Orbital ordering and frustrations

Abstract

An orbital ordering occurs in many transition metal compounds with Jahn-Teller ions and plays an important role in these materials. At the same time, exchange interactions in orbitally degenerate systems are inherently frustrated, even in materials with simple crystal lattices. We discuss the origin of this frustration, considering in detail materials with a cubic and triangular lattice of transition metal ions. We also discuss possible types of ground states of such systems, e.g., disordered orbital liquids and ordering due to the order-from-disorder mechanism.

6 figures, accepted for publication in Journal of Physics A: Mathematical and General

References in corpus (8)

• Quantum Melting of Magnetic Order due to Orbital Fluctuations
• Orbital liquid in three dimensional Mott insulator: $LaTi{O}_3$
• Spin Dynamics and Orbital State in LaTiO_3
• Orbital ordering in frustrated Jahn-Teller systems
• Order from disorder: Quantum spin gap in magnon spectra of LaTiO_3
• Quantum melting of magnetic long-range order near orbital degeneracy. Classical phases and Gaussian fluctuations
• Spin and orbital excitation spectrum in the Kugel-Khomskii model
• Quantum disorder versus order-out-of-disorder in the Kugel-Khomskii model

Cited by in corpus (58)

• Spin and orbital frustration in MnSc_2S_4 and FeSc_2S_4
• Finite-temperature phase diagram of the Heisenberg-Kitaev model
• Topological spin crystals by itinerant frustration
• Square skyrmion crystal in centrosymmetric itinerant magnets
• Frustration and quantum criticality
• Fingerprints of spin-orbital entanglement in transition metal oxides
• Orbital order in classical models of transition-metal compounds
• Spin--orbital interaction for face-sharing octahedra: Realization of a highly symmetric SU(4) model
• Antiferromagnetic Kitaev Interaction in $f$-Electron Based Honeycomb Magnets
• Spin excitations in the frustrated triangular lattice antiferromagnet NaYbO${}_2$
• Directional Ordering of Fluctuations in a Two-dimensional Compass Model
• Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
• Orbital-quenching-induced magnetism in Ba_2NaOsO_6
• Role of Orbitals in the Physics of Correlated Electron Systems
• Effective magnetic interactions in spin-orbit coupled $d^4$ Mott insulators
• Spectral properties of orbital polarons in Mott insulators
• Compass-Heisenberg Model on the Square Lattice : Spin Order and Excitations
• Molecular spin-orbit excitations in the J_eff = 1/2 frustrated spinel GeCo${}_2$O${}_4$
• Orbital ordering in transition-metal compounds: I. The 120-degree model
• Spontaneous symmetry breaking in a generalized orbital compass model
• Quantum 120-degree model on pyrochlore lattice: orbital ordering in MnV2O4
• Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids
• Spin-orbital resonating valence bond liquid on a triangular lattice: Evidence from finite-cluster diagonalization
• Magnetic properties of nanoscale compass-Heisenberg planar clusters
• Dilution Effects in Two-dimensional Quantum Orbital System
• Hidden dimer order in the quantum compass model
• Disorder driven spin-orbital liquid behaviour in the Ba${}_3$XSb${}_2$O${}_9$ materials
• Jahn-Teller Inactivity and Magnetic Frustration in GeCo${}_2$O${}_4$ Probed by Ultrasound Velocity Measurements
• Interplay between multipolar spin interactions, Jahn-Teller effect and electronic correlation in a $J_{eff}=\frac{3}{2}$ insulator
• Entangled spin-orbital phases in the bilayer Kugel-Khomskii model
• Elastic Instabilities within Antiferromagnetically Ordered Phase in the Orbitally-Frustrated Spinel GeCo${}_2$O${}_4$
• Exact solution for a quantum compass ladder
• Multiflavor Mott insulators in quantum materials and ultracold atoms
• Symmetry properties and spectra of the two-dimensional quantum compass model
• Orbital structure and magnetic ordering in stoichiometric and doped crednerite CuMnO2
• Effects of interorbital hopping on orbital fluctuations and metal-insulator transitions: Extended linearized dynamical mean-field theory
• Orbital ice: an exact Coulomb phase on the diamond lattice
• Role of the spin-orbit coupling in the Kugel-Khomskii model on the honeycomb lattice
• A Potts model for the distortion transition in LaMnO${}_3$
• The Quantum Compass Model on the Square and Simple Cubic Lattices
• Charge and orbital order in transition metal oxides
• Jahn-Teller versus quantum effects in the spin-orbital material LuVO3
• Spin--orbital physics in transition metal oxides
• Anisotropy of the paramagnetic susceptibility in LaTiO${}_3$: The electron-distribution picture in the ground state
• Mechanism of hole propagation in the orbital compass models
• Charge transfer model for the electronic structure of layered ruthenates
• From fidelity to entanglement of entropy of the one-dimensional transverse-field quantum compass model
• Multiband $d-p$ model and self-doping in the electronic structure of Ba${}_2$IrO${}_4$
• Ground state of a spin-1/2 Heisenberg-Ising two-leg ladder with XYZ intra-rung coupling
• Ground state properties of the Heisenberg-compass model on the square lattice
• Monte Carlo study of the critical properties of the three-dimensional 120-degree model
• True nature of long-range order in a plaquette orbital model
• Orbital Compass Model as an Itinerant Electron System
• Cu-Sb dumbbell arrangement in the spin-orbital liquid candidate Ba${}_3$CuSb${}_2$O${}_9$
• A hybrid-exchange density-functional theory study of the electronic structure of ${\mathrm{MnV}}_2{\mathrm{O}}_4$: Exotic orbital ordering in the cubic structure
• Elastic study of electric quadrupolar correlation in the paramagnetic state of a frustrated quantum magnet $\mathrm{T}{\mathrm{b}}_{2+\delta }\mathrm{T}{\mathrm{i}}_{2-\delta }{\mathrm{O}}_7$
• Realization of Nearly Dispersionless Bands with Strong Orbital Anisotropy from Destructive Interference in Twisted Bilayer MoS2
• Intersite Coulomb repulsion driven quadrupole instability and magnetic ordering in the orbital frustrated Ba${}_2$MgReO${}_6$