Orbital order and fluctuations in Mott insulators

Abstract

Basic mechanisms controlling orbital order and orbital fluctuations in transition metal oxides are discussed. The lattice driven classical orbital picture, e.g. like in manganites LaMnO${}_3$, is contrasted to the quantum behavior of orbitals in frustrated superexchange models as realised in pseudocubic titanites ATiO${}_3$ and vanadates AVO${}_3$. In YVO${}_3$, the lattice and superexchange effects strongly compete -- this explains the extreme sensitivity of magnetic states to temperature and doping. Lifting the $t_{2g}$ orbital degeneracy by a relativistic spin-orbital coupling is considered on example of the layered cobaltates. We find that the spin-orbital mixing of low-energy states leads to unusual magnetic correlations in a triangular lattice of the CoO${}_2$ parent compound. Finally, the magnetism of sodium-rich compounds Na${}_{1-x}$CoO${}_2$ is discussed in terms of a spin/orbital polaronic liquid.

48 pages, 5 figures; typos corrected, journal reference added

References in corpus (1)

• Orbital order and fluctuations in Mott insulators

Cited by in corpus (291)

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• One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization
• Topological quantum phase transitions of anisotropic AFM Kitaev model driven by magnetic field
• The free energy of anisotropic quantum spin systems: Functional integral representation
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• Orbital liquid in the $e_g$ orbital Hubbard model in $d=\infty$ dimensions
• Spontaneous magnetization and magnetic susceptibility of LaVO3
• Quantum gap and spin-wave excitations in the Kitaev model on a triangular lattice
• Emergence of quadrupolar order under magnetic field in $5d^2$ double perovskites
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• Phase coexistence and negative thermal expansion in the triple perovskite iridate Ba${}_3$CoIr${}_2$O${}_9$
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