Order from disorder: Quantum spin gap in magnon spectra of LaTiO_3

Abstract

A theory of the anisotropic superexchange and low energy spin excitations in a Mott insulator with t_{2g} orbital degeneracy is presented. We observe that the spin-orbit coupling induces frustrating Ising-like anisotropy terms in the spin Hamiltonian, which invalidate noninteracting spin wave theory. The frustration of classical states is resolved by an order from disorder mechanism, which selects a particular direction of the staggered moment and generates a quantum spin gap. The theory explains well the observed magnon gaps in LaTiO_3. As a test case, a specific prediction is made on the splitting of magnon branches at certain momentum directions.

5 pages, 2 figures, final version

Cited by in corpus (58)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Models and Materials for Generalized Kitaev Magnetism
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Excitonic Magnetism in Van Vleck-type d^4 Mott Insulators
• How chemistry controls electron localization in 3d1 perovskites: A Wannier-function study
• Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3
• Fingerprints of spin-orbital physics in cubic Mott insulators: Magnetic exchange interactions and optical spectral weights
• Kitaev-Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices
• Spin-orbit-entangled electronic phases in 4$d$ and 5$d$ transition-metal compounds
• Orbital Physics in the Perovskite Ti Oxides
• Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3
• The Quantum Compass Model on the Square Lattice
• Magnetoelastic coupling in RETiO3 (RE = La, Nd, Sm, Gd, Y)
• Orbital ordering and frustrations
• Spin-Orbital Entanglement and Violation of the Goodenough-Kanamori Rules
• Magnetic Order and Dynamics in an Orbitally Degenerate Ferromagnetic Insulator
• Fingerprints of spin-orbital entanglement in transition metal oxides
• Phase Diagram and Quantum Order by Disorder in the Kitaev $K_1$-$K_2$ Honeycomb Magnet
• Z_2-vortex lattice in the ground state of the triangular Kitaev-Heisenberg model
• Quantum behavior of Orbitals in Ferromagnetic Titanates: Novel Orderings and Excitations
• Orbital ordering in frustrated Jahn-Teller systems
• Orbital order in classical models of transition-metal compounds
• Evidence for Jahn-Teller distortions at the antiferromagnetic transition in LaTiO${}_3$
• Directional Ordering of Fluctuations in a Two-dimensional Compass Model
• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Frustration and entanglement in the $t_{2g}$ spin--orbital model on a triangular lattice: valence--bond and generalized liquid states
• Order-by-disorder and spin-orbital liquids in a distorted Heisenberg-Kitaev model
• Optical study of orbital excitations in transition-metal oxides
• Orbital liquid in ferromagnetic manganites: The orbital Hubbard model for $e_g$ electrons
• Theory of orbital state and spin interactions in ferromagnetic titanates
• Dielectric properties and dynamical conductivity of LaTiO3: From dc to optical frequencies
• Quantum order by disorder in the Kitaev model on a triangular lattice
• Orbital ordering in charge transfer insulators
• Compass-Heisenberg Model on the Square Lattice : Spin Order and Excitations
• Mechanism of basal-plane antiferromagnetism in the spin-orbit driven iridate Ba2IrO4
• Exchange interactions, Jahn-Teller coupling, and multipole orders in pseudospin one-half $5{\mathbf{d}}^2$ Mott insulators
• Quantum spin liquid in the semiclassical regime
• Highly-anisotropic exchange interactions of $j_{\mathrm{eff}}=1/2$ iridium moments on the fcc lattice in La${}_{2}B$IrO${}_6$ ($B$ $=$ Mg, Zn)
• One-dimensional orbital fluctuations and the exotic magnetic properties of YVO${}_3$
• Spin-orbital resonating valence bond liquid on a triangular lattice: Evidence from finite-cluster diagonalization
• G-type antiferromagnetism and orbital ordering due to the crystal field from the rare-earth ions induced by the GdFeO_3-type distortion in RTiO_3 with R=La, Pr, Nd and Sm
• Spin-orbital excitation continuum and anomalous electron-phonon interaction in the Mott insulator LaTiO${}_3$
• Cooperative Jahn-Teller Distortion in PrO2
• Defect states and excitations in a Mott insulator with orbital degrees of freedom: Mott-Hubbard gap versus optical and transport gaps in doped systems
• Quantum versus thermal fluctuations in the fcc antiferromagnet: alternative routes to order by disorder
• Hidden Symmetries and their Consequences in $t_{2g}$ Cubic Perovskites
• Multiplet effects in orbital and spin ordering phenomena: A hybridization-expansion quantum impurity solver study
• Coupled spin-lattice fluctuations in a compound with orbital degrees of freedom: the Cr based dimer system Sr3Cr2O8
• Jahn-Teller versus quantum effects in the spin-orbital material LuVO3
• Anisotropy of the paramagnetic susceptibility in LaTiO${}_3$: The electron-distribution picture in the ground state
• Compass and Kitaev models -- Theory and Physical Motivations
• Orbital Ordering and Orbital Fluctuations in Transition Metal Oxides
• Landau Expansion for the Kugel-Khomskii $t_{2g}$ Hamiltonian
• True nature of long-range order in a plaquette orbital model
• Dynamics of photo-induced ferromagnetism in oxides with orbital degeneracy
• Quantum selection of order and dynamic properties of Kitaev-Heisenberg ferromagnet on a triangular lattice
• Temperature-dependent magnetic anisotropy from directional-dependent interactions