Quantum order by disorder and accidental soft mode Er2Ti2O7

TL;DR

This paper develops an effective quantum spin model for Er2Ti2O7, explaining experimental observations through quantum order by disorder and predicting a non-Goldstone mode consistent with neutron scattering data.

Contribution

It introduces a pseudo-dipolar spin-1/2 model that accounts for quantum order by disorder and explains the continuous transition in Er2Ti2O7.

Findings

Quantum fluctuations select a non-coplanar spin structure.

Presence of a non-Goldstone low-energy mode.

Resolution of the continuous transition puzzle.

Abstract

Motivated by recent neutron scattering experiments, we derive and study an effective "pseudo-dipolar" spin-1/2 model for the XY pyrochlore antiferromagnet Er2Ti2O7. While a bond-dependent in-plane exchange anisotropy removes any continuous symmetry, it does lead to a one-parameter `accidental' classical degeneracy. This degeneracy is lifted by quantum fluctuations in favor of the non-coplanar spin structure observed experimentally -- a rare experimental instance of quantum order by disorder. A non-Goldstone low-energy mode is present in the excitation spectrum in accordance with inelastic neutron scattering data. Our theory also resolves the puzzle of the experimentally observed continuous ordering transition, absent from previous models.