Ni-Mn-Ti-based all-d-metal Heusler alloys have become a hot research topic in the field of metal functional materials due to their excellent mechanical properties and elastocaloric effect. However, the relatively large critical stress and transition hysteresis limit its practical applications. Some researchers have found that doping Fe in Ni-Mn-based alloys can not only reduce hysteresis, but also greatly improve the mechanical properties of alloys. Based on this, the effects of Fe doping on phase stability, martensitic transformation and magnetic properties of Ni_50–xMn_37.5Ti_12.5Fe_x (x = 3.125, 6.25, 9.375) Heusler alloys are systematically studied by first principles calculation. The corresponding magnetic states of the austenite and martensite of the alloy systems are determined according to the results of the formation energy. The variations of the lattice constants and the phase stability of the austenite and martensite with the increase of Fe content in the alloy systems are revealed, and the associated mechanism is elucidated. The atomic and total magnetic moments of the austenite and martensite in the Ni_50–xMn_37.5Ti_12.5Fe_x (x = 3.125, 6.25, 9.375) systems are calculated. Based on the results of electronic structure, the essential reasons for the magnetic state changes of the alloys are further explained.

In the Ni_50–xMn_37.5Ti_12.5Fe_x alloy system, the lattice constant of austenite decreases gradually with the increase of Fe doping amount. The stability of austenite phase and martensite phase decrease with the increase of Fe doping amount. Under the different compositions, the formation energy of martensite is always lower than that of austenite, indicating that the alloy can undergo martensite transformation. The energy difference ΔE, electron concentration e/a and density of electrons n of the alloy show a decreasing trend, indicating that the driving force of martensitic transformation decreases, and the corresponding martensitic transformation temperature decreases with the increase of Fe atom doping.

The austenite of the alloy is ferromagnetic and the martensite is antiferromagnetic. After the martensitic transformation, the distance between Mn-Mn atoms decreases, and the magnetic moments of Mn_Mn and Mn_Ti atoms are arranged in antiparallel manner, resulting in the total magnetic moments being almost zero. The magnetic properties of the two phases are little affected by the amount of Fe atom doping. The peak density of electronic states in the Fermi surface of martensite phase is lower than that of austenite phase, indicating that martensite phase has a more stable electronic structure than austenite phase. During the transition from austenite to martensite, there is a Jahn-Teller splitting effect at the peak of the down-spin density of states near the Fermi surface. The aim of this paper is to provide guidance for designing the composition design and optimizing the property of the Ni-Mn-Ti-Fe alloy.