Spin-frame field theory of a three-sublattice antiferromagnet

TL;DR

This paper develops a nonlinear field theory for a three-sublattice hexagonal antiferromagnet, describing its spin dynamics, vortex shapes, and universal relations among spin-wave velocities.

Contribution

It introduces a novel spin-frame field theory with three coupling constants, revealing universal relations and vortex properties in a three-sublattice antiferromagnet.

Findings

Spin-wave velocities satisfy a universal relation.

Vortices have elliptical shapes with eccentricity linked to Lamé parameters.

The theory relates sublattice magnetizations and spin chirality.

Abstract

We present a nonlinear field theory of a three-sublattice hexagonal antiferromagnet. The order parameter is the spin frame, an orthogonal triplet of vectors related to sublattice magnetizations and spin chirality. The exchange energy, quadratic in spin-frame gradients, has three coupling constants, only two of which manifest themselves in the bulk. As a result, the three spin-wave velocities satisfy a universal relation. Vortices generally have an elliptical shape with the eccentricity determined by the Lam\'e parameters.