Spin--orbital physics in transition metal oxides

TL;DR

This paper reviews the spin-orbital superexchange interactions in transition metal oxides, highlighting their role in magnetic and optical properties, intrinsic frustration, quantum fluctuations, and the evolution of phase transitions in RVO3 perovskites.

Contribution

It provides a comprehensive overview of spin-orbital superexchange, emphasizing the effects of lattice symmetry, frustration, and entanglement on the properties of Mott insulators with orbital degrees of freedom.

Findings

Orbital superexchange obeys cubic symmetry, unlike spin superexchange.

Intrinsic frustration and entanglement lead to disordered quantum states.

Explains the evolution of transition temperatures in RVO3 series.

Abstract

We present the main features of the spin-orbital superexchange which describes the magnetic and optical properties of Mott insulators with orbital degrees of freedom. In contrast to the SU(2) symmetry of spin superexchange, the orbital part of the superexchange obeys the lower cubic symmetry of the lattice and is intrinsically frustrated. This intrinsic frustration and spin-orbital entanglement induce enhanced quantum fluctuations, and we point out a few situations where this leads to disordered states. Strong coupling between the spin and orbital degrees of freedom is discussed on the example of the $R$VO$_3$ perovskites, with $R$ standing for rare-earth ion, La,...,Lu. We explain the observed evolution of the orbital $T_{\rm OO}$ and N\'eel $T_{N1}$ transition temperature in the $R$VO$_3$ series with decreasing ionic radius $r_R$. A few open problems and the current directions of research in the field of spin-orbital physics are pointed out.