Neutron and x-ray spectroscopy

Transcription

1 Neutron and x-ray spectroscopy B. Keimer Max-Planck-Institute for Solid State Research outline 1. self-contained introduction neutron scattering and spectroscopy x-ray scattering and spectroscopy 2. application to correlated-electron materials bulk interfaces

2 Neutron and x-ray spectroscopy outline 1. weak correlations: Pb, Nb 2. intermediate correlations: Sr 2 RuO 4 3. strong correlations: YBa 2 Cu 3 O 6+x 4. orbital degeracy: La 1-x Ca x MnO 3 (Y,La)TiO 3 5. oxide heterostructures

3 Neutron and x-ray spectroscopy outline 1. weak correlations: Pb, Nb 2. intermediate correlations: Sr 2 RuO 4 3. strong correlations: YBa 2 Cu 3 O 6+x 4. orbital degeracy: La 1-x Ca x MnO 3 (Y,La)TiO 3 5. oxide heterostructures

4 Electron-phonon interaction electron-phonon interaction in simple metals predicted by ab-initio LDA example MgB 2 Kong et al., PRB 2001 strong coupling short phonon lifetime typical phonon linewidth: μev

5 Inelastic nuclear neutron scattering K) K)} phonon creation neutron energy loss phonon annihilaion neutron energy gain

6 Neutron spectroscopy 2 h 2 2 hω = ( k f ki ) 2m q = k k f i analyzer coil 1 coil 2 monochromator sample detector triple axis spectrometer: excitation energy ~ mev energy resolution ~ mev triple axis spin echo spectrometer: excitation energy ~ mev energy resolution ~ μev 3 orders of magnitude gain in energy resolution possible to resolve excitation lifetimes in solids

7 TRISP Spectrometer at FRM-II

8 Electron-phonon interaction in Pb phonon dispersions Brockhouse et al., PR 1963 ab-initio lattice dynamics L. Boeri, MPI-FKF

9 Electron-phonon interaction in Pb lifetime renormalization below superconducting T c = 7.2 K E energy gap Pb phonon energy T c T Keller et al., PRL 2006

10 Electron-phonon interaction in Pb E phonon energy energy gap Δ ξ Δ (0.07 T c ) Δ (0.8 T c ) Aynajian et al. Science 2008

11 Electron-phonon interaction in Pb superconducting energy gap merges with second linewidth maximum at low T

12 Electron-phonon interaction in Pb Aynajian et al. Science 2008 series of linewidth maxima persists up to T >> T c most likely origin: Kohn anomalies but not predicted in TA branch by ab-initio LDA calculations

13 Accident? niobium Aynajian et al. Science 2008 no! same effect observed in Nb also rules out spin-orbit coupling as origin

14 Origin: Kohn anomaly? acoustic phonons in TaS 2 quasi-2d metal q 0 q y q 0 q x Kohn anomaliy precursor to charge-density-wave formation at T = 122 K Moncton et al., PRB 1977

15 Electron-phonon interaction in Pb and Nb scenario many-body effects beyond LDA: spin/charge density wave fluctuations dynamical nesting Kohn anomalies interference between SDW/CDW and superconducting fluctuations limits growth of superconducting energy gap not anticipated by theory calculations needed!

16 Neutron and x-ray spectroscopy outline 1. weak correlations: Pb, Nb 2. intermediate correlations: Sr 2 RuO 4 3. strong correlations: YBa 2 Cu 3 O 6+x 4. orbital degeracy: La 1-x Ca x MnO 3 (Y,La)TiO 3 5. oxide heterostructures

17 Inelastic magnetic neutron scattering fluctuation-dissipation theorem dynamical magnetic susceptibility response to time- and position-dependent magnetic field

18 Stoner model ), ( ) ( 1 ), ( ), ( 0 0 ω χ ω χ ω χ q q J q q = enhanced by electronic correlations (RPA) + Δ = + + k k q k k q k i E E E f E f q ε ω ω χ ) ( ) ( ) ( ), 0 ( h susceptibility of electron band Fermi sphere E q continuum J(q) peaked at q=0, sufficiently strong ferromagnetism e.g. Fe, Ni

19 Sr 2 RuO 4 layered structure isostructural to layered cuprates electron configuration 3d 4 electrons in t 2g orbitals e g t 2g

20 Sr 2 RuO 4 spin excitations ARPES Fermi surface strongly nested band susceptibility Mazin et al., PRL 1999

21 Sr 2 RuO 4 spin excitations inelastic magnetic neutron scattering Braden et al., PRB 2002 signal explained by bare band susceptibility no apparent role in driving p-wave superconductivity

22 Neutron and x-ray spectroscopy outline 1. weak correlations: Pb, Nb 2. intermediate correlations: Sr 2 RuO 4 3. strong correlations: YBa 2 Cu 3 O 6+x 4. orbital degeracy: La 1-x Ca x MnO 3 (Y,La)TiO 3 5. oxide heterostructures

23 YBa 2 Cu 3 O 6+x CuO 2 CuO 2 O 2- (2p 6 ) Cu 2+ (3d 9 ) x 2 -y 2 3z 2 -r 2 yz xz xy two-dimensional electronic structure no orbital degeneracy

24 YBa 2 Cu 3 O 6+x x-ray linear dichroism absorption cross section much greater for E ab-plane x 2 -y 2 orbital partially occupied peak position independent of doping (Zhang-Rice singlet state) Nücker et al., PRB 1995

25 YBa 2 Cu 3 O 6+x 400 K temperature antiferromagnetic Mott insulator strange metal 100 K superconductor charge carrier density in CuO 2 layers

26 Inelastic magnetic neutron scattering polarization factor spin-spin correlation function Heisenberg antiferromagnet, magnon creation ˆQηˆ a = 0, 1 q, K m K m ) K m,

27 YBa 2 Cu 3 O 6 magnons H = Σ ij (J S i (a,b) S j (a,b) ) + Σ i (J 1 S i (a) S i (b) + J 2 S i (b) S i (a) ) E 200 mev layer b layer a J 2 J 1 70 mev (π,π) acoustic q optic J exchange parameters from magnon dispersions J ~ 100 mev J 1 ~ 10 mev J 2 ~ 0.01 mev Tranquada et al., PRB 1989 Reznik et al., PRB 1996

28 YBa 2 Cu 3 O 6+x 400 K temperature antiferromagnetic Mott insulator strange metal 100 K superconductor charge carrier density in CuO 2 layers

29 YBCO 6.6 spin dynamics untwinned YBCO 6.6 (T c = 61K) along a* along b* (π,π) (π,π) two-dimensional hour glass dispersion also seen in YBCO 7 and other high-t c cuprates Hinkov et al. Nature 2004 Nature Phys. 2007

30 YBCO 6.6 spin dynamics T < T c hour glass dispersion T > T c hour glass replaced by vertical dispersion very large in-plane anisotropy Hinkov et al., Nature Phys. 2007

31 Band susceptibility in superconducting state 2 2 ) ( 1 ) ( ) ( 4 1 ) ( ) ( ) ( ) ( ) ( ) ( } ) (1 ) (1 ) (1 { ), ( k k k k i E E E f E f E E i E E E f E f E E i E E E f E f E E k E q k q k k q k q k k q k k q k k k q k k q k q k k q k k q k k k q k k q k q k k q k k q k k + Δ = = Σ Δ +Δ Δ +Δ + Δ +Δ ε ε ω χ δ ω ε ε δ ω ε ε δ ω ε ε coherence factor Fermi factor scattering of thermally excited pairs pair annihilation pair creation band dispersion, measured from E F yields only broad features, inconsistent with experiment

32 Spin exciton model simplest formalism: RPA Imχ χ (q, ω ) = 1 χ 0 (q, ω ) J(q) χ (q, ω ) collective mode: 0 energy gap Δ single particle spin flips ω q (π,π) hour glass reproduced upper cutoff of neutron spectrum direct measure of bulk Δ(q) Eremin et al., PRL 2005 see also: many other RPA calculations agrees well with other probes of Δ(q)

33 Spin exciton model Pailhes et al., PRL 2003, PRL 2006 J 1 interlayer exchange interaction Imχ odd even collective mode odd even gap estimated based on RPA single particle spin flips ω energy gap

34 Spin dynamics in superconducting state neutron intensity maps square at high energies ellipse at low energies Hinkov et al., Nature Phys see also: Mook et al., Nature 2000 Hayden et al., Nature 2004 RPA calculation parameters from ARPES & LDA overall behavior consistent with experiment but: hard to reproduce spectral weight anisotropy at low E Yamase & Metzner, PRB 2006

35 Static stripes? generic magnetic dispersion low energies: quasi-1d high energies: 1D predicted intensity maps at high energies Vojta & Ulbricht, PRL 2004 q stripe q stripe streaks at high energy predicted for untwinned samples inconsistent with square pattern observed in YBCO 6.6 Yao et al., PRB etc.

36 Fluctuating stripes? calculations incorporating directional stripe fluctuations low energy high energy Vojta et al., PRL 2006 can reproduce large anisotropy at low energies, square at high energies but: too many free parameters effect of superconductivity not described

37 YBCO 6+x transport properties in-plane resistivity anisotropy high-field phase diagram YBCO 6.45 YBCO 6.6 YBCO 6.45 YBCO 6.6 Ando et al., PRL 2002 Sun et al., PRL 2005

38 Comparison: YBCO 6.45 and YBCO 6.6 YBa 2 Cu 3 O 6.6 (T c = 61 K) -large spingap - qualitative difference between superconducting and normal states YBa 2 Cu 3 O 6.45 (T c = 35 K) - small or absent spin gap Q-integrated intensity 0 5 K 70 K 290 K T = 5K T = 40 K T = 100 K T = 290 K - spectrum evolves smoothly through T c energy (mev)

39 YBCO 6.45 constant-energy cuts 3 mev 7 mev 50 mev E = 3 mev, T = 5 K along a* E > 15 mev E < 15 mev isotropic large anisotropy incommensurate along a* commensurate along b* one-dimensional geometry Hinkov et al., Science 2008

40 Phase transition Hinkov et al. Science 2008 phase transition at ~ 150 K spin system spontaneously develops 1D incommensurate modulation weak structural in-plane anisotropy selects unique incommensurate domain

41 Magnetic order? muon spin relaxation E ~ 1 μev slow electronic spin relaxation for T 10 K static magnetic order for T 2 K

42 Nematic order? data from Ando et al., PRL 2002 Hinkov et al. Science 2008 T 150 K: pronounced increase of intensity of low-energy, 1D incommensurate spin fluctuations resistivity anisotropy isotropic-nematic transition broadened by disorder, finite energy, finite field nematic transition two orders-of-magnitude higher than onset of magnetic order

43 Analogies 1. nematic liquid-crystal in weak electric field 2. electronic nematic phase in Sr 3 Ru 2 O 7 in-plane component of H aligns nematic director Borzi et al., Science 2007

44 Dynamical scaling YBCO 6.45 La 1.96 Sr 0.04 CuO 4 Keimer et al. PRB 1992 signature of proximity to quantum phase transition

45 YBa 2 Cu 3 O 6+x 400 K temperature antiferromagnetic Mott insulator strange metal 100 K superconductor charge carrier density in CuO 2 layers additional ordered phases near Mott insulator

46 Electronic liquid crystals YBCO 6.6 YBCO 6.45 electronic nematic phase fourfold rotational symmetry spontaneously broken translational symmetry unbroken Kivelson et al., Nature 1998 Pomeranchuk instability renormalization group calculations spontaneous formation of open Fermi surface Halboth & Metzner, PRL 2000 Yamase & Kohno, JPSJ 2000

47 Neutron and x-ray spectroscopy outline 1. weak correlations: Pb, Nb 2. intermediate correlations: Sr 2 RuO 4 3. strong correlations: YBa 2 Cu 3 O 6+x 4. orbital degeracy: La 1-x Ca x MnO 3 (Y,La)TiO 3 5. oxide heterostructures

48 Example: manganates phase diagram LaMnO 3 antiferromagnetic Mott insulator La 0.7 Ca 0.3 MnO 3 ferromagnetic metal

49 Elastic neutron scattering from LaMnO 3 nuclear Bragg reflections extract lattice structure & lattice parameters magnetic Bragg reflections for T < T N extract magnetic structure

50 LaMnO 3 lattice structure from neutron/x-ray diffraction octahedra distorted below ~ 800K MnO 6 octahedra Rodriguez-Carvajal et al., PRB 1998

51 LaMnO 3 lattice structure Jahn-Teller distortion e g O 2- (2p 6 ) Mn 3+ (3d 4 ) x 2 -y 2 3z 2 -r 2 t 2g yz xz xy

52 LaMnO 3 x-ray linear dichroism Castleton & Altarelli, PRB 2002

53 LaMnO 3 orbital & spin order superexchange rules identical orbitals: strong, antiferromagnetic T < T O : orbital order locks in exchange interactions orthogonal orbitals: weak, ferromagnetic T < T N << T O : spin order

54 LaMnO3 orbital & spin order

55 (La,Y)TiO 3 structure O 2- (2p 6 ) x 2 -y 2 3z 2 -r 2 Ti 3+ (3d 1 ) TiO 6 octahedra yz xz xy one electron in t 2g orbitals larger orbital degeneracy weaker lattice coupling than in e g systems

56 (La,Y)TiO 3 spin & orbital order LaTiO 3 G-type antiferromagnet YTiO 3 ferromagnet orbital order according to electronic structure calculations: dumbell orbitals planar orbitals no orbital ordering transitions observed up to at least 700 K orbital degeneracy lifted by lattice distortions? orbital fluctuations?

57 Orbital excitations ground state orbiton excitation Raman scattering photon energy tuned to intersite transitions excitation in final state: - phonon - magnon - orbiton? d i 3 d j 5 (d i 4 d j 4 )* d i 4 d j 4

58 Raman scattering from orbitons Ulrich et al. PRL 2006 peak above 2-magnon, 2-phonon ranges below charge excitations known from IR spectra orbital excitation

59 Resonant inelastic x-ray scattering 350 LaTiO 3 photon energy tuned to intra-atomic absorption edge 300 E = ev t 2g T = 13 K 2p 1 3d (2p 2 3d 1 )* 2p 2 3d 1 larger photon momentum than Raman Intensity (cnts / 4 hr) dispersion of orbital excitations Energy (ev) Ulrich et al., PRB 2008 and unpublished

60 Neutron and x-ray spectroscopy outline 1. weak correlations: Pb, Nb 2. intermediate correlations: Sr 2 RuO 4 3. strong correlations: YBa 2 Cu 3 O 6+x 4. orbital degeracy: La 1-x Ca x MnO 3 (Y,La)TiO 3 5. oxide heterostructures

61 New physics at interfaces H V H R H I H doped semiconductor H V H I semiconductor heterostructure D. Tsui et al.

62 YBCO-LCMO interface YBa 2 Cu 3 O 7 (YBCO): high-t c superconducor La 0.7 Ca 0.3 MnO 3 (LCMO): metallic ferromagnet antagonistic order parameters at interface

63 YBCO-LCMO interface Z. Zhang, U. Kaiser different magnetic environment different valence state different crystal field different covalent bonding different stoichiometry (oxygen vacancies/interstitials) can superconductivity be modified/created at interfaces?

64 YBCO-LCMO superlattices neutron reflectivity Braggreflectionsdueto structural and magnetic periodicity magnetic circular dichroism at L- absorption edges element-specific magnetization Chakhalian et al., Nature Phys Stahn et al., PRB 2005 ferromagnetic polarization of Cu in YBCO direction antiparallel to Mn

65 Spin polarization at interface magnetization profile superexchange across interface Chakhalian et al., Nature Phys. 2006

66 Temperature dependence of spin polarization Cu magnetization closely follows Mn moment large antiferromagnetic Cu-Mn exchange interaction

67 Exchange coupling across interface assume bulk orbital occupancy is maintained at interface x 2 -y 2 3z 2 -r 2 LCMO J < 0 YBCO x 2 -y 2 weak ferromagnetic exchange across interface expected from superexchange rules inconsistent with experiment orbital reconstruction?

68 X-ray linear dichroism interface sensitivity through cap layers FY bulk sensitive TEY low electron escape depth probes first interface

69 Orbitals at interface Chakhalian et al. Science 2007 FY matches data on bulk YBCO TEY shifted ~ 0.2 electrons / Cu ion transferred across interface not subject to Zhang-Rice singlet formation almost isotropic partial occupation of Cu 3z 2 -r 2 orbital orbital reconstruction

70 Cluster calculations possible origins different crystal fields at interface unlikely covalent bonding? Cu x 2 -y 2 AB Mn 3z 2 -r 2 Cu 3z 2 -r 2 B exact-diagonalization calculations on small clusters covalent bonding realistic

71 Exchange coupling across orbitally reconstructed interface J > 0 LCMO YBCO Cu 3z 2 -r 2 orbital partially occupied strong antiferromagnetic exchange across interface reduced in-plane antiferromagnetic correlations combination explains large ferromagnetic susceptibility, suppression of metallicity and superconductivity of YBCO near interface

72 Oxide heterostructure research program understand and manipulate orbital and spin polarization at interfaces create dense correlated-electron systems with controlled interactions new quantum phases? FQHE in semiconductors lateral (nano)-structuring CoFe 2 O 4 nanopillars in BaTiO 3 matrix Zheng et al., Science 2004

73 La 2 CuO 4 & LaNiO 3 electronic structure La 2 CuO 4 spin-1/2 2D bond network O 2- (2p 6 ) Cu 2+ (3d 9 ) LaNiO 3 spin-1/2 3D bond network O 2- (2p 6 ) Ni 3+ (3d 7 ) orbitally orbitally non-degenerate degenerate Mott insulator metal x 2 -y 2 x 2 -y 2 3z 2 -r 2 3z 2 -r 2 yz xz yz xz xy xy

74 Strain-induced orbital polarization X-ray linear dichroism in La 1-x Sr x MnO 3 thin films SrTiO 3 substrate: c/a=0.98 LaAlO 3 substrate: c/a=1.04 XAS (V, H) [a.u.] u.c. V (E//ab) H (E//c) LSMO STO XAS (V, H) [a.u.] u.c. V (E//ab) H (E//c) LSMO LAO V-H [a.u.] x 2 -y 2 V-H [a.u.] z 2 r Photon Energy [ev] Photon Energy [ev] z 2 x 2 -y 2 z-in e g x 2 -y 2 z-out e g z 2 t 2g yz xz t 2g xy xy yz xz Aruta et al., Phys. Rev. B 2006

75 LaNiO 3 -LaMO 3 superlattices Chaloupka & Khaliullin, PRL D electronic structure x 2 -y 2 orbital favored cuprate Hamiltonian?

76 LaNiO 3 -LaMO 3 superconductivity? mean-field superconducting transition temperature cuprates LaNiO 3 -LaMO 3 Chaloupka & Khaliullin, PRL 2008

77 LaNiO 3 -LaAlO 3 structure TEM nonresonant x-ray reflectivity (LNO/LAO)=(12/24)X67 A Reflectivity (a.u.) nm q z (A -1 ) Kim Zhang, Kaiser, van Aken nm

78 LaNiO 3 -LaAlO 3 soft x-ray reflectivity Reflectivity (a.u.) L 2 Ni E = ev SL (001) SL (002) Vertical Horiz θ V(σ) H(π) q z (A -1 ) forbidden superlattice peak charge distribution of valence electrons atomic structure signature of interface-induced charge order see also Stahn et al., PRB 2005 Smadici et al., PRL 2007

79 RNiO 3 phase diagrams Torrance et al., PRB 1992 Mazin et al., PRL 2007 competing instabilities in bulk nickelates: antiferromagnetism charge order

80 Conclusions YBCO-LCMO superlattices orbital and magnetic polarization at interface interface-induced antiferromagnetic insulating state (?) LaNiO 3 -LaAlO 3 superlattices interface-induced charge-ordering instability (not present in bulk) Can high-temperature superconductivity be generated by suppressing competing instability?

81 Oxide heterostructure toolkit ferromagnet high-t C superconductor ferromagnet high-t C superconductor substrate structure magnetization orbital occupation charge transport TEM, XRD neutrons, XMCD XLD, RXS FTIR