Soft modes in the easy plane pyrochlore antiferromagnet

TL;DR

This paper investigates the complex low-temperature behavior of the easy-plane pyrochlore antiferromagnet, revealing a continuous manifold of states and the effects of thermal fluctuations and disorder on its magnetic order.

Contribution

It demonstrates the existence of a large continuous manifold of states below the phase transition and analyzes the role of thermal fluctuations and disorder in selecting magnetic order.

Findings

Existence of a N^{2/3} dimensional manifold of states below the transition

Thermal fluctuations induce a first-order phase transition to long-range order

Order by disorder occurs as temperature approaches zero

Abstract

Thermal fluctuations lift the high ground state degeneracy of the classical nearest neighbour pyrochlore antiferromagnet, with easy plane anisotropy, giving a first order phase transition to a long range ordered state. We show, from spin wave analysis and numerical simulation, that even below this transition a continuous manifold of states, of dimension N^{2/3} exist (N is the number of degrees of freedom). As the temperature goes to zero a further `order by disorder' selection is made from this manifold. The pyrochlore antiferromagnet Er_2Ti_2O_7, is believed to have an easy plane anisotropy and is reported to have the same magnetic structure. The latter is perhaps surprising, given that the dipole interaction lifts the degeneracy of the classical model in favour of a different structure. We interpret our results in the light of these facts.