Magnetocaloric and Exchange Bias effects in Ni$_{50}$Mn$_{35.8}$Sn$_{14.2}$ alloy*

Heusler alloys have been a subject of intense research because of their intriguing physical properties. We have studied magnetic and magnetocaloric properties of such an alloy with composition Ni$_{50}$Mn$_{35.8}$Sn$_{14.2}$. The system undergoes two transitions upon cooling: (i) a ferromagnetic transition in austenite phase at T$_{\mathrm{C}}^{\mathrm{A}} \sim $310 K and (ii) the martensitic transition at T$_{\mathrm{MA}} \sim $ 165 K. Using Maxwell's equation, the magnetic entropy change ($\Delta $S$_{\mathrm{M}})$ is calculated from the is magnetization vs. field curves following heating, cooling, and loop protocols. A large inverse magnetocaloric effect (IMCE) is observed at T$_{\mathrm{MA}}$ in addition to the conventional magnetocaloric effect (CMCE) at T$_{\mathrm{C}}^{\mathrm{A}}$. While $\Delta $S$_{\mathrm{M}}$ is protocol dependent, we have demonstrated that a universal curve can be constructed to describe temperature (T) dependence of $\Delta $S$_{\mathrm{M}}$ corresponding to IMCE without rescaling of the T-axis and irrespective of measurement protocol. Such a universal behavior of IMCE is different from that of CMCE. The system also shows an exchange bias effect below T$_{\mathrm{MA}}$ due to phase coexistence.