How spin-orbital entanglement depends on the spin-orbit coupling in a Mott insulator

TL;DR

This paper explores how spin-orbital entanglement in a Mott insulator varies with the strength of spin-orbit coupling, revealing regimes of negligible and high entanglement with implications for different material classes.

Contribution

It provides a numerical analysis of how spin-orbit coupling influences spin-orbital entanglement in a 1D model, identifying conditions for entanglement emergence and phases.

Findings

Large spin-orbit coupling can induce significant entanglement.

Weak spin-orbit coupling effects are negligible in certain insulators.

High spin-orbit coupling can lead to a distinct XXZ phase.

Abstract

The concept of the entanglement between spin and orbital degrees of freedom plays a crucial role in understanding various phases and exotic ground states in a broad class of materials, including orbitally ordered materials and spin liquids. We investigate how the spin-orbital entanglement in a Mott insulator depends on the value of the spin-orbit coupling of the relativistic origin. To this end, we numerically diagonalize a 1D spin-orbital model with the 'Kugel-Khomskii' exchange interactions between spins and orbitals on different sites supplemented by the on-site spin-orbit coupling. In the regime of small spin-orbit coupling w.r.t. the spin-orbital exchange, the ground state to a large extent resembles the one obtained in the limit of vanishing spin-orbit coupling. On the other hand, for large spin-orbit coupling the ground state can, depending on the model parameters, either still show negligible spin-orbital entanglement, or can evolve to a highly spin-orbitally entangled phase with completely distinct properties that are described by an effective XXZ model. The presented results suggest that: (i) the spin-orbital entanglement may be induced by large on-site spin-orbit coupling, as found in the 5d transition metal oxides, such as the iridates; (ii) for Mott insulators with weak spin-orbit coupling of Ising-type, such as e.g. the alkali hyperoxides, the effects of the spin-orbit coupling on the ground state can, in the first order of perturbation theory, be neglected.