, D. G. Schlom, L. Maritato, and G. Ghiringhelli, Phys. Rev. B 80, 140405(R) (2009), 41 Giacomo Ghiringhelli
LAO/STO XAS: measurements and and Ti4+ calc. Looking for Ti3+ signal at the interface: → Ti4+ is 3d0 → Ti3+ is 3d1 (like in LaTiO3) Ti L2,3 XAS can be perfectly simulated in single ion model (just play with Slater integrals and lifetime broadening) 42 Giacomo Ghiringhelli
LAO/STO XAS: linear dichroism Linear Dichroism: LD = Iz - Ix = Ic – Iab = IH-IV Remember : (001) surface M. Salluzzo, J. C. Cezar, N. B. Brookes, V. Bisogni, G. M. De Luca, C. Richter, S. Thiel, J. Mannhart, M. Huijben, A. Brinkman, G. Rijnders, and G. Ghiringhelli, Phys. Rev. Lett. 102, 166804 (2009), 43 Giacomo Ghiringhelli
LAO/STO: anisotropy of empty 3d orbitals →NO detectable 3d1 signal! →In plane orbitals ar pulled down towards EF Vacuum Interf. Bulk LAO Interf. 44 Giacomo Ghiringhelli
Interface of STO with other materials 0.08 C. Aruta et al, unpublished LD The trend confirms the LDnorm (arb.u.) 0.04 role of the apical 0.00 oxygen at interface: LD -0.04 LAO is stronger when the LGO NGO overlayer has smaller -0.08 458 460 462 464 466 468 lattice parameter Photon energy (eV) XMCD When coupled to manganites a 3d1 contribution appears with ferromagnetism, revealed by XMCD F.Y. Bruno, et al. Phys. Rev. Lett. 106 147205 (2011) 45 Giacomo Ghiringhelli
Ferromagnetic signal in cuprates La2/3Ca1/3MnO3 YBa2Cu3O7 superlattice 46 Giacomo Ghiringhelli
Cuprates: weak ferromagnetism 47 Giacomo Ghiringhelli
Cuprates XMCD: not only a question of interface Benfatto et al. PRB 74 024416 (2006) Djaloszinsky-Moriya interaction at the origin of weak ferromagnetism in AF undoped compounds (La2CuO4). XMCD absent in Sr2CuO2Cl2. We find XMCD in doped compounds too. 48 Giacomo Ghiringhelli
Cuprates XMCD: evaluating the canting angle 49 Giacomo Ghiringhelli
Second order processes What about looking at the emitted x-rays after a resonant absorption? We can access local and collective excitations. Electric dipole selection rules are not an obstacle. Photon momentum can be used to probe dispersion. h out x eout spin sample y z h in polarisation 50 Giacomo Ghiringhelli
RIXS: a resonant inelastic scattering Etransferred=h in-h out |i> h in h out 3dn+1L Charge Transfer |f> 3dn* dd excitations |g> RIXS probes charge neutral local excitations 51 Giacomo Ghiringhelli
RIXS in a metal (if it had worked...) E J-DOS EF Eloss h out -h in 0 h in h out The excited electron is bound: the whole process creates excitations across the Fermi level (somehow similarly to optical absorption). h out depends on h in. Actually spactra a re domiated by fluorescence... Giacomo Ghiringhelli
Resonant fluorescence, or XES E Projected DOS EF h out h in h out The excited electron is “lost”: its final energy is not important and the emission spectrum is independent of h in. Giacomo Ghiringhelli
RIXS works well if there is a gap Gapped systems: Charge neutral excit.: Excitations inside Charge excit.: sharp peaks in the gap the gap continuum E Eloss h out -h in 0 EF Excitation De- excitation s E eout h out h in Strongly correlated systems usually give nice RIXS spectra Time Ground Intermediate Fin al state states states Giacomo Ghiringhelli
Low energy excitations in L2,3 edge RIXS elastic excited states (C) Intensity (arb. units) -7 -6 -5 -4 -3 -2 -1 0 1 Relative emitted energy (eV) Energy loss Giacomo Ghiringhelli
Electronic, magnetic and vibrational excitations in RIXS What excitations can we observe by RIXS? Phonons Magnetic Electronic dd Optical gap CT 1meV 10meV 100meV 1eV 10eV Giacomo Ghiringhelli
L edge RIXS : energy and momentum transfer Resonant Inelastic X-ray Scattering: • an energy loss experiment e E’, k’, ’ pl • made with photons of high energy S am • at a core absorption resonance E, k, Energy Scattering plane h = E - E’ k’ Conservation laws: • Energy q = k-k’ • Momentum Momentum • “Angular momentum” k Giacomo Ghiringhelli
Photon momentum and kinematics Photons vs Neutrons: energy and momentum Wavevector of particles used in inelastic scattering Thermal neutrons 10 n s u tro 1 Ne 1st Brillouin zone boundary k (Ang ) -1 K edges 0.1 L edges 0.01 M edges s on ot 1E-3 Ph 1m 10m 100m 1 10 100 1k 10k 100k energy (eV) Giacomo Ghiringhelli
Cuprates: the “easy” case In cuprates Cu is divalent: Cu2+ 3d9 CuO This makes XAS almost trivial: 1 peak only 3d9 (2p3/2)33d10 928 930 932 934 Photon Energy (eV) RIXS can be calculated even by hand: 3d9 (2p3/2)33d10 (3d9)* Even for magnetic excitations (spin waves), because fast collision approximation is a very good approximation 59 Giacomo Ghiringhelli
dd excitations in Cu2+ systems x2-y2 x2-y2, z2 eg b1 z2 a1 d states 10Dq 10Dq xy b2 yz,zx xy, yz,zx t2g eg Spherical Cubic Tetragonal Interatomic O3 Oh D4h exchange x2-y2 b1 z2 a1 10Dq xy b2 yz,zx eg 3d9 2p53d10 3d9 Giacomo Ghiringhelli
Cu L3 edge RIXS: CuO, La2CuO4, Malachite Cu2+ in square approximately 21 planar coordination Cu-O distances: Intensity (ph. s-1 eV-1) CuO CuO 1.7 – 2-2 Ang 14 LCO 1.9 – 2.4 Ang Malachite 1.9 – 2.6 Ang La2CuO Different Cu2+ 4 x2 7 coordination, symmetry, Cu2(OH) CO3 hybridization 2 0 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 Different dd excitations Energy loss (eV) 61 Giacomo Ghiringhelli
Layered cuprates By using the calculated RIXS cross sections to fit the data the energy of all the 3d orbitals can be obtained from teh RIXS spectra for any compound. M. Moretti Sala, V. Bisogni, L. Braicovich, C. Aruta, G. Balestrino, H. Berger, N. B. Brookes, G.M. De Luca, D. Di Castro, M. Grioni, M. Guarise, P. G. Medaglia, F. Miletto Granozio, M. Minola, M. Radovic, M. Salluzzo, T. Schmitt, K.-J. Zhou, G. Ghiringhelli, New J. Phys. 13, 043026 (2011) Giacomo Ghiringhelli
Ni L3 edge: NiO, NiCl2 Ni2+ (3d8) in octahedral coordination c 40 Intensity (ph. s-1 eV-1) z y x b a NiO 20 z x y NiCl 2 0 a b -4 -3 -2 -1 0 Energy loss (eV) 63 Giacomo Ghiringhelli
Ni2+ in NiO: dependence on incident photon energy 852 853 854 855 856 857 858 Intensity (arb.u.) NiO Ni L3 XAS S P 5 852 853 854 855 856 857 NiO-5 S P 858 P 5 RIXS NiO NiCl 2 4 -4 x5 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 Incident photon energy (eV) RIXS Intensity (ph. s eV -1 ) -1 G. Ghiringhelli et al , Phys Rev Lett 102, 027401 (2009) 64 Giacomo Ghiringhelli
Many excited states relative scattered photon energy (eV) Crystal -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 -4.0 -3.5 field model: Sugano-Tanabe diagrams Ni L RIXS 3 (x2-y2), (z2) intensity (arb. u.) F eg 10Dq H t2g (xy), (yz), (zx) 1.5 10Dq (eV) 1.0 0.5 Single ion 1 G 3 P 1D 3 F 0.0 Octahedral C.F. 1 1 T2g 1 3 A1g 1g T 3 T2g E1g 1 3 A2g 3d spin-orbit T 3 1g T1g Exchange 1 1.5 E 1 g T2g 1.0 10Dq (eV) 0.5 1 3 0.0 G P 1D 3 F Single ion 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 relative state energy (eV) Octahedral C.F. G. Ghiringhelli et al, J. Phys. Cond. Mat. 17, 5397 (2005) S.G.Chiuzbaian, G. Ghiringhelli et al, Phys. Rev. Lett. 95, 197402 (2005) 65 Giacomo Ghiringhelli
Mn L3 edge: MnO, LaMnO3 15 Mn2+ and Mn3+ in octahedral coordination Intensity (ph. s-1 eV-1) 10 Mn2+: 3d5 MnO 5 LaMnO3 x10 0 Mn3+: 3d4 -10 -5 0 Energy loss (eV) 66 Giacomo Ghiringhelli
An application to thin film: Mn2+ in LaxMnO3 RIXS shows that Mn2+ is at LaxMnO3-d/STO films site A, ie, it replaces La3+ x=La/Mn ratio for x<1 becomes FM (self doping) XAS reveals the presence of Mn2+ for x<1 MnO x=0.66 x=0.88 x=0.98 x=1.07 P. Orgiani, A. Galdi, C. Aruta, V. Cataudella, G. De Filippis, C.A. Perroni, V. Marigliano Ramaglia, R. Ciancio, N.B. Brookes, M. Giacomo Ghiringhelli Moretti Sala, G. Ghiringhelli, and L. Maritato, Phys. Rev. B 82, 205122 (2010)
STO/LAO superlattice: RIXS at Ti L3 68 Giacomo Ghiringhelli
Cuprates: not only dd excitations 600 Sr2CuO2Cl2 500 400 300 200 100 0 -8 -6 -4 -2 0 Energy loss Giacomo Ghiringhelli (eV)
La2CuO4: 2D spin ½ Heisenberg AF insulator Oxygen Copper DIRECT SPACE RECIPROCAL SPACE nuclear BZ ( , ) (0,0) ( ,0) magnetic BZ Elementary magnetic excitations are spin waves Giacomo Ghiringhelli
Dispersing peaks: magnetic excitations SAXES & Swiss Light Sour ce Politecnico di Milano La2CuO4 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 Energy loss (eV) Giacomo Ghiringhelli
LCO, comparing with INS: these are magnons! La2CuO4 R. Coldea et al, Phys. Rev. Lett. 86, 5377 (2001). L. Braicovich, J. van den Brink, V. Bisogni, M. Moretti Sala, L. Ament, N.B. Brookes, G.M. de Luca, M. Salluzzo, T. Schmitt, and G. Ghiringhelli PRL 104 077002 (2010) Giacomo Ghiringhelli
Another example: magnons in SCOC Sr2CuO2Cl2 M. Guarise, B. Dalla Piazza, M. Moretti Sala, G. Ghiringhelli, L. Braicovich, H. Berger, J.N. Hancock, D. van der Marel, T. Schmitt, V.N. Strocov, L.J.P. Ament, J. van den Brink, P.-H. Lin, P. Xu, H. M. Rønnow, and M. Grioni. Phys. Rev. Lett. 105, 157006 (2010) Giacomo Ghiringhelli
What happens in doped, SC cuprates? NdBCO Superconducting: Tc= 65K Insulating (annealed) 300 300 200 200 100 100 Intensity (a.u.) Intensity (a.u.) 0 0 -100 -100 -200 -200 -0.6 -0.4 -0.2 0.0 0.2 -0.6 -0.4 -0.2 0.0 0.2 Energy (eV) Energy (eV) Giacomo Ghiringhelli
YBCO and NdBCO family (Keimer, Le Tacon) Giacomo Ghiringhelli
Theory of magnetic RIXS (1) Single ion cross section Linear spin wave theory 76 Giacomo Ghiringhelli
Theory of magnetic RIXS (2) 77 Giacomo Ghiringhelli
CaCuO2/SrTiO3 superlattice: superconductor D. Di Castro, M. Salvato, A. Tebano, D. Innocenti, P. G. Medaglia, M. Cirillo, and G. Balestrino, arXiv1107.2239v1 (2011) 78 Giacomo Ghiringhelli
CaCuO2/SrTiO3 superlattice: RIXS 100 CCO bulk 400 SL n = 2 SL n=2 Norm. Intensity (arb. u.) SL n = 3 80 SL n=3 bulk CCO 300 Energy (meV) 60 200 40 100 20 0 0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.0 2.5 2.0 1.5 1.0 q// Energy Loss (eV) M. Minola, D. Di Castro, G. Ghiringhelli, M. Moretti Sala, N. B. Brookes, P.G. Medaglia, A. Tebano, G. Balestrino and L. Braicovich, unpublished 79 Giacomo Ghiringhelli
Instrumentation and perspectives With high resolution L edge RIXS We can probe orbital and magnetic excitations In layered cuprates we can map E(q) of magnons and we can thus complement optical spectroscopy, EELS and INS EXPERIMENTS the limitations are still E resolution and intensity. AXES at the ESRF SAXES at the SLS Giacomo Ghiringhelli
From AXES (ESRF, ID08) to SAXES (SLS, ADRESS) SAXES & Swiss Light Sour ce Politecnico di Milano INFM A dvanced X -Ray Emission Spectroscopy Since 1994: AXES at beam line Since 2007: SAXES at beam line ID08 of the ESRF ADRESS of the SLS L = 2.2 m L = 5.0 m Design: E/ E = 2,000 at Cu L3 (930 eV) Design: E/ E = 12,000 at Cu L3 2010: E/ E = 5,000 at Cu L3 2008: E/ E = 10,000 at Cu L3 C. Dallera et al. J. Synchrotron Radiat. 3, 231 (1996) G. Ghiringhelli, et al Rev. Sci. Instrum. 77, 113108 (2006) G. Ghiringhelli et al., Rev. Sci. Instrum. 69, 1610 (1998) V. Strocov, T. Schmitt, L. Patthey et al, J. Synch. Rad., 17, 631 (2010). M. Dinardo et al., Nucl, Instrum. Meth A 570, 176 (2007) Same optical scheme: • VLS spherical grating • CCD detector Different length L Giacomo Ghiringhelli
The future of RIXS instrumentation ЄRIXS:The Єuropean RIXS facility (N.B Brookes) E down to 30 meV at Cu L3 and 10 meV at Ti L3 10 m Other high resolution RIXS projects: • Centurion, at NSLS II (Brookhaven Nat Lab) • Diamond (UK) • MAX IV (Sweden) • NSRRC (Taiwan) • ... 82 Giacomo Ghiringhelli
Bibliography 83 Giacomo Ghiringhelli

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X-Ray Absorption Spectroscopy

  • 1.
    MAX-PLANCK-UBC CENTRE FOR QUANTUM MATERIALS International Summer School on Surfaces and Interfaces in Correlated Oxides 30th August, 2011 Giacomo Ghiringhelli Dipartimento di Fisica Politecnico di Milano Italy giacomo.ghiringhelli@fisi.polimi.it
  • 2.
    Introducing myself... Picture of POLIMI Keywords: • Synchrotron radiation • Soft x-rays • Resonant spectroscopy • 3d transition metal oxides 2 Giacomo Ghiringhelli
  • 3.
    Summary 1. Why synchrotron radiation? • Main properties • Absorption edges and x-ray energies 2. XAS: x-ray absorption spectroscopy • Basic process and the choice of absorption edges • XLD and XMCD: polarization dependent XAS • Some examples on oxide interfaces 3. RIXS: resonant inelastic x-,ray scattering • A second order process • dd excitations • Magnetic excitations 3 Giacomo Ghiringhelli
  • 4.
    Synchrotron radiation, summary 4 Giacomo Ghiringhelli
  • 5.
    Undulators: many photons 5 Giacomo Ghiringhelli
  • 6.
    Undulators: polarization control Elettroni Campo Luce polarizzata magnetico linearmente Lu ce po lar izz ata circolarmente Elettroni Campo magnetico Full control of the polarization at the source: • Linear horizontal or vertical or any orientation (more difficult) • Circular Right or Left handed 6 Giacomo Ghiringhelli
  • 7.
    Beam line High quality mirrors, gratings and crystals are needed to make the beam monochromatic (bandas narrow as possible) and to focalize it onto the sample State of the art beam lines for resonant spectroscopy Parameter Typical figures Flux at the sample 1010 - 1013 photons/s Beam size at sample (hoz x ver) 50 m x 5 m - 1 mm x 1 mm Energy bandpass: UV (20 – 50 eV) 10 - 50 meV soft x rays (300 – 1000 eV) 50 – 500 meV hard x rays (2 - 10 keV) 50 – 500 meV 7 Giacomo Ghiringhelli
  • 8.
    X-ray spectroscopy for3d Transition Metal systems E 3dTM oxides X-ray resonant spectroscopies Ev • XAS: x-ray absorption 4sp spectroscopy EF 3d • XLD and XMCD: polarization dependent XAS Ox 2p • RIXS: resonant inelastic x-ray 3p scattering • Resonant reflectivity • Resonant Elastic X-ray 2p Scattering • Resonant Photoemission 1s 8 Giacomo Ghiringhelli
  • 9.
    X-ray Absorption measurements X rays Tunable or X rays Monochromator “white” source e nA Detection: • transmission (only hard x-rays) • fluorescence yield • electron yield (including drain current) 9 Giacomo Ghiringhelli
  • 10.
    X-ray Absorption CrossSection log scale 2.5 OK 1 530 eV Cu L2,3 CuO 930-950 eV 2.0 Absorption coefficient (arb. u.) Cu 0.1 M edges 1.5 0.01 Cu K 9000 eV 1.0 1E-3 Linear 0.5 scale 1E-4 0.0 10 100 1000 10000 Photon Energy (eV) 10 Giacomo Ghiringhelli
  • 11.
    Resonances in theXAS 3d TM E Oxygen Rare Earths 4sp 6s,5d EFermi 3d 2p 4f 2s M2,3 edges (28-77 eV) 3p K edge 530 eV 1s L2,3 edges (400-950 eV) 2p M4,5 edges 3d (830-1580 eV) K edge (4.5-9.0 keV) 1s L2,3 edges 2p (5.5-10 keV) Strong resonances 11 Giacomo Ghiringhelli
  • 12.
    Core levels C O Si Sc Fe Zn Y Mo Cd Ce Gd Lu Au Th 3dTM 4dTM RE Actinides 100000 K Hard X-Rays L3 10000 Binding energy (eV) M3 M5 Soft X-Rays 1000 100 UV 2p3/2 3p 10 1s 3/2 3d5/2 4p3/2 4d5/2 0 10 20 30 40 50 60 70 80 90 100 Atomic number Z Giacomo Ghiringhelli 12 - Politecnico di Milano; Source: X-ray data booklet, Lawrence Berkeley National Laboratory GG 25/03/02 18:29:59
  • 13.
    3p: M2,3 edgeXAS Spin-Orbit splitting Spin-Orbit splitting Source: S. Nakai, et al PRB 9, 1870 (1974) 13 Giacomo Ghiringhelli
  • 14.
    2p: L2,3 edgeXAS Spin-Orbit Spin-Orbit splitting splitting Mn L2,3 XAS L3 L3 La0.7Sr0.3MnO3 NiO Ni metal 850 855 860 L2 NiO MnO Ni metal 850 860 870 880 640 645 650 655 660 Photon Energy (eV) photon energy (eV) Source: G. Ghiringhelli, N.B. Brookes et al unpublished Source: C. Aruta, G. Ghiringhelli et al unpublished 14 Giacomo Ghiringhelli
  • 15.
    Atomic model Total E 3dTM - O 2p53dn+2L 2p53dn+1 M.S.: Multiplet Splitting C.I.: Configuration 3dn+1L Interaction 3dn |g> XAS probes orbital occupation C.I. M.S. 15 Giacomo Ghiringhelli
  • 16.
    L3 XAS andmultiplets Excit ation De- excitation s eout E CuO h ou t 3d h in 2p3/2 928 930 932 934 Photon Energy (eV) Excited Ti me Ground Ground states Intermediate Fin al MnO state stat es stat es state Resonant scattering without relaxation of intermediate state 3d n 2p53d n+1 CuO: 3d9  3d10 One single peak NiO: 3d8  3d9 Many peaks MnO: 3d5  3d6 636 638 640 642 644 646 photon energy (eV) 16 Giacomo Ghiringhelli
  • 17.
    L3 XAS andvalence L3 L2 2.1 eV CuO: Cu2+ is 3d9 Cu2O: Cu1+ is 3d10 CuO Cu2O Cu metal: 3d104s1 930 935 940 Photon Energy (eV) Source: M. Grioni et al PRB 45, 3309 (1992) Source: M. Finazzi et al PRB 61, 4629 (2000) 17 Giacomo Ghiringhelli
  • 18.
    X-ray absorption intensity Fermi golden rule Joint density Matrix element of states, separated by energy h Electric dipole perturbation associated to a photon 18 Giacomo Ghiringhelli
  • 19.
    Electric dipole selectionrules f ε r i 3 * r R Ri dr f Y ε u rYi d * f Radial integral Angular integral Mind the nodes of R! 4 0 NB what matters is Rf , ε ur Y1 3 in the presence of the core hole! Selection rules (via Wigner- Eckart) l=0 Transitions pd l=1 Y2m '* Y1 p Y1m m=-1,0,+1 p=-1,0,+1 l=2 m’=m-1,m,m+1 19 Giacomo Ghiringhelli
  • 20.
    Crystal field z Cu: x2-y2 orbital x2-y2, z2 x2-y2 eg b1 z2 a1 x d states 10Dq 10Dq xy b2 yz,zx xy, yz,zx t2g eg y Spherical Cubic Tetragonal O3 Oh D4h 20 Giacomo Ghiringhelli
  • 21.
    3d split states t2g states z eg states e zx z z z x y z x x y x y y b2 xy x b1 x2-y2 a1 z2 e yz y 21 Giacomo Ghiringhelli
  • 22.
    2p states alloccupied: Spherical harmonics and orbitals anisotropy in final states spherical distribution 3d states partly empty: |Y1-1|2 = |Y11|2 |Y10|2 2 |Y2-2|2 = |Y22|2 |Y2-1|2 = |Y22|2 |Y20| Y1-1= Y11= Y10= 22
  • 23.
    2p to 3dtransitions 2p3/2 photon 3d • Spherical distribution • Anisotropic occupation • No well defined spin due to crystal field state • Possible spin polarization • Spin “parallel” to (FM or AF) orbital moment • Spin-orbit interaction not always negligible RCP = Y11 LCP = Y1-1 z-linear = Y10 x-linear = (Y1-1+Y11)/sqrt(2) 23 Giacomo Ghiringhelli
  • 24.
    Transition of ahole from 3d to 2p 3d photon 2p3/2 Example: transition to a 3d(x2-y2) orbital RCP = Y11 Initial state 3d hole is 100% spin down Final state 2p hole has main spin up character 24 Giacomo Ghiringhelli
  • 25.
    Linear polarization ofx-rays: orbital occupation Empty 3d state Empty 3d state E E z h in h in z E E x x y y b1 x2-y2 (Y2-2+Y22) a1 z2 Y20 High absorption (Y1-1+Y11) Weak absorption No absorption Y10 High absorption 25 Giacomo Ghiringhelli
  • 26.
    3d hole symmetryin cuprates 3d9 (2p3/2)33d10 h E Result: the hole in Cu2+ has 100% x2-y2 symmetry 26 Giacomo Ghiringhelli
  • 27.
    Linear polarization ofx-rays: magnetization orientation Atomic spin Atomic spin orientation orientation E E h in h in E E M M Different absorption Same absorption MAGNETIC LINEAR DICHROISM: Works for Ferro and AntiFerro 27 Giacomo Ghiringhelli
  • 28.
    Circular polarization ofx-rays and ferromagnetic materials XAS-MCD: x-ray absorption magnetic circular dichroism E z M Fermi level LCP 3d m L3: 2p3/2 3d 3d RCP M L2: 2p1/2 3d j=3/2 2p j=1/2 2p 3/2 sample number of matrix free states elements RCP m=-1 z transition rates z m=1 LCP absorption XAS-MCD LCP RCP experimental geometry M L3 28 Giacomo Ghiringhelli
  • 29.
    XMCD: sum rules For late 3dTM sum rules allow to extract spin and orbital magnetic moments directly from spectra without the need of theoretical simulations of spectra 8 40 Fe (L3+L2) Co Ni 7 6 L3 L2 L3 L2 L3 L2 30 Integrated Intensity (arb. units) 5 (L3+L2) Intensity (arb. units) 4 20 3 (L3+L2) 2 10 1 0 0 (L3+L2) (L3+L2) (L3) (L3+L2) -1 (L3) (L3) -2 -10 700 720 740 760 780 800 820 840 860 880 900 Photon energy (eV) 29 Giacomo Ghiringhelli
  • 30.
    XAS: some examples Manganite thin films • Strain and orbital occupation • Magnetic anisotropy (FM and AF) STO/LAO interface Cuprates: ferromagnetism 30 Giacomo Ghiringhelli
  • 31.
    Films of La2/3Sr1/3MnO3:strain and phase separation Manganites: Mn3+: 3d4 → Mn3+/Mn4+ Mn4+: 3d3 → CMR LaMnO3 Mott Hubbard Insulator: → Phase separation Mn – Mn fluctuations → Orbital ordering more likely than O - Mn 31 Giacomo Ghiringhelli
  • 32.
    Manganites XAS: strainand orbital occupation 8 100 u.c. V (E//ab) XAS (V, H) [a.u.] 6 H (E//c) SrTiO3 substrate c/a=0.98 z2 4 x2- y2 z2 eg 2 z-in x2-y2 LSMO 0 Doct 0.3 STO t2g yz xz V-H [a.u.] 0.0 yz xz xy -0.3 xy -0.6 Linear Dichroism=IXAS//ab-IXAS//c 637 644 651 658 Preferential occupation of in-plane 3dx2-y2 orbitals Photon Energy [eV] 8 100 u.c. V (E//ab) LaAlO3 substrate c/a=1.04 XAS (V, H) [a.u.] 6 H (E//c) 4 x2- y2 x2- y2 z2 2 eg 0 0.3 LSMO z-out z2 Doct 0.0 xy V-H [a.u.] -0.3 t2g yz xz xy -0.6 LAO yz xz 637 644 651 658 Photon Energy [eV] Preferential occupation of the out-of-plane 3dz2–r2 orbitals 32 Giacomo Ghiringhelli
  • 33.
    Manganites XAS: strainand dimensionality How strain and reduced dimensionality influence magnetic and orbital anisotropies 33 Giacomo Ghiringhelli
  • 34.
    Manganites XAS: ferromagneticbehavior XMCD: FM hysteresis loops 34 Giacomo Ghiringhelli
  • 35.
    Manganites XAS: lineardichroism LD: magnetic and orbital anisotropy 35 Giacomo Ghiringhelli
  • 36.
    Manganites XAS: magneticlinear dichroism MLD: ferromagnetic and antiferromagnetic anisotropy 36 Giacomo Ghiringhelli
  • 37.
    Manganite superlattices (SrMnO3)n/(LaMnO3)2n LaMnO3 : Mott insulator, Mn3+, 3d4, AFM SrMnO3 : band insulator, Mn4+, 3d3, AFM Koida et al, PRB 66 144418 (2002) 37 Bhattacharya et al, PRL 100 257003 (2008) Giacomo Ghiringhelli
  • 38.
    Manganite superlattices: theeffect of layer thickness n = 1, 5, 8 SMO film LMO film MnO2 La LaO Sr MnO2 O Mn LaO MnO2 SrO MnO2 C. Adamo et al, App. Phys. Lett. 92, 112508 (2008) 38 Giacomo Ghiringhelli
  • 39.
    LMO/SMO: linear dichroism XLD at room T, no magnetic order, the dichroism is given only by the orbital occupation C. Aruta, C. Adamo, A. Galdi, P. Orgiani, V. Bisogni, N. B. Brookes, J. C. Cezar, P. Thakur, C. A. Perroni, G. De Filippis, V. Cataudella, D. G. Schlom, L. Maritato, and G. Ghiringhelli, Phys. Rev. B 80, 140405(R) (2009), 39 Giacomo Ghiringhelli
  • 40.
    LMO/SMO: linear dichroism XLD at low T,magnetic+orbital signal, we take out the room T XLD to remain with the magnetic dichroism only C. Aruta, C. Adamo, A. Galdi, P. Orgiani, V. Bisogni, N. B. Brookes, J. C. Cezar, P. Thakur, C. A. Perroni, G. De Filippis, V. Cataudella, D. G. Schlom, L. Maritato, and G. Ghiringhelli, Phys. Rev. B 80, 140405(R) (2009), 40 Giacomo Ghiringhelli
  • 41.
    LMO/SMO: linear dichroism What do we learn about magnetic (AFM+FM) ordering? C. Aruta, C. Adamo, A. Galdi, P. Orgiani, V. Bisogni, N. B. Brookes, J. C. Cezar, P. Thakur, C. A. Perroni, G. De Filippis, V. Cataudella, D. G. Schlom, L. Maritato, and G. Ghiringhelli, Phys. Rev. B 80, 140405(R) (2009), 41 Giacomo Ghiringhelli
  • 42.
    LAO/STO XAS: measurementsand and Ti4+ calc. Looking for Ti3+ signal at the interface: → Ti4+ is 3d0 → Ti3+ is 3d1 (like in LaTiO3) Ti L2,3 XAS can be perfectly simulated in single ion model (just play with Slater integrals and lifetime broadening) 42 Giacomo Ghiringhelli
  • 43.
    LAO/STO XAS: lineardichroism Linear Dichroism: LD = Iz - Ix = Ic – Iab = IH-IV Remember : (001) surface M. Salluzzo, J. C. Cezar, N. B. Brookes, V. Bisogni, G. M. De Luca, C. Richter, S. Thiel, J. Mannhart, M. Huijben, A. Brinkman, G. Rijnders, and G. Ghiringhelli, Phys. Rev. Lett. 102, 166804 (2009), 43 Giacomo Ghiringhelli
  • 44.
    LAO/STO: anisotropy ofempty 3d orbitals →NO detectable 3d1 signal! →In plane orbitals ar pulled down towards EF Vacuum Interf. Bulk LAO Interf. 44 Giacomo Ghiringhelli
  • 45.
    Interface of STOwith other materials 0.08 C. Aruta et al, unpublished LD The trend confirms the LDnorm (arb.u.) 0.04 role of the apical 0.00 oxygen at interface: LD -0.04 LAO is stronger when the LGO NGO overlayer has smaller -0.08 458 460 462 464 466 468 lattice parameter Photon energy (eV) XMCD When coupled to manganites a 3d1 contribution appears with ferromagnetism, revealed by XMCD F.Y. Bruno, et al. Phys. Rev. Lett. 106 147205 (2011) 45 Giacomo Ghiringhelli
  • 46.
    Ferromagnetic signal incuprates La2/3Ca1/3MnO3 YBa2Cu3O7 superlattice 46 Giacomo Ghiringhelli
  • 47.
    Cuprates: weak ferromagnetism 47 Giacomo Ghiringhelli
  • 48.
    Cuprates XMCD: notonly a question of interface Benfatto et al. PRB 74 024416 (2006) Djaloszinsky-Moriya interaction at the origin of weak ferromagnetism in AF undoped compounds (La2CuO4). XMCD absent in Sr2CuO2Cl2. We find XMCD in doped compounds too. 48 Giacomo Ghiringhelli
  • 49.
    Cuprates XMCD: evaluatingthe canting angle 49 Giacomo Ghiringhelli
  • 50.
    Second order processes What about looking at the emitted x-rays after a resonant absorption? We can access local and collective excitations. Electric dipole selection rules are not an obstacle. Photon momentum can be used to probe dispersion. h out x eout spin sample y z h in polarisation 50 Giacomo Ghiringhelli
  • 51.
    RIXS: a resonantinelastic scattering Etransferred=h in-h out |i> h in h out 3dn+1L Charge Transfer |f> 3dn* dd excitations |g> RIXS probes charge neutral local excitations 51 Giacomo Ghiringhelli
  • 52.
    RIXS in ametal (if it had worked...) E J-DOS EF Eloss h out -h in 0 h in h out The excited electron is bound: the whole process creates excitations across the Fermi level (somehow similarly to optical absorption). h out depends on h in. Actually spactra a re domiated by fluorescence... Giacomo Ghiringhelli
  • 53.
    Resonant fluorescence, orXES E Projected DOS EF h out h in h out The excited electron is “lost”: its final energy is not important and the emission spectrum is independent of h in. Giacomo Ghiringhelli
  • 54.
    RIXS works wellif there is a gap Gapped systems: Charge neutral excit.: Excitations inside Charge excit.: sharp peaks in the gap the gap continuum E Eloss h out -h in 0 EF Excitation De- excitation s E eout h out h in Strongly correlated systems usually give nice RIXS spectra Time Ground Intermediate Fin al state states states Giacomo Ghiringhelli
  • 55.
    Low energy excitationsin L2,3 edge RIXS elastic excited states (C) Intensity (arb. units) -7 -6 -5 -4 -3 -2 -1 0 1 Relative emitted energy (eV) Energy loss Giacomo Ghiringhelli
  • 56.
    Electronic, magnetic andvibrational excitations in RIXS What excitations can we observe by RIXS? Phonons Magnetic Electronic dd Optical gap CT 1meV 10meV 100meV 1eV 10eV Giacomo Ghiringhelli
  • 57.
    L edge RIXS: energy and momentum transfer Resonant Inelastic X-ray Scattering: • an energy loss experiment e E’, k’, ’ pl • made with photons of high energy S am • at a core absorption resonance E, k, Energy Scattering plane h = E - E’ k’ Conservation laws: • Energy q = k-k’ • Momentum Momentum • “Angular momentum” k Giacomo Ghiringhelli
  • 58.
    Photon momentum andkinematics Photons vs Neutrons: energy and momentum Wavevector of particles used in inelastic scattering Thermal neutrons 10 n s u tro 1 Ne 1st Brillouin zone boundary k (Ang ) -1 K edges 0.1 L edges 0.01 M edges s on ot 1E-3 Ph 1m 10m 100m 1 10 100 1k 10k 100k energy (eV) Giacomo Ghiringhelli
  • 59.
    Cuprates: the “easy”case In cuprates Cu is divalent: Cu2+ 3d9 CuO This makes XAS almost trivial: 1 peak only 3d9 (2p3/2)33d10 928 930 932 934 Photon Energy (eV) RIXS can be calculated even by hand: 3d9 (2p3/2)33d10 (3d9)* Even for magnetic excitations (spin waves), because fast collision approximation is a very good approximation 59 Giacomo Ghiringhelli
  • 60.
    dd excitations inCu2+ systems x2-y2 x2-y2, z2 eg b1 z2 a1 d states 10Dq 10Dq xy b2 yz,zx xy, yz,zx t2g eg Spherical Cubic Tetragonal Interatomic O3 Oh D4h exchange x2-y2 b1 z2 a1 10Dq xy b2 yz,zx eg 3d9 2p53d10 3d9 Giacomo Ghiringhelli
  • 61.
    Cu L3 edgeRIXS: CuO, La2CuO4, Malachite Cu2+ in square approximately 21 planar coordination Cu-O distances: Intensity (ph. s-1 eV-1) CuO CuO 1.7 – 2-2 Ang 14 LCO 1.9 – 2.4 Ang Malachite 1.9 – 2.6 Ang La2CuO Different Cu2+ 4 x2 7 coordination, symmetry, Cu2(OH) CO3 hybridization 2 0 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 Different dd excitations Energy loss (eV) 61 Giacomo Ghiringhelli
  • 62.
    Layered cuprates By using the calculated RIXS cross sections to fit the data the energy of all the 3d orbitals can be obtained from teh RIXS spectra for any compound. M. Moretti Sala, V. Bisogni, L. Braicovich, C. Aruta, G. Balestrino, H. Berger, N. B. Brookes, G.M. De Luca, D. Di Castro, M. Grioni, M. Guarise, P. G. Medaglia, F. Miletto Granozio, M. Minola, M. Radovic, M. Salluzzo, T. Schmitt, K.-J. Zhou, G. Ghiringhelli, New J. Phys. 13, 043026 (2011) Giacomo Ghiringhelli
  • 63.
    Ni L3 edge:NiO, NiCl2 Ni2+ (3d8) in octahedral coordination c 40 Intensity (ph. s-1 eV-1) z y x b a NiO 20 z x y NiCl 2 0 a b -4 -3 -2 -1 0 Energy loss (eV) 63 Giacomo Ghiringhelli
  • 64.
    Ni2+ in NiO:dependence on incident photon energy 852 853 854 855 856 857 858 Intensity (arb.u.) NiO Ni L3 XAS S P 5 852 853 854 855 856 857 NiO-5 S P 858 P 5 RIXS NiO NiCl 2 4 -4 x5 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 Incident photon energy (eV) RIXS Intensity (ph. s eV -1 ) -1 G. Ghiringhelli et al , Phys Rev Lett 102, 027401 (2009) 64 Giacomo Ghiringhelli
  • 65.
    Many excited states relative scattered photon energy (eV) Crystal -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 -4.0 -3.5 field model: Sugano-Tanabe diagrams Ni L RIXS 3 (x2-y2), (z2) intensity (arb. u.) F eg 10Dq H t2g (xy), (yz), (zx) 1.5 10Dq (eV) 1.0 0.5 Single ion 1 G 3 P 1D 3 F 0.0 Octahedral C.F. 1 1 T2g 1 3 A1g 1g T 3 T2g E1g 1 3 A2g 3d spin-orbit T 3 1g T1g Exchange 1 1.5 E 1 g T2g 1.0 10Dq (eV) 0.5 1 3 0.0 G P 1D 3 F Single ion 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 relative state energy (eV) Octahedral C.F. G. Ghiringhelli et al, J. Phys. Cond. Mat. 17, 5397 (2005) S.G.Chiuzbaian, G. Ghiringhelli et al, Phys. Rev. Lett. 95, 197402 (2005) 65 Giacomo Ghiringhelli
  • 66.
    Mn L3 edge:MnO, LaMnO3 15 Mn2+ and Mn3+ in octahedral coordination Intensity (ph. s-1 eV-1) 10 Mn2+: 3d5 MnO 5 LaMnO3 x10 0 Mn3+: 3d4 -10 -5 0 Energy loss (eV) 66 Giacomo Ghiringhelli
  • 67.
    An application tothin film: Mn2+ in LaxMnO3 RIXS shows that Mn2+ is at LaxMnO3-d/STO films site A, ie, it replaces La3+ x=La/Mn ratio for x<1 becomes FM (self doping) XAS reveals the presence of Mn2+ for x<1 MnO x=0.66 x=0.88 x=0.98 x=1.07 P. Orgiani, A. Galdi, C. Aruta, V. Cataudella, G. De Filippis, C.A. Perroni, V. Marigliano Ramaglia, R. Ciancio, N.B. Brookes, M. Giacomo Ghiringhelli Moretti Sala, G. Ghiringhelli, and L. Maritato, Phys. Rev. B 82, 205122 (2010)
  • 68.
    STO/LAO superlattice: RIXSat Ti L3 68 Giacomo Ghiringhelli
  • 69.
    Cuprates: not onlydd excitations 600 Sr2CuO2Cl2 500 400 300 200 100 0 -8 -6 -4 -2 0 Energy loss Giacomo Ghiringhelli (eV)
  • 70.
    La2CuO4: 2D spin½ Heisenberg AF insulator Oxygen Copper DIRECT SPACE RECIPROCAL SPACE nuclear BZ ( , ) (0,0) ( ,0) magnetic BZ Elementary magnetic excitations are spin waves Giacomo Ghiringhelli
  • 71.
    Dispersing peaks: magneticexcitations SAXES & Swiss Light Sour ce Politecnico di Milano La2CuO4 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 Energy loss (eV) Giacomo Ghiringhelli
  • 72.
    LCO, comparing withINS: these are magnons! La2CuO4 R. Coldea et al, Phys. Rev. Lett. 86, 5377 (2001). L. Braicovich, J. van den Brink, V. Bisogni, M. Moretti Sala, L. Ament, N.B. Brookes, G.M. de Luca, M. Salluzzo, T. Schmitt, and G. Ghiringhelli PRL 104 077002 (2010) Giacomo Ghiringhelli
  • 73.
    Another example: magnonsin SCOC Sr2CuO2Cl2 M. Guarise, B. Dalla Piazza, M. Moretti Sala, G. Ghiringhelli, L. Braicovich, H. Berger, J.N. Hancock, D. van der Marel, T. Schmitt, V.N. Strocov, L.J.P. Ament, J. van den Brink, P.-H. Lin, P. Xu, H. M. Rønnow, and M. Grioni. Phys. Rev. Lett. 105, 157006 (2010) Giacomo Ghiringhelli
  • 74.
    What happens indoped, SC cuprates? NdBCO Superconducting: Tc= 65K Insulating (annealed) 300 300 200 200 100 100 Intensity (a.u.) Intensity (a.u.) 0 0 -100 -100 -200 -200 -0.6 -0.4 -0.2 0.0 0.2 -0.6 -0.4 -0.2 0.0 0.2 Energy (eV) Energy (eV) Giacomo Ghiringhelli
  • 75.
    YBCO and NdBCOfamily (Keimer, Le Tacon) Giacomo Ghiringhelli
  • 76.
    Theory of magneticRIXS (1) Single ion cross section Linear spin wave theory 76 Giacomo Ghiringhelli
  • 77.
    Theory of magneticRIXS (2) 77 Giacomo Ghiringhelli
  • 78.
    CaCuO2/SrTiO3 superlattice: superconductor D. Di Castro, M. Salvato, A. Tebano, D. Innocenti, P. G. Medaglia, M. Cirillo, and G. Balestrino, arXiv1107.2239v1 (2011) 78 Giacomo Ghiringhelli
  • 79.
    CaCuO2/SrTiO3 superlattice: RIXS 100 CCO bulk 400 SL n = 2 SL n=2 Norm. Intensity (arb. u.) SL n = 3 80 SL n=3 bulk CCO 300 Energy (meV) 60 200 40 100 20 0 0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.0 2.5 2.0 1.5 1.0 q// Energy Loss (eV) M. Minola, D. Di Castro, G. Ghiringhelli, M. Moretti Sala, N. B. Brookes, P.G. Medaglia, A. Tebano, G. Balestrino and L. Braicovich, unpublished 79 Giacomo Ghiringhelli
  • 80.
    Instrumentation and perspectives With high resolution L edge RIXS We can probe orbital and magnetic excitations In layered cuprates we can map E(q) of magnons and we can thus complement optical spectroscopy, EELS and INS EXPERIMENTS the limitations are still E resolution and intensity. AXES at the ESRF SAXES at the SLS Giacomo Ghiringhelli
  • 81.
    From AXES (ESRF,ID08) to SAXES (SLS, ADRESS) SAXES & Swiss Light Sour ce Politecnico di Milano INFM A dvanced X -Ray Emission Spectroscopy Since 1994: AXES at beam line Since 2007: SAXES at beam line ID08 of the ESRF ADRESS of the SLS L = 2.2 m L = 5.0 m Design: E/ E = 2,000 at Cu L3 (930 eV) Design: E/ E = 12,000 at Cu L3 2010: E/ E = 5,000 at Cu L3 2008: E/ E = 10,000 at Cu L3 C. Dallera et al. J. Synchrotron Radiat. 3, 231 (1996) G. Ghiringhelli, et al Rev. Sci. Instrum. 77, 113108 (2006) G. Ghiringhelli et al., Rev. Sci. Instrum. 69, 1610 (1998) V. Strocov, T. Schmitt, L. Patthey et al, J. Synch. Rad., 17, 631 (2010). M. Dinardo et al., Nucl, Instrum. Meth A 570, 176 (2007) Same optical scheme: • VLS spherical grating • CCD detector Different length L Giacomo Ghiringhelli
  • 82.
    The future ofRIXS instrumentation ЄRIXS:The Єuropean RIXS facility (N.B Brookes) E down to 30 meV at Cu L3 and 10 meV at Ti L3 10 m Other high resolution RIXS projects: • Centurion, at NSLS II (Brookhaven Nat Lab) • Diamond (UK) • MAX IV (Sweden) • NSRRC (Taiwan) • ... 82 Giacomo Ghiringhelli
  • 83.
    Bibliography 83 Giacomo Ghiringhelli