Modelling & Simulation
Simultaneous sampling of atomic and magnetic degrees of freedom in iron using bond-order potentials
Martin Staadt, ICAMS, Ruhr-Universität Bochum, Bochum, Germany
Magnetism plays a key role in the description of iron at all temperatures. The body-centered cubic (bcc) phase of iron at room temperature is stabilized by magnetism. With increasing temperature, iron undergoes a transition from a ferromagnetic to a paramagnetic state, a structural transition from bcc to face-centered cubic and another structural transition back to bcc before it finally melts. It is known from experiments that magnon-phonon coupling is important for both structural and magnetic transitions in iron. Up to now, simulations of iron often lag a proper treatment of paramagnetism and of the interplay between atomic and magnetic degrees of freedom which are often described by separate models.
We use bond-order potentials to sample atomic and magnetic degrees of freedom, simultaneously using a unified description. This includes a non-collinear description of the spins. With a Metropolis Monte Carlo sampling algorithm, we sample atomic displacements and electronic degrees of freedom including spin directions and magnitudes to obtain reliable ensemble averages. The fast and efficient algorithm allows us to sample large systems that are necessary to accurately model paramagnetism and includes an explicit treatment of the electronic structure.
With our approach, we sample the bcc phase of iron in the isothermal-isobaric ensemble in a temperature range from 100K to 1600K. Monitoring the spin ordering, we correctly observe the transition from the ferromagnetic state at low temperatures to the paramagnetic state at high temperatures. We calculate the magnetization at different temperatures and accurately predict the Curie temperature. The heat capacity shows a peak at the Curie temperature indicating the second-order phase transition.
Our approach provides excellent qualitative agreement with experimental observations of magnetic properties of iron.