Dynamic simulation of structural phase transitions in magnetic iron

The occurrence of bcc-fcc ($\ensuremath{\alpha}\ensuremath{-}\ensuremath{\gamma}$) and fcc-bcc ($\ensuremath{\gamma}\ensuremath{-}\ensuremath{\delta}$) phase transitions in magnetic iron stems from the interplay between magnetic excitations and lattice vibrations. However, this fact has never been confirmed by a direct dynamic simulation, treating noncollinear magnetic fluctuations and dynamics of atoms, and their coupling at a finite temperature. Starting from a large set of data generated by ab initio simulations, we derive noncollinear magnetic many-body potentials for bcc and fcc iron, describing fluctuations of atomic coordinates in the vicinity of near perfect lattice positions. We then use spin-lattice dynamic simulations to evaluate the difference between the free energies of bcc and fcc phases, assessing their relative stability within a unified dynamic picture. We find two intersections between the bcc and fcc free energy curves, which correspond to the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\gamma}$ bcc-fcc and $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\delta}$ fcc-bcc phase transitions. The maximum bcc-fcc free energy difference over the temperature interval between the two phase transitions is 2 meV per atom, in agreement with other experimental and theoretical estimates.