Spin-orbit coupling induced orbital entanglement in a three-band Hubbard model

TL;DR

This paper investigates how spin-orbit coupling influences the ground state phases of a three-band Hubbard model, revealing new orbital-entangled states and their relevance to materials like Sr$_2$VO$_4$.

Contribution

It introduces a generalized Hartree-Fock approach to map the phase diagram, identifying novel orbital-entangled phases induced by spin-orbit coupling and exchange interactions.

Findings

Discovery of additional orbital-entangled phases due to spin-orbit coupling.

Identification of a phase with vanishing magnetic moments and antiferro-octupolar order.

Material analysis shows Sr$_2$VO$_4$ is near a phase boundary involving these phases.

Abstract

The effect of the spin-orbit coupling on the ground state properties of the square-lattice three-band Hubbard model with a single electron per site is studied by a generalized Hartree-Fock approximation. We calculate the full phase diagram and show that there appear additional orbital-entangled phases brought about by competition of various exchange channels or by the spin-orbit coupling in addition to conventional states stabilized by the Kugel-Khomskii mechanism. One of these phases previously proposed to explain magnetic properties of Sr$_2$VO$_4$ is characterized by vanishing dipolar magnetic moments and antiferro-octupolar ordering. We calculated microscopic parameters for this material and demonstrate that it is located near a phase boundary of two orbital-entangled and two conventional antiferromagnetic ferro-orbital states.