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

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.