Ab initiostudy of structural and magnetic properties of Si-dopedFe2P

Abstract

Ab initio electronic-structure methods are used to study the properties of ${\text{Fe}}_{2}{\text{P}}_{1\ensuremath{-}x}{\text{Si}}_{x}$ in ferromagnetic and paramagnetic states. The site preference and lattice relaxation are calculated with the projector augmented wave method as implemented in the Vienna ab initio simulation package. The paramagnetic state is modeled by the disordered local magnetic moment scheme, and the chemical and magnetic disorder is treated using the coherent potential approximation in combination with the exact muffin-tin orbital formalism. The calculated lattice parameters, atomic positions, and magnetic properties are in good agreement with the experimental and other theoretical results. In contrast to the observation, for the ferromagnetic state the body centered orthorhombic structure (bco, space group $I\underset{̱}{mm2}$) is predicted to have lower energy than the hexagonal structure (hex, space group $P\overline{6}2m$). The zero-point spin fluctuation energy difference is found to be large enough to stabilize the hex phase. For the paramagnetic state, the hex structure is calculated to be the stable phase and the computed total energy versus composition indicates a hex to bco crystallographic phase transition with increasing Si content. The phonon vibrational free energy, estimated from the theoretical equation of state, turns out to stabilize the hexagonal phase, whereas the electronic and magnetic entropies favor the low symmetry orthorhombic structure.