Magnetocaloric and Critical Behaviors of ${\rm Ni}_{0.5}{\rm Mn}_{0.5-{\rm x}}{\rm Sn}_{\rm x}$ Heusler Alloys

This work presents the magnetocaloric effect (MCE) and critical behaviors of bulk Ni_0.5Mn_0.5-xSn_x alloys (x=0.14 and 0.15) prepared by an arc-melting method. Under an external field of 50 kOe, we have observed the coexistence of the inverse MCE with a maximum magnetic entropy change (ΔS_max) of 1.39 J·kg^-1·K^-1 at 218 K (associated with the martensitic-austenitic transition), and normal MCE with a minimum magnetic entropy change (ΔS_min) of -4.97 J·kg^-1·K^-1 at 308 K (associated with the ferromagnetic-paramagnetic transition in the austenitic phase) in x=0.14 . Meanwhile, the magnetic entropy changes for x=0.15 keeps normal negative, with ΔS_min=-4.55 J·kg^-1·K^-1 at 315 K. Interestingly, the ferromagnetic-paramagnetic transition in the austenitic phases for both alloys is found to be second-order type. Having used the Arrott-Noakes method, the critical exponents obtained for x=0.14 are β = 0.451 and γ = 1.217, and for x=0.15 are β = 0.501 and γ = 0.963, which are close to those expected for the mean-field model (β = 0.5 and γ = 1). This reveals that a long-range-order ferromagnetic interaction dominates in the austenitic phase. A small deviation from the theoretical values, particularly for x=0.14, is assigned to magnetic inhomogeneity induced by the martensitic-austenitic transition.