Nature of finite-temperature transition in anisotropic pyrochlore Er 2 Ti 2 O 7

We study the finite-temperature transition in a model XY antiferromagnet on a pyrochlore lattice, which describes the pyrochlore material Er2Ti2O7. The ordered magnetic structure selected by thermal fluctuations is sixfold degenerate. Nevertheless, our classical Monte Carlo simulations show that the critical behavior corresponds to the three-dimensional XY universality class. We determine an additional critical exponent nu(6) = 0.75 > nu characteristic of a dangerously irrelevant scaling variable. Persistent thermal fluctuations in the ordered phase are revealed in Monte Carlo simulations by the peculiar coexistence of Bragg peaks and diffuse magnetic scattering, the feature also observed in neutron diffraction experiments.