Theoretical analysis of single-ion anisotropy in $d^3$ Mott insulators

TL;DR

This paper provides a theoretical analysis of single-ion anisotropy in $d^3$ Mott insulators, revealing how various interactions influence magnetic anisotropy beyond the traditional models.

Contribution

The authors derive a comprehensive model for single-ion anisotropy considering crystal fields, distortions, Hund's coupling, and spin-orbit interactions beyond the LS coupling scheme.

Findings

Single-ion anisotropy can be favored by spin-orbit coupling at magnetic sites or anions.

The anisotropy depends on the strength of spin-orbit couplings and lattice distortions.

Application to $ m{CrX}_3$ shows variable anisotropy behavior based on material parameters.

Abstract

An effective spin model for Mott insulators is determined by the symmetries involved among magnetic sites, electron fillings, and their interactions. Such a spin Hamiltonian offers insight to mechanisms of magnetic orders and magnetic anisotropy beyond the Heisenberg model. For a spin moment S bigger than 1/2, single-ion anisotropy is in principle allowed. However, for $d^3$ Mott insulators with large cubic crystal field splitting, the single-ion anisotropy is absent within the LS coupling, despite S = 3/2 local moment. On the other hand, preferred magnetic moment directions in $d^3$ materials have been reported, which calls for a further theoretical investigation. Here we derive the single-ion anisotropy interaction using the strong-coupling perturbation theory. The cubic crystal field splitting including $e_g$ orbitals, trigonal distortions, Hund's coupling, and spin-orbit coupling beyond the LS scheme are taken into account. For compressed distortion, the spin-orbit coupling at magnetic sites can favor either the easy-axis or the easy-plane while that of anions leads to easy-axis anisotropy. We apply the theory on $\rm{CrX}_3$ with X = Cl and I, and show the dependence of the single-ion anisotropy on the strength of the spin-orbit couplings of both magnetic and anion sites. Significance of the single-ion anisotropy in ideal two-dimensional magnets is also discussed.