Order-by-disorder in the XY pyrochlore antiferromagnet

We investigate the properties of the XY pyrochlore antiferromagnet with infinite local <111> planar anisotropy. We identify the ground states and show that the configurational ground state entropy is subextensive. By computing the free energy due to harmonic fluctuations and by carrying out Monte Carlo simulations, we find that the model exhibits thermal order-by-disorder leading to low-temperature long-range order consisting of discrete magnetic domains. In doing so, we set aside doubts that order-by-disorder survives in the thermodynamic limit in this model. We compute the spin wave spectrum and show that thermal and quantum fluctuations select the same magnetic structure. With a previously unreported finite-size scaling analysis of Monte Carlo data, we confirm that the transition is first order for the XY model. Using Monte Carlo simulations, we find that the state selected by thermal fluctuations in this XY pyrochlore antiferromagnet can survive the addition of sufficiently weak nearest-neighbor pseudo-dipolar interactions or long-range dipolar interactions to the spin Hamiltonian. Quite interestingly, the resulting state selected by thermal order-by-disorder is metastable below some temperature. We discuss our results in relation to the Er2Ti2O7 and Er2Sn2O7 pyrochlore antiferromagnets.