Microscopic origin of magnetism in monolayer $3d$ transition metal dihalides

TL;DR

This paper investigates the microscopic origins of magnetism in monolayer $MX_2$ transition metal dihalides, revealing how spin-orbit coupling and ligand effects influence magnetic interactions in these two-dimensional materials.

Contribution

It provides a detailed analysis of how ligand elements and electron filling affect magnetic interactions and spin-orbit effects in monolayer $MX_2$ materials, using first-principles approaches.

Findings

Spin-orbit coupling effects can be tuned via ligand elements.

3d transition metals contribute minimally to anisotropic exchange.

Heavy ligands induce anisotropic exchange and single-ion anisotropy at specific fillings.

Abstract

Motivated by the recent wealth of exotic magnetic phases emerging in two-dimensional frustrated lattices, we investigate the origin of possible magnetism in the monolayer family of triangular lattice materials $MX_2$ ($M$={V, Mn, Ni}, $X$={Cl, Br, I}). We first show that consideration of general properties such as filling and hybridization enables to formulate trends for the most relevant magnetic interaction parameters. In particular, we observe that the effects of spin-orbit coupling (SOC) can be effectively tuned through the ligand elements as the considered 3$d$ transition metal ions do not strongly contribute to the anisotropic component of the inter-site exchange interaction. Consequently, we find that the corresponding SOC matrix-elements differ significantly from the atomic limit. In a next step and by using two complementary approaches based on first principles, we extract realistic effective spin models and find that in the case of heavy ligand elements, SOC effects manifest in anisotropic exchange and single-ion anisotropy only for specific fillings.