Ising Like Order by Disorder In The Pyrochlore Antiferromagnet with Dzyaloshinskii-Moriya Interactions

TL;DR

This paper demonstrates that quantum and thermal fluctuations induce a specific discrete order in the pyrochlore antiferromagnet with Dzyaloshinskii-Moriya interactions, overcoming classical degeneracy.

Contribution

It reveals that order out of disorder occurs in the pyrochlore antiferromagnet with Dzyaloshinskii-Moriya interactions, reducing degeneracy to a discrete symmetry and showing robustness against symmetric exchange anisotropy.

Findings

Quantum and thermal fluctuations break continuous degeneracy.

Discrete $ ext{Z}_3 imes ext{Z}_2$ symmetry emerges.

Order persists despite symmetric exchange interactions.

Abstract

It is shown that the mechanism of order out of disorder is at work in the antisymmetric pyrochlore antiferromagnet. Quantum as well as thermal fluctuations break the continuous degeneracy of the classical ground state manifold and reduce its symmetry to $\mathbb{Z}_3 \times \mathbb{Z}_2$. The role of anisotropic symmetric exchange is also investigated and we conclude that this discrete like ordering is robust with respect to these second order like interactions. The antisymmetric pyrochlore antiferromagnet is therefore expected to order at low temperatures, whatever the symmetry type of its interactions, in both the classical and semi classical limits.