Motivated by recent neutron scattering experiments, we derive and study an effective “pseudodipolar” spin-$1/2$ model for the $XY$ pyrochlore antiferromagnet ${\mathrm{Er}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. 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 noncoplanar 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.

• Received 2 April 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.077204