  A three-dimensional phase-field model is proposed for simulating the magnetic
martensitic phase transformation. The model considers a paramagnetic cubic
austenite to ferromagnetic tetragonal martensite transition, as it occurs in
magnetic Heusler alloys like Ni2 MnGa, and is based on a Landau 2-3-4
polynomial with temperature dependent coefficients. The
paramagnetic-ferromagnetic transition is recaptured by interpolating the
micromagnetic energy as a function of the order parameter for the ferroelastic
domains. The model is numerically implemented in real space by finite element
(FE) method. FE simulations in the martensitic state show that the model is
capable to correctly recapture the ferroelastic and -magnetic microstructures,
as well as the influence of external stimuli. Simulation results indicate that
the paramagnetic austenite to ferromagnetic martensite transition shifts
towards higher temperatures when a magnetic field or compressive stress is
applied. The dependence of the phase transition temperature shift on the
strength of the external stimulus is uncovered as well. Simulation of the phase
transition in magnetocaloric materials is of high interest for the development
of energy-efficient magnetocaloric cooling devices.
