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

Dorota Gotfryd,Ekaterina M Pärschke,Andrzej M Oleś,Jiří Chaloupka,Krzysztof Wohlfeld

doi:10.1103/physrevresearch.2.013353

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.

Highlights

IntroductionThe low-lying excited states can be described as weakly interacting quasiparticles, carrying the quantum numbers of the constituents forming the system
In order to better understand the physics behind the observations (i) and (ii) discussed at the end of the previous subsection, here we study in great detail the onset of the spinorbital entanglement once β = −α
In this paper we studied the spin-orbital entanglement in a Mott insulator with spin and orbital degrees of freedom

Summary

Introduction

The low-lying excited states can be described as weakly interacting quasiparticles, carrying the quantum numbers of the constituents forming the system. Such physics is realized, for instance, by the ions in conventional crystals, spins in ordered magnets, or electrons in Fermi liquids [1]. An interesting situation occurs when the answer to the above question is negative and we are left with a “fully quantum” interacting many-body problem [2,3]

Objectives

Methods

Results

Discussion

Conclusion