Phase stability, ordering, and magnetism of single-phase fcc Fe-Au alloys

Motivated by experimental evidence of L1$_0$ ordering in single-phase fcc Fe-Au nanoparticles, we study the structural thermodynamics of Fe-Au alloys. First, separate cluster expansions for fcc and bcc lattices are constructed for fully optimized ferromagnetic structures using density functional theory calculations. The optimized structures were assigned to fcc or bcc lattice by a structural filter. Although the lowest formation enthalpy at 50\% Au is reached in the bcc lattice, the fcc lattice is preferred for the random alloy. Dynamical stability of specific orderings strongly depends on the magnetic configuration. To analyze the ordering tendencies of the fcc alloy, we restrict uniform lattice relaxations and separate the contributions of chemical interaction and local relaxations. By using the effective tetrahedron model (Ruban \emph{et al.}, Phys. Rev. B 67, 214302 (2003)) and explicit calculations for ordered and special quasi-random structures, we find that the local relaxation energies depend weakly on the magnetization. Although the L1$_0$ ordering is the ground state at 50\% Au on the ideal lattice, local relaxations make it unfavorable compared to the random alloy. Moderate compression due to the size effect tends to slightly stabilize the L1$_0$ ordering.