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Spin-Orbit Mott Insulators: Magnetism, Order, and Excitations

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Spin-Orbit Mott Insulators: Magnetism, Order, and Excitations Spin-Orbit Mott Insulators: Magnetism, Order, and Excitations George Jackeli Max-Planck Institute & University of Stuttgart, Germany Andronikashvili Institute of Physics, Tbilisi, Georgia Winter School “Computational Magnetism’ Vienna, 20-23 Feb , 2017 1 Thanks to Judit Romhanyi Leon Balents (MPI -> OIST) (KITP) H. Takagi (MPI Stuttgart & Uni Tokyo) BJ. Kim (MPI Stuttgart), V. Kataev (IFW Dresden) 2 ‘There is no learning without having to pose a question’ Richard Feynman (Nobel prize’65) 3 Transition metal oxides: many challenges d- electrons are partially filled and not very extended Interactions dominate over kinetic energy Many degrees of freedom are at work Orbital Spin Charge Lattice Metal to Magnetic Insulator High-Tc Superconductivity Colossal Magnetoresistance Unexpected variety of phases and transitions between them 4 Most of the elements are Transition metals 5 Relativistic in origin, Coulomb force Spin-orbit coupling Orbital Spin Charge Lattice Enhance interplay by going to heavy TM elements: A Route to Novel Collective States & Phenomena 6 Symmetry breaking by various multipoles Monopole charge order broken sym. translational 7 Symmetry breaking by various multipoles Monopole Dipole charge order ferroelectricity broken sym. magnetism translational inversion time reversal rotations 8 Symmetry breaking by various multipoles Monopole Dipole Quadrupole charge order ferroelectricity broken sym. magnetism orbital order translational inversion spin nematics time reversal rotations rotations 9 Symmetry breaking by various multipoles Monopole Dipole Quadrupole Octupole charge order ferroelectricity broken sym. magnetism orbital order translational inversion spin nematics hidden order time reversal rotations inversion rotations time reversal 10 No Symmetry breaking: Quantum Liquid plain 11 No Symmetry breaking: Quantum Liquid plain full bodied 12 Outline Introduction Mott insulator, Orbital degeneracy, Spin-orbital exchange interactions Spin-orbit coupled Mott insulators Local electronic structure, Exchange in total angular momentum j-basis Experimental implications: j=1/2 systems: Iridates and Ruthenates, j=3/2 systems: Vanadates, Molybdates,and Osmates 13 Mott Insulator one electron per site 14 Mott Insulator one electron per site half-filled band: metal DOS E 15 Mott Insulator one electron per site half-filled band: metal DOS U t E 16 Mott Insulator one electron per site half-filled band: insulator DOS gap U t E Coulomb repulsion U>>t Kinetic energy, Charges become localized and gapped Sir Nevill Mott (Nobel prize’77) 17 Mott Insulator one electron per site half-filled band: insulator DOS gap U t E Coulomb repulsion U>>t Kinetic energy, Charges become localized and gapped Sir Nevill Mott (Nobel prize’77) Low energy degrees are magnetic: Spins interacting via Heisenberg exchange Werner Heisenberg (Nobel prize’32) 18 Ferro and Antiferromagnetism 19 Ferro and Antiferromagnetism known to ancient Greek tribe Ferromagnet near town Magneisa 20 Ferro and Antiferromagnetism known to ancient Greek tribe Ferromagnet near town Magneisa Antiferromagnet proposed by Louis Neel (Nobel prize’70) 21 Ferro and Antiferromagnetism known to ancient Greek tribe Ferromagnet near town Magneisa Antiferromagnet proposed by Louis Neel (Nobel prize’70) 22 Ferro and Antiferromagnetism known to ancient Greek tribe Ferromagnet near town Magneisa Antiferromagnet proposed by Louis Neel (Nobel prize’70) criticized by Lev Landau (Nobel prize’62) AFM order parameter was hidden 23 Ferro and Antiferromagnetism known to ancient Greek tribe Ferromagnet near town Magneisa Antiferromagnet proposed by Louis Neel (Nobel prize’70) detected by neutron scattering criticized by Lev Landau (Nobel prize’62) AFM order parameter was hidden Bertram Brockhouse Clifford Shull (Nobel prize’94) (Nobel prize’94) 24 Orbital Degeneracy eg Z2 X2-Y2 d-level t2g XY XZ Transition metal ion YZ 25 Three different couplings & regimes in spin-orbital systems Jahn-Teller coupling-EJT EJT orbitals are rigidly ordered: spin-only Heisenberg model 26 Three different couplings & regimes in spin-orbital systems Jahn-Teller coupling-EJT exchange interactions- J EJT spin exchange depends on orbital occupancy: directional character of orbitals are rigidly ordered: orbitals induces frustration spin-only Heisenberg model ? 27 Coupled spin-orbital exchange (Kugel-Khomskii type models) Cambridge University Press 2014 28 Coupled spin-orbital exchange (Kugel-Khomskii model) weaker FM 29 Coupled spin-orbital exchange (Kugel-Khomskii model) weaker FM stronger AFM 30 Coupled spin-orbital exchange (Kugel-Khomskii model) weaker FM stronger AFM Exchange couplings: Orbital degrees are static Pott’s-like! 31 Directional orbitals on a family of lattices XY XZ YZ 32 Ground state manifold: Hard core dimers GJ & Ivanov PRB (2007) GJ & Khomskii PRL (2008) Ground state manifold is spanned by hard-core dimer coverings Spins are bound into spin-singlet on dimer bonds: Spin gaped phase = Extensive orientational degeneracy infinitely many ways of covering Different coverings are orthogonal due to orbitals 33 Three different couplings & regimes in spin-orbital systems Jahn-Teller coupling-EJT exchange interactions- J spin-orbit coupling-λ EJT spin exchange depends on orbital occupancy: directional character of spins & orbitals locally orbitals induces frustration orbitals are rigidly ordered: entangled: spin-only Heisenberg model orbital frustration & directional character are converted to isospins ? 34 Orbital Degeneracy eg Z2 X2-Y2 d-level t2g L=2 XY YZ XZ l=1 35 Orbital Degeneracy eg Z2 X2-Y2 d-level t2g L=2 XY YZ XZ l=1 L=-l=1 36 spin - orbit correlations Ir= 77 (lucky number) Heisenberg vs bond-Ising couplings 37 V= 23 (V+Ir=100) octupolar order spin - orbit correlations Ir= 77 (lucky number) Heisenberg vs bond-Ising couplings 38 Mo=42 V= 23 (answer to ultimate question…) (V+Ir=100) valence bond glass octupolar order spin - orbit correlations Ir= 77 (lucky number) Heisenberg vs bond-Ising couplings 39 Mo=42 V= 23 (answer to ultimate question…) (V+Ir=100) valence bond glass octupolar order spin - orbit correlations Ir= 77 Os=76 (lucky number) (???) Heisenberg vs unusual ‘spin’ textures bond-Ising couplings 40 Spin-orbit coupling in t2g shell Cambridge University Press 1970 41 Spin-orbit coupling in t2g shell A. Abragam and B. Bleaney (1970) 42 Spin-orbit coupling in t2g shell A. Abragam and B. Bleaney (1970) 3λ/2 43 j=1/2 systems: Iridates and Ruthenates 44 Spin-orbit coupling in t2g shell A. Abragam and B. Bleaney (1970) d5 (Ir4+, Ru3+…) g=2 3λ/2∼600µες 45 ’Zoo’ of Iridate compounds A2IrO4 A3Ir2O7 A2BIrO6 , , - A IrO α β γ 2 3 A4Ir3O8 46 ’Zoo’ of Iridate compounds A2IrO4 A3Ir2O7 A2BIrO6 , , - A IrO α β γ 2 3 A4Ir3O8 47 ’Zoo’ of Iridate compounds A2IrO4 A3Ir2O7 A2BIrO6 , , - A IrO α β γ 2 3 A4Ir3O8 48 ’Zoo’ of Iridate compounds A2IrO4 A3Ir2O7 A2BIrO6 , , - A IrO α β γ 2 3 A4Ir3O8 All of them are Mott insulators! 49 Spin-Orbit assisted Mott transition 50 Kramers doublet of Ir4+ Isospin exchange inherit the bond symmetry 51 Kramers doublet of Ir4+ GJ & Khaliullin PRL (2009) Isospin exchange inherit the bond symmetry 52 Kramers doublet of Ir4+ GJ & Khaliullin PRL (2009) Isospin exchange inherit the bond symmetry 53 Kramers doublet of Ir4+ GJ & Khaliullin PRL (2009) Isospin exchange inherit the bond symmetry + _ Destructive quantum interference Heisenberg term is suppressed 54 Kramers doublet of Ir4+ GJ & Khaliullin PRL (2009) Isospin exchange inherit the bond symmetry X Destructive quantum interference Heisenberg term is suppressed 55 Kramers doublet of Ir4+ GJ & Khaliullin PRL (2009) Isospin exchange inherit the bond symmetry JH X 56 Crystal structure of Sr2IrO4 Staggered rotation of octahedra around c-axis by α∼11ο 57 Magnetic structure of Sr2IrO4 Cao et al., PRB ‘98 FM moment MFM~0.1µB : too small for a saturated FM too large for a weak FM -2 [e.g. in La2CuO4: 0.2x10 µB] Canted AFM in xy-plane ? Spin canting angle φ∼α 58 Microscopic Hamiltonian of Sr2IrO4 GJ & Khaliullin PRL (2009) Dominant interactions (no Hund’s coupling) φ 59 Microscopic Hamiltonian of Sr2IrO4 GJ & Khaliullin PRL (2009) Dominant interactions (no Hund’s coupling) φ No true anisotropy (Heisenberg model in rotated basis): -if spins are confined in xy-plane they are canted -if not they form collinear Neel order along z-axis 60 Microscopic Hamiltonian of Sr2IrO4 GJ & Khaliullin PRL (2009) Dominant interactions (no Hund’s coupling) φ No true anisotropy (Heisenberg model in rotated basis): -if spins are confined in xy-plane they are canted -if not they form collinear Neel order along z-axis Hund’s coupling selects in-plane canted structure 61 62 Heisenberg-like Magnetism of Sr2IrO4 Kim et al, PRL’12 63 Heisenberg-like Magnetism of Sr2IrO4 Kim et al, PRL’12 Fujiyama et al, PRL’12 64 Heisenberg-like Magnetism of Sr2IrO4 Kim et al, PRL’12 Fujiyama et al, PRL’12 Takayama, GJ, et al PRB’16 65 Hexagonal Iridates A2IrO3 (A=Na, Li) 66 Pseudospins on a Honeycomb layer of A2IrO3 GJ & Khaliullin PRL (2009) O z x y Ir 67 Pseudospins on a Honeycomb layer of A2IrO3 GJ & Khaliullin PRL (2009) Kitaev Model O z Ann. Phys’06 x y Ir Fundamental Physics Prize’14 68 Kitaev Honeycomb Model A. Kitaev, Ann. Phys’06 exactly soluble 2D quantum model spin liquid ground-state zz Fractional excitations: xx yy Majorana Fermions, Dirac spectrum only NN two-spin correlations (Baskaran et al PRL’07) Exact dynamic spin structure factor (Knolle et al PRL’14) Raman spectra (Knolle et al PRL’15) 69 Kitaev Honeycomb Model A. Kitaev, Ann. Phys’06 exactly soluble 2D quantum model spin liquid
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