Calculation of Multipolar Exchange Interactions in Spin-Orbital Coupled Systems

TL;DR

This paper introduces a novel computational method for calculating multipolar exchange interactions in spin-orbit coupled systems, revealing complex magnetic behaviors in Uranium dioxide.

Contribution

The paper develops a new multipolar tensor expansion method within LDA+U calculations to accurately compute exchange interactions in spin-orbit coupled materials.

Findings

Antiferromagnetic superexchange in dipoles

Ferromagnetic coupling in quadrupoles

Spin-lattice interactions comparable to superexchange

Abstract

A new method of computing multipolar exchange interaction in spin-orbit coupled systems is developed using multipolar tensor expansion of the density matrix in LDA+U electronic structure calculation. Within mean-field approximation, exchange constants can be mapped into a series of total energy calculations by pair-flip technique. Application to Uranium dioxide shows an antiferromagnetic superexchange coupling in dipoles but ferromagnetic in quadrupoles which is very different from past studies. Further calculation of spin-lattice interaction indicates it is of the same order with superexchange and characterizes the overall behavior of quadrupolar part as a competition between them.