Fingerprints of spin-orbital entanglement in transition metal oxides

Abstract

The concept of spin-orbital entanglement on superexchange bonds in transition metal oxides is introduced and explained on several examples. It is shown that spin-orbital entanglement in superexchange models destabilizes the long-range (spin and orbital) order and may lead either to a disordered spin-liquid state or to novel phases at low temperature which arise from strongly frustrated interactions. Such novel ground states cannot be described within the conventionally used mean field theory which separates spin and orbital degrees of freedom. Even in cases where the ground states are disentangled, spin-orbital entanglement occurs in excited states and may become crucial for a correct description of physical properties at finite temperature. As an important example of this behaviour we present spin-orbital entanglement in the $R$VO${}_3$ perovskites, with $R$=La,Pr,...,Yb,Lu, where such finite temperature properties of these compounds can be understood only using entangled states: ($i$) thermal evolution of the optical spectral weights, ($ii$) the dependence of transition temperatures for the onset of orbital and magnetic order on the ionic radius in the phase diagram of the $R$VO${}_3$ perovskites, and ($iii$) dimerization observed in the magnon spectra for the $C$-type antiferromagnetic phase of YVO${}_3$. Finally, it is shown that joint spin-orbital excitations in an ordered phase with coexisting antiferromagnetic and alternating orbital order introduces topological constraints for the hole propagation and will thus radically modify transport properties in doped Mott insulators where hole motion implies simultaneous spin and orbital excitations.

54 pages, 15 figures, topical review

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Cited by in corpus (28)

• Theory of Current-Induced Angular Momentum Transfer Dynamics in Spin-Orbit Coupled Systems
• Spin--orbital interaction for face-sharing octahedra: Realization of a highly symmetric SU(4) model
• Effective magnetic interactions in spin-orbit coupled $d^4$ Mott insulators
• Noncollinear Magnetic Order Stabilized by Entangled Spin-Orbital Fluctuations
• Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study
• Von Neumann Entropy Spectra and Entangled Excitations in Spin-Orbital Models
• Spin-Orbital Order Modified by Orbital Dilution in Transition Metal Oxides: From Spin Defects to Frustrated Spins Polarizing Host Orbitals
• Exotic spin orders driven by orbital fluctuations in the Kugel-Khomskii model
• Exact treatment of magnetism-driven ferroelectricity in the one-dimensional compass model
• Quantum phase transitions in exactly solvable one-dimensional compass models
• Spin-orbital order in undoped manganite LaMnO3 at finite temperature
• Frustration and Entanglement in Compass and Spin-Orbital Models
• Orbital Symmetry and Orbital Excitations in High-$T_c$ Superconductors
• Spin-orbital exchange of strongly interacting fermions on the $p$-band of a two-dimensional optical lattice
• Optical conductivity due to orbital polarons in systems with orbital degeneracy
• Green's function variational approach to orbital polarons in KCuF3
• Charge transfer model for the electronic structure of layered ruthenates
• Locally tunable disorder and entanglement in the one-dimensional plaquette orbital model
• Strain-induced spin-nematic state and nematic susceptibility arising from $2\times 2$ Fe clusters in KFe${}_{0.8}$Ag${}_{1.2}$Te${}_2$
• Quantum entanglement, local indicators and effect of external fields in the Kugel-Khomskii model
• Striped critical spin liquid in a spin-orbital entangled RVB state in a projected entangled-pair state representation
• Hole propagation in the orbital compass models
• DMRG studies on linear-exchange quantum spin models in one dimension
• Exotic Spin Order due to Orbital Fluctuations
• Evolution of Spin-Orbital Entanglement with Increasing Ising Spin-Orbit Coupling
• Quantum versus classical polarons in a ferromagnetic CuO${}_3$-like chain
• Quantum phase transitions in the Kitaev--Heisenberg model on a single hexagon
• Orbital liquid in the $e_g$ orbital Hubbard model in $d=\infty$ dimensions