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Abstract

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 (fcc) 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 and the fcc phase of iron in the isothermal-isobaric ensemble in a temperature range from 100K to 2000K. Monitoring the spin ordering, we correctly observe the transition from the ferromagnetic state at low temperatures to the paramagnetic state at high temperatures in bcc and extract the Curie temperature. Additionally, we investigate the influence of a single vacancy on the magnetization of the bcc phase.