Energetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet

TL;DR

This paper explores how anisotropic interactions and excited state effects can energetically select ordered states in Er2Ti2O7, highlighting the limited role of simple exchange interactions and the potential importance of fluctuations.

Contribution

It demonstrates that anisotropies from excited crystal field states, combined with anisotropic exchange, can energetically select ordered states in Er2Ti2O7.

Findings

Nearest neighbour exchange alone is insufficient for state selection.

Anisotropies from excited states contribute to long-range order.

Experimental Bragg peak variations are reproduced by the model.

Abstract

We consider the possibility that the discrete long-range ordered states of Er2Ti2O7 are selected energetically at the mean field level as an alternative scenario that suggests selection via thermal fluctuations. We show that nearest neighbour exchange interactions alone are not sufficient for this purpose, but that anisotropies arising from excited single ion crystal field states in Er2Ti2O7, together with appropriate anisotropic exchange interactions, can produce the required long range order. However, the effect of the single ion anisotropies is rather weak so we expect thermal or quantum fluctuations, in some guise, to be ultimately important in this material. We reproduce recent experimental results for the variation of magnetic Bragg peak intensities as a function of magnetic field.