Magnetic phases for two $t_{2g}$ holes with spin-orbit coupling and crystal field

TL;DR

This paper explores the magnetic phases of two holes in $t_{2g}$ orbitals within a square-lattice Mott insulator, considering strong spin-orbit coupling and crystal field effects, using various theoretical models and exact diagonalization.

Contribution

It introduces a comprehensive analysis combining exact diagonalization, an effective triplon model, and a semiclassical approach to map the magnetic phase diagram under different conditions.

Findings

Magnetic phase diagram depends on crystal field and spin-orbit coupling.

Quantum and semiclassical models largely agree on phase boundaries.

Excitation spectra characterize different magnetic phases.

Abstract

We investigate two holes in the the $t_{2g}$ levels of a square-lattice Mott insulator with strong spin-orbit coupling. Exact diagonalization of a spin-orbital model valid at strong onsite interactions, but arbitrary spin-orbit coupling and crystal field is complemented by an effective triplon model (valid for strong spin-orbit coupling) and by a semiclassical variant of the model. We provide the magnetic phase diagram depending on crystal field and spin-orbit coupling, which largely agrees for the semiclassical and quantum models, as well as excitation spectra characterizing the various phases.