Degenerate manifolds, helimagnets, and multi-$\mathbf{Q}$ chiral phases in the classical Heisenberg antiferromagnet on the face-centered-cubic lattice

TL;DR

This paper explores the complex ground state phases of a classical Heisenberg antiferromagnet on the face-centered-cubic lattice, revealing diverse magnetic orders, degenerate manifolds, and exact configurations with implications for related models.

Contribution

It provides a comprehensive analysis of the phase diagram including new degenerate manifolds and exact ground states, advancing understanding of frustrated magnetic systems.

Findings

Identification of commensurate and helimagnetic phases

Discovery of subextensive degenerate manifolds

Exact ground state configurations in real space

Abstract

We present a detailed study of the ground state phase diagram of the classical frustrated Heisenberg model on the face-centered-cubic lattice. By considering exchange interactions up till third nearest neighbors, we find commensurate, helimagnetic, as well as noncollinear multi-{\bf Q} orders which include noncoplanar and chiral spin structures. We reveal the presence of subextensively degenerate manifolds that appear at triple points and certain phase boundaries in the phase diagram. Within these manifolds, the spin Hamiltonian can be recast as a complete square of spins on finite motifs, permitting us to identify families of exact ground state spin configurations in real space -- these include randomly stacked ferro- or antiferromagnetically ordered planes and interacting ferromagnetic chains, among others. Finally, we critically investigate the ramifications of our findings on the example of the Ising model, where we exactly enumerate all the states numerically for finite clusters.