Low-field behavior of an X Y pyrochlore antiferromagnet: Emergent clock anisotropies

Using Er2Ti2O7 as motivation, we investigate finite-field properties of XY pyrochlore antiferromagnets. In addition to a fluctuation-induced six-fold anisotropy present in zero field, an external magnetic field induces a combination of two-, three-, and six-fold clock terms as a function of its orientation, providing for rich and controllable magnetothermodynamics. For Er2Ti2O7, we predict a phase transition in a weak magnetic field H vertical bar vertical bar [001]. Re-entrant transitions are also found for H vertical bar vertical bar [111]. We extend these results to the whole family the XY pyrochlore antiferromagnets and show that presence and number of low-field transitions for different orientations can be used for locating a given material in the parameter space of anisotropic pyrochlores. Finite-temperature classical Monte Carlo simulations serve to confirm and illustrate these analytic predictions.