*

Rare-earth pyrochlore oxides (A₂B₂O₇) can host a wealth of exotic phenomena due to geometric- and exchange-frustration. Er₂Sn₂O₇ is especially interesting in this regard as, based on available estimates of the exchange interactions, it lies near a phase boundary in the anisotropic exchange parameter space, between two antiferromagnetic states: the Palmer-Chalker states (where Er₂Sn₂O₇ orders) and the Γ₅ states. A natural tool to probe such multi-phase competition is the application of an external magnetic field, but until now the absence of single crystals made such approach difficult to analyze. In this talk, we report specific heat measurements on single crystals of Er₂Sn₂O₇ under fields applied along the three high symmetry directions, [111], [110], and [100]. Each field direction provides a distinct phase diagram, but with the shared feature that one (sometimes even two) reentrant lobe(s) appear above a threshold field of 0.2 T. The nature of this reentrance can be understood semi-quantitatively through classical Monte-Carlo simulations and mean field theory, the details of which will be described in a presentation by D. Pereira.