Understanding reentrance in frustrated magnets: the case of the Er₂Sn₂O₇ pyrochlore

In frustrated magnets, most of the theoretical focus has been devoted to the physics near zero temperature. However, a number of frustrated magnetic materials develop long-range order at a nonzero critical temperature (T_c), therefore, it is important to ask if the physics near T_c can inform our understanding of the ground state physics. We investigate this question through a detailed single crystal study of Er₂Sn₂O₇, a frustrated pyrochlore antiferromagnet known to reside near the boundary of two classical phases. We propose an original mechanism for the phenomenon of reentrance, where an ordered phase is surrounded on both sides by the same less ordered phase as an external parameter is tuned. While reentrance has been found in a variety of systems, the microscopic mechanisms behind it are not often studied in detail. We show Er₂Sn₂O₇ has multiple instances of reentrance in its experimental field vs temperature phase diagram, and through extensive theoretical calculations, we propose that the origins of this reentrance are linked to soft modes arising from T=0 phase competition. The ground state phase competition enhances thermal fluctuations that entropically stabilize the ordered phase, leading to increased transition temperatures for specific field values, and thus reentrance.