Theory of Multiple Reentrant Phenomena in the XY Pyrochlore Er₂Sn₂O₇

Rare-earth pyrochlore magnets are known to exhibit a variety of exotic phenomena. The dipolar XY pyrochlore magnets in particular act as playgrounds for effects like order-by-disorder, multiphase competition, and strong quantum fluctuations. Er₂Sn₂O₇, a member of the XY pyrochlore family, has recently been synthesized as a single crystal and studied under a magnetic field. The resulting (H,T) phase diagram reveals multiple reentrant lobes for fields applied in the [100], [110], and [111] directions. In this talk, I will discuss our efforts to understand these reentrant phenomena from the theoretical front, drawing from variational mean-field theory, classical Monte Carlo simulations, and classical spin wave analysis. I will argue that the reentrant lobes are related to a complex multiphase competition, in which the changing ground state degeneracy in a field is associated with the apparition of soft mode excitations. We expect our reasoning to be applicable to other rare-earth pyrochlores and frustrated magnets in general, especially for systems with a discrete ground state degeneracy.