Understanding multicaloric effects in anisotropic magnets via a mean-field approach

Materials with magnetic anisotropy can serve as a model object for exploring the multicaloric effect because their thermodynamic state alterations can be achieved either through the application of a magnetic field H or/and by mechanically rotating the sample in the magnetic field using torque τ. In such materials, the total entropy change $\Delta S_T$ arises from two distinct contributions: (1) the conventional magnetocaloric effect (MCE) or paraprocess $\Delta S_{\left(m\right)}$ and (2) the rotational MCE $\Delta S_{\phi }$ . In this manuscript, using molecular field model which enables a separation of contributions to the total entropy change $\Delta S_T$ from conventional $\Delta S_{\left(m\right)}$ and rotational $\Delta S_{\phi }$ , we have determined cross-coupling multicaloric coefficients ${\chi }_{\tau ,H}={\left(\frac{\mathrm{\partial \tau }}{\mathrm{\partial H}}\right)}_{T,\theta }$ and ${\chi }_{H,\tau }=-{\left(\frac{\mathrm{\partial m}}{\mathrm{\partial \theta }}\right)}_{T,H}$ for anisotropic magnetic materials and show that they satisfy the basic thermodynamic identities. We also confirmed that the total multicaloric effect in the material with magnetic anisotropy can be accurately expressed as the sum of the individual magnetocaloric effects induced by separate application of the H and τ, minus the magnetic entropy change arising from thermodynamic cross-coupling between the subsystems of the solid: $\hspace{0.17em}\Delta S_T=\Delta S_{T,\tau }^{\left(H\right)}+\Delta S_{T,H}^{\left(\theta \right)}-\hspace{0.17em}\Delta S_{\mathrm{coupling}}$ .