Critical behavior and exponent parameters of the austenitic phase in Ni50-x Pr x Mn37Sn13 alloys with x=1

We fabricated Huesler alloy ingots of Ni50-x Pr (x) Mn37Sn13 with x = 0 - 5 by using an arcmelting method. Crystalline-structural analyses revealed the coexistence of austenitic and martensitic phases in the samples with x = 0 and 1, in which the volume fraction of the austenitic phase for x = 1 was higher than that for x = 0. With higher Pr concentrations, x > 1, Pr- and Ni3Sn-related secondary phases, which reduced the magnetic order of the alloys, were formed. Thus, only the sample with x = 1 was more suitable for studying the critical behavior. Based on Landau's phase-transition theory and Banerjee's criteria, we found that this sample undergoes a second-order magnetic phase transition (SOMT) at a temperature around the Curie temperature T (C) a parts per thousand 299 K. Using the modified Arrott plots, asymptotic relations, and a universal scaling law, we determined the values of the critical exponents beta = 0.501 +/- 0.009 and gamma = 1.045 +/- 0.006. These values are very close to those expected for the mean-field theory with beta = 0.5 and gamma = 1, proving the existence of long-range ferromagnetic (FM) order in the sample with x = 1. Particularly, around at temperature T (C) , the magnetic-entropy change reaches the maximum value (a dagger S (max) ). Its magnetic-field dependences can be described by using a power law |a dagger S (max) | ae H (n) , where n = 0.687 is close to the value 0.677 calculated from the theoretical relation n = 1 + (beta - 1)/(beta + gamma). We believe that the doping of a suitable Pr amount in Ni50-x Pr (x) Mn37Sn13 (x a parts per thousand 1) promotes the formation of the austenitic phase and results in long-range FM order. However, the persistence of the martensitic phase and secondary phases favors short-range FM order and thus decreases the FM order in Ni50-x Pr (x) Mn37Sn13.