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Neutron diffraction and symmetry analysis of the martensitic transformation in Co-doped Ni$_2$MnGa

Martensitic transformations are strain driven displacive transitions governing the mechanical and physical properties in intermetallic materials. This is the case in Ni$_2$MnGa, where the martensite transition is at the heart of the striking magnetic shape memory and magneto-caloric properties. Interestingly, the martensitic transformation is preceded by a pre-martensite phase, and the role of this precursor and its influence on the martensitic transition and properties is still a matter of debate. In this work, we report on the influence of Co doping (Ni$_{50-x}$Co$_x$Mn$_{25}$Ga$_{25}$ with x = 3 and 5) on the martensitic transformation path in stoichiometric Ni$_2$MnGa by neutron diffraction. The use of the superspace formalism to describe the crystal structure of the modulated martensitic phases, joined with a group theoretical analysis allows unfolding the different distortions featuring the structural transitions. Finally, a general Landau thermodynamic potential of the martensitic transformation, based on the symmetry analysis is outlined. The combined use of phenomenological and crystallographic studies highlights the close relationship between the lattice distortions at the core of the Ni$_2$MnGa physical properties and, more in general, on the properties of the martensitic transformations in the Ni-Mn based Heusler systems.