Magnetism in correlated-electron materials

Transcription

1 Magnetism in correlated-electron materials B. Keimer Max-Planck-Institute for Solid State Research focus on delocalized electrons in metals and superconductors localized electrons: Hinkov talk outline 1. introduction 2. interplay between magnetism and unconventional superconductivity 3. oxide heterostructures

2 What are correlated electrons? electron-electron Coulomb interactions + quantum mechanics very weak independent electrons: ordinary metal very strong electron crystal: Mott insulator strongly correlated electrons in d- or f-electron metals: prone to crystallization transport dominated by electron-electron interactions, very different from ordinary metals new theory of metals?

3 Bulk complex oxides: colossal response example: colossal magnetoresistance in manganese oxides Na 0.7 CoO 2 Tomioka et al., PRB 1996 example: colossal thermopower in cobalt oxides Wang et al., Nature 2003

4 Competing phases manganates cuprates ruthenates cobaltates Dagotto, Science 2005 extreme variety of macroscopic properties, microscopic structures

5 High temperature superconductivity Hinkov Keimer ~ 400 K temperature antiferromagnetic Mott insulator strange metal ~ 100 K superconductor normal metal charge carrier density in CuO 2 layers metallicity and superconductivity in doped Mott insulator electron correlations key to microscopic description superconductivity driven by repulsive Coulomb interactions?

6 Cooper-Pairs quantum-mechanical wave function analogous to hydrogen atom Ψ electron = ϕ ( r ) s s = ±, 2 Ψ = ϕ ( r + r ) ϕ r r ) Cooper central relative ( 1 2 S quantum numbers relative angular momentum l = 0, 1, 2, (s, p, d, ) total spin S = 0, 1 1 S = 0 = ; S 2 1 ( ) = 1 = ( + ),, electrons are identical particles antisymmetry of wave function e.g. l = 0 ϕ relative symmetric S antisymmetric 2 l S 0 0 Hg, Pb, Al, MgB 2, 1 1 Sr 2 RuO high-t c superconductors signature of strong correlations, electronically driven superconductivity

7 d-wave superconductivity experimental confirmation: π-loop YBa 2 Cu 3 O 7 Au contact Nb (s-wave superconductor) 2eΦ c = 2πn + π Φ = ( n + π c 1 ) = ( n ) flux quantization: 0 half-integer flux quanta e Φ=Φ 0 /2 Hilgenkamp et al., Nature 2003 Φ

8 Fermi-liquid theory lifetime = line width = 0 E(k) narrower bands linewidth 0 unless E E F E (k) k k noninteracting electrons quasiparticles : electrons dressed by interactions adiabatic continuity Is Fermi liquid theory valid in strongly correlated metals?

9 Experimental methods: spectroscopy experimental determination of dynamics and excited states electron spin q-averaged muons NMR q-resolved neutrons electron charge optics tunneling photoemission electrons x-rays crystal lattice neutrons (nuclei) x-rays (core electrons)

10 Experimental methods: spectroscopy experimental determination of dynamics and excited states electron spin q-averaged muons NMR q-resolved neutrons ( Ronnow talk) electron charge optics tunneling photoemission electrons x-rays crystal lattice neutrons (nuclei) x-rays (core electrons)

11 Angle-resolved photoemission spectroscopy angle-resolved measurement of photoelectric effect k i 2m 2m = k = sin Θ Ekin = sin Θ hν Eband eφ f 2 2 for layered materials with quasi-two-dimensional electronic structure reconstruct electron bands from E kin, emission angle θ of photoelectron

12 Materials: Ruddlesden-Popper series two-dimensional bond network three-dimensional bond network

13 Electronic structure lattice structure electronic structure e g O 2- (2p 6 ) x 2 -y 2 3z 2 -r 2 M n+ t 2g yz xz xy MO 6 octahedra

14 Example Sr 2 RuO 4 layered structure isostructural to layered cuprates electron configuration 3d 4 e g t 2g superconductivity minute concentration of nonmagnetic impurities pure Sr 2 RuO 4 McKenzie & Maeno, RMP 2003

15 Sr 2 RuO 4 charge excitations ARPES sharp quasiparticles everywhere Fermi surface agrees with band structure calculations Fermi liquid theory valid Damascelli et al., PRL 2000

16 Sr 2 RuO 4 spin excitations p-wave pairing by ferromagnetic spin fluctuations? inelastic magnetic neutron scattering no pronounced ferromagnetic fluctuations inelastic scattering signal peaked at incommensurate q origin of incommensurate excitations? Braden et al., PRB 2002

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

18 Sr 2 RuO 4 spin excitations band susceptibility of Sr 2 RuO 4 incommensurate peaks due to Fermi surface nesting Mazin et al., PRL 1999 explains incommensurate spin excitations in neutron scattering data no apparent role in driving p-wave superconductivity pairing mechanism still elusive

19 High temperature superconductivity example: YBa 2 Cu 3 O 6+x CuO 2 O 2- (2p 6 ) Cu 2+ (3d 9 ) x 2 -y 2 3z 2 -r 2 CuO 2 yz xz xy two-dimensional electronic structure single band, no orbital degeneracy

20 Charge excitations in high-t c superconductors ARPES spectra q ~ (π, π) segments with broad spectra connected by wave vector q ~ (π, π) interaction with spin excitations? Fermi-liquid quasiparticles only in some segments of momentum space Fermi-liquid theory insufficient Kaminski et al., PRB 2005

21 Spin excitations in high-t c superconductors YBa 2 Cu 3 O 6+x T < T c energy momentum intensity intensity q = (π, π) temperature (K) sharp magnetic excitations in superconducting state unusual hour glass dispersion strongly coupled to superconducting electrons short-range magnetic order, spin-fluctuation driven Cooper pairing

22 Magnetically driven Cooper pairing assumption: short-range antiferromagnetic order single electron generates string of broken bonds S=0 Cooper pair does not disrupt magnetic order nearest neighbors favorable for Cooper pair formation next-nearest-neighbors unfavorable d-wave symmetry of pair wave function optimal binding energy for Cooper pair _ + + _

23 Microscopic model: spin excitons simplest formalism: Stoner model χ (q, ω ) = 1 χ 0 (q, ω ) J(q) χ (q, ω ) 0 Imχ collective mode: energy gap Δ single-particle spin flips ω q (π,π) Eremin et al., PRL 2005 explains hour glass dispersion as consequence of d-wave anisotropy of energy gap

24 Current frontier: strange metal state above T c T < T c T > T c Hinkov et al., Nature Phys hour glass dispersion replaced by vertical dispersion not explained by any microscopic model Hinkov talk

25 Metallic manganates La 2 2x Sr 1+2x Mn 2 O 7 O 2- (2p 6 ) Mn 3+ (3d 4 ) x 2 -y 2 3z 2 -r 2 yz xz xy conduction electron localized core spin

26 Metallic manganates La 1.2 Sr 1.8 Mn 2 O 7 Tokura et al. Ann Rev. Mat. Sci ferromagnetic transition at T c ~ 130K resistivity decreases below T c

27 Double exchange interaction effective hopping amplitude t eff ~ cos ϕ/2 conduction electron core spin S=3/2 Mn 3+ Mn 4+ ϕ kinetic energy of conduction electrons minimized for parallel core spins drives ferromagnetic transition

28 Metallic manganates La 1.2 Sr 1.8 Mn 2 O 7 Fermi surface ARPES spectra for T < T c (0,0.3) (0.3,0) Mannella et al., Nature 2006 quasiparticle peak only along diagonal directions no quasiparticles for Fermi surface segments connected by (0.3,0) and (0,0.3)

29 Metallic manganates x-ray, elastic nuclear neutron scattering broad features from lattice distortions with in-plane wave vectors (q x, q y ) ~ (0.3, 0) and (0,0.3) Vasiliu-Doloc et al., PRL 2000 intensity Δ q ~ 1/ ξ ξ = correlation length in real space Δ q q short-range lattice distortions

30 Metallic manganates possible origin of large scattering: orbital/lattice polarons Mn 4+ Mn 3+ Mn 4+ local lattice distortion around moving electron

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

32 Oxide heterostructures SrTiO 3 -LaAlO 3 field effect transistor Thiel et al., Science 2006 ZnO-Mg 1-x Zn x O quantum Hall effect Tsukazaki et al., Science 2007

33 YBCO-LCMO superlattices ferromagnetic and superconducting oxides 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

34 YBCO-LCMO superlattices U. Kaiser et al. different magnetic environment different valence state different crystal field different covalent bonding

35 YBCO-LCMO superlattices neutron reflectivity Bragg reflections due to 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 superconductor direction antiparallel to Mn

36 Magnetic reconstruction at interface Chakhalian et al., Nature Phys magnetization profile

37 Orbital reconstruction at interface Chakhalian et al. Science 2007 valence electron orbital bulk interface completely different transport & magnetic properties at interface

38 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