Antiperovskite compounds have been attracting a lot of attention because of their unique and remarkable properties. Although antiperovskite metallic compounds Mn3XN (X = Ni, Pd, Pt) have been successfully prepared as potential magnetic materials, the structural, electronic, elastic and thermodynamic properties are still unclear. So, in this work, we apply the first-principles calculations to investigate the physical properties of Mn3XN. The results of formation enthalpy show that Mn3XN compounds are thermodynamically stable and follow the order of Mn3NiN > Mn3PdN > Mn3PtN. The results of band structure and density of states prove that all Mn3XN compounds are magnetic metals and the magnetism of Mn3XN comes mainly from the contribution of Mn atoms. The calculated bulk modulus and shear modulus of Mn3PtN are bigger than the Mn3PdN and Mn3NiN. Especially, we give the three-dimensional Young's modulus surface and the projection surface on different planes for three compounds. With respect to the anisotropic characteristics, Mn3PdN may be a potentially isotropic material and Mn3NiN has the most obvious anisotropy. The sound velocities of the three compounds in different directions are calculated to obtain the Debye temperature. The Debye temperatures of Mn3NiN, Mn3PdN, Mn3PtN are calculated to be 445 K, 423 K and 408 K, respectively. Importantly, the Debye temperature increases with the increasing of pressure and the decreasing of temperature. Finally, we give the critical pressure and charge density difference of three compounds.
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