The ground state phases of orbitally degenerate spinel oxides

TL;DR

This paper reviews the microscopic spin-orbital Hamiltonian and ground state properties of spin-1/2 spinel oxides with orbital degeneracy, highlighting quantum fluctuation effects and mechanisms lifting degeneracy.

Contribution

It introduces the role of quantum fluctuations in lifting classical degeneracy and describes the resulting non-magnetic spin-singlet dimer ground state in orbitally degenerate spinel oxides.

Findings

Classical ground state degeneracy is lifted by quantum fluctuations.

System favors a spin-singlet dimer manifold.

Residual degeneracy persists due to dimer orientations.

Abstract

I review the microscopic spin-orbital Hamiltonian and ground state properties of spin one-half spinel oxides with threefold $t_{2g}$ orbital degeneracy. It is shown that for any orbital configuration a ground state of corresponding spin only Hamiltonian is infinitely degenerate in the classical limit. The extensive classical degeneracy is lifted by the quantum nature of the spins, an effect similar to order-out-of-disorder phenomenon by quantum fluctuations. This drives the system to a non-magnetic spin-singlet dimer manifold with a residual degeneracy due to relative orientation of dimers. The magneto-elastic mechanism of lifting the ``orientational'' degeneracy is also briefly reviewed.