Active orbital degree of freedom and potential spin-orbit-entangled moments in Kitaev magnet candidate BaCo$_2$(AsO$_4$)$_2$

TL;DR

This study uses advanced computational methods to reveal that BaCo$_2$(AsO$_4$)$_2$ hosts active orbital degrees of freedom and spin-orbit-entangled moments, supporting its potential as a Kitaev quantum spin liquid candidate.

Contribution

It provides detailed electronic structure analysis showing active orbital degrees of freedom and spin-orbit entanglement in BaCo$_2$(AsO$_4$)$_2$, advancing understanding of Co-based Kitaev materials.

Findings

Co$^{2+}$ ions have a high spin $S=3/2$ configuration.

Trigonal distortion is insufficient to quench orbital degrees of freedom.

Spin-orbit coupling induces spin-orbit-entangled moments and Kitaev interactions.

Abstract

Candidate materials for Kitaev spin liquid phase have been intensively studied recently because of their potential applications in fault-tolerant quantum computing. Although most of the studies on Kitaev spin liquid have been done in 4$d$ and 5$d$ based transition metal compounds, recently there has been a growing research interest in Co-based quasi-two-dimensional honeycomb magnets, such as BaCo$_2$(AsO$_4$)$_2$ because of formation of spin-orbit-entangled $J_{\rm eff}$ = 1/2 pseudospin moments at Co$^{2+}$ sites and potential realizations of Kitaev-like magnetism therein. Here, we obtain high-accuracy crystal and electronic structure of BaCo$_2$(AsO$_4$)$_2$ by employing a combined density functional and dynamical mean-field theory calculations, which correctly capture the Mott-insulating nature of the target system. We show that Co$^{2+}$ ions form a high spin configuration, $S=3/2$, with an active $L_{\rm eff}=1$ orbital degree of freedom, in the absence of spin-orbit coupling. The size of trigonal distortion within CoO$_6$ octahedra is found to be not strong enough to completely quench the orbital degree of freedom, so that the presence of spin-orbit coupling can give rise to the formation of spin-orbit-entangled moments and the Kitaev exchange interaction. Our finding supports recent studies on potential Kitaev magnetism in this compound and other Co-based layered honeycomb systems.