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

Using Er₂Ti₂O₇ as motivation, we investigate finite-field properties of X Y 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 ∥[001 ] . Re-entrant transitions are also found for H ∥[111 ] . We extend these results to the whole family the X Y 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.