Er2Ti2O7:Evidence of quantum order by disorder in a frustrated antiferromagnet

${\mathrm{Er}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ has been suggested to be a realization of the frustrated $〈111〉\mathrm{XY}$ pyrochlore lattice antiferromagnet, for which theory predicts fluctuation-induced symmetry breaking in a highly degenerate ground state manifold. We present a theoretical analysis of the classical model compared to neutron scattering experiments on the real material, both below and above $T_N=1.173\mathrm{}\left(2\right)\mathrm{}\mathrm{K}.$ The model correctly predicts the ordered magnetic structure, suggesting that the real system has order stabilized by zero-point quantum fluctuations that can be modeled by classical spin wave theory. However, the model fails to describe the excitations of the system, which show unusual features.