Nonlinear field theory of a 3-sublattice hexagonal antiferromagnet

We derive the nonlinear field theory of a 3-sublattice hexagonal antiferromagnet. The order parameter can be parametrized as a rigid body made by the three vectors of sublattice magnetizations oriented at 120º to one another. Like in the linear spin-wave theory developed by us previously [1], the exchange energy density has three coupling constants reminiscent of the Lame parameters describing the elasticity of a hexagonal solid. Our theory generalizes the older work of Dombre and Read [2] for a triangular lattice, which turns out to be a special case with higher spatial symmetry. We show that a vortex in a 3-sublattice antiferromagnet with easy-plane anisotropy generally has an elliptical core, with the ellipticity determined by the ratio of Lame parameters.

[1] S. Dasgupta and O. Tchernyshyov, Phys. Rev. B 102, 144417.

[2] T. Dombre and N. Read, Phys. Rev. B 39, 6797.