Resolving the importance of soft mode excitations on the magnetocaloric effect of frustrated Heisenberg magnets in the liquid-He regime

Frustrated magnetic oxides are ideal candidates for magnetocaloric refrigeration due to suppressed ordering temperatures. Materials design has focused on tuning magnetic moments, their interactions, and density, but less so on the frustrating lattice. Prior theoretical work predicted an enhancement of the magnetocaloric cooling rate via a macroscopic number of soft mode excitations that arise due to the classical ground state degeneracy. The number of these modes is directly determined by the geometry of the frustrating lattice. Among corner-sharing geometries, the pyrochlore has 3/2 as many modes as the garnet and kagome lattices, while the number of soft modes for the edge-sharing fcc is sub-extensive. Here, we study the role of soft modes in the magnetocaloric effect of four large-spin Gd³⁺ (S=7/2) Heisenberg antiferromagnets on a kagome, garnet, pyrochlore, and fcc lattice. Measurements of the magnetic entropy change at fields up to 9 T provide qualitative agreement with the theoretical prediction. We find that the superexchange dominates the observed magnetocaloric effect in the liquid-He regime (2-20 K) rather than the soft mode excitations. Our results may inform future materials design in terms of dimensionality, degree of magnetic frustration, and lattice geometry.