Critical behavior near the ferromagnetic-paramagnetic transformation in the austenite phase of Ni₄₃Mn₄₆Sn₈X₃ (X = In and Cr) Heusler alloys

In this work, we present a detailed study on the magnetic property and critical behavior in the austenitic phase of Ni₄₃Mn₄₆Sn₈X₃ alloys with X = Cr and In, which were prepared by an arc-melting method in an argon ambience. The M(T) curve of the Cr sample (X = Cr) exhibits a single magnetic phase transition at the Curie temperature of the ferromagnetic (FM) austenitic phase with T^A_C = 303 K. In contrast, the In sample (X = In) exhibits multiple magnetic phase transitions, including a magnetic phase transition from a FM state to weakly magnetic state at T^M_C = 165 K of the martensitic phase, a martensitic transition from the weakly magnetic to the FM austenite phase at T^M-A = 259 K, and a magnetic phase transition from the FM to paramagnetic (PM) at T^A_C = 297 K of the austenite phase. Based on the Landau theory and M(H) data measured at different temperatures, we pointed that the FM-PM phase transitions around T^A_C in both samples were the second-order phase transition. Our results suggest an existence of the long-range FM interactions in the austenite phase. A small deviation from the mean-field theory of the critical exponents has been also observed pointing out an existence of the inhomogeneous magnetism that could be associated with the presence of the anti-FM interactions in these samples. Besides, their effective exponents β_eff(ε) and γ_eff(ε) have been also calculated.