Order-by-Disorder in the XY Pyrochlore Antiferromagnet Revisited

TL;DR

This study revisits the XY pyrochlore antiferromagnet, demonstrating how thermal fluctuations induce long-range magnetic order and how this order persists under weak perturbations, with implications for related materials like Er2Ti2O7.

Contribution

It provides a comprehensive analysis of order-by-disorder phenomena in the XY pyrochlore antiferromagnet, combining analytical and numerical methods to confirm the stability of the ordered state.

Findings

Thermal fluctuations select a specific magnetic structure.

The ordered state survives weak pseudo-dipolar interactions.

The spin wave spectrum aligns with the selected magnetic order.

Abstract

We investigate the properties of the XY pyrochlore antiferromagnet with local <111> planar anisotropy. We find the ground states and show that the configurational ground state entropy is subextensive. By computing the free energy due to harmonic fluctuations and by carrying out Monte Carlo simulations, we confirm earlier work indicating that the model exhibits thermal order-by-disorder leading to low temperature long-range order consisting of discrete magnetic domains. We compute the spin wave spectrum and show that thermal and quantum fluctuations select the same magnetic structure. Using Monte Carlo simulations, we find that the state selected by thermal fluctuations in this XY pyrochlore antiferromagnet can survive the addition of sufficiently weak nearest-neighbor pseudo-dipolar interactions to the spin Hamiltonian. We discuss our results in relation to the Er2Ti2O7 pyrochlore antiferromagnet.