Repulsive magneto-structural interaction in the ferromagnetic shape memory alloys Ni₂Mn_1+xIn_1-x

A phenomenological theory is presented to study the multiferroic system in the shape memory alloys Ni₂Mn_1+xIn_1-x with the Heusler-type structure, where the phase transitions are characterized by the two order parameters, i.e., the martensitic distortion e₃ and the magnetization M. The Landau free energy is expanded in powers of e₃ and M with including the Zeeman energy and the energy increase by the uniaxial force on e₃. The resultant free energy is applied to analyze the experimental results, such as the phase diagram in the temperature-concentration plane and the reentrant ferromagnetism by increasing temperature. The magnetic fields are shown to cause the ferromagnetic-ferromagnetic or metamagnetic transitions as observed. Further, it is predicted that the uniaxial force can dominate the appearance of the ferromagnetism in some alloys. It is found that these exotic behaviors of this alloy system are all ascribed to the repulsive interaction between e₃ and M, which originates from their biquadratic term. Through the present analyses, it is verified that this repulsive interaction is expected in other alloy systems Ni₂Mn _1+xX_1-x (X=Sn, Sb) and makes a contrast to the attractive interaction realized in another group of the alloy systems including Ni _2+xMn_1-xGa and Ni₂Mn_1-xCu _xGa.