Critical Anisotropies of a Geometrically-Frustrated Triangular-Lattice Antiferromagnet

TL;DR

This paper investigates the critical anisotropy needed for the stability of various ground states in a geometrically-frustrated triangular-lattice antiferromagnet, using spin-wave analysis to map phase boundaries.

Contribution

It provides a detailed calculation of critical anisotropy for multiple sublattice phases, revealing phase boundary behaviors and stability conditions.

Findings

Critical anisotropy varies with exchange parameters.

Phase boundaries show discontinuities in critical anisotropy.

3-SL phase has higher critical anisotropy at certain boundaries.

Abstract

This work examines the critical anisotropy required for the local stability of the collinear ground states of a geometrically-frustrated triangular-lattice antiferromagnet (TLA). Using a Holstein-Primakoff expansion, we calculate the spin-wave frequencies for the 1, 2, 3, 4, and 8-sublattice (SL) ground states of a TLA with up to third neighbor interactions. Local stability requires that all spin-wave frequencies are real and positive. The 2, 4, and 8-SL phases break up into several regions where the critical anisotropy is a different function of the exchange parameters. We find that the critical anisotropy is a continuous function everywhere except across the 2-SL/3-SL and 3-SL/4-SL phase boundaries, where the 3-SL phase has the higher critical anisotropy.