Thermodynamics of ferrotoroidic materials: Toroidocaloric effect

The three primary ferroics, namely ferromagnets, ferroelectrics, and ferroelastics, exhibit corresponding large (or even giant) magnetocaloric, electrocaloric, and elastocaloric effects when a phase transition is induced by the application of an appropriate external field. Recently the suite of primary ferroics has been extended to include ferrotoroidic materials in which there is an ordering of toroidic moments in the form of magnetic-vortex-like structures, examples being LiCo(PO4)(3) and Ba2CoGe2O7. In the present work we formulate the thermodynamics of ferrotoroidic materials. Within a Landau free energy framework we calculate the toroidocaloric effect by quantifying isothermal entropy change (or adiabatic temperature change) in the presence of an applied toroidic field when usual magnetization and polarization may also be present simultaneously. We also obtain a nonlinear Clausius-Clapeyron relation for phase coexistence.