We develop a dynamical simulation model for magnetic iron where atoms are treated as classical particles with intrinsic spins. The atoms interact via scalar many-body forces as well as via spin orientation dependent forces of the Heisenberg form. The coupling between the lattice and spin degrees of freedom is described by a coordinate-dependent exchange function where the spin orientation dependent forces are proportional to the gradient of this function. The spin-lattice dynamics simulation approach extends the existing magnetic potential treatment to the case where the energy of interaction between the atoms depends on the relative noncollinear orientations of spins. An algorithm for integrating the linked spin-coordinate equations of motion is based on the second-order Suzuki-Trotter decomposition for noncommuting operators of evolution for coordinate and spin variables. The notions of the spin thermostat and the spin temperature are introduced through the combined application of the Langevin spin dynamics and the fluctuation-dissipation theorem. We investigate several applications of the method, performing microcanonical ensemble simulations of adiabatic spin-lattice relaxation of periodic arrays of 180°domain walls, and isothermal-isobaric ensemble dynamical simulations of thermally equilibrated homogeneous systems at various temperatures. The predicted isothermal magnetization curve agrees well with the experimental data for a broad range of temperatures. The equilibrium as well as time-correlation functions of spin orientations exhibit the presence of short-range magnetic order above the Curie temperature. Furthermore, short-range order spin fluctuations are shown to contribute to the thermal expansion of the material. Our analysis illustrates the significant part played by the spin degrees of freedom in the dynamics of motion of atoms in magnetic iron and iron-based alloys. It also shows that the spin-lattice dynamics algorithm developed in this paper offers a viable way of performing large-scale dynamical atomistic simulations of magnetic materials.

We systematically investigated the structure, electronic properties, zone-center phonon modes, and structure instability of four cubic perovskite BiMO 3 compounds, with three of the M ions being IIIB metals ͑Al, Ga, and In͒ and one IIIA transition-metal Sc, using first-principles density-functional calculations. Optimized lattice parameters, bulk moduli, band structures, densities of states, as well as charge density distributions are calculated and compared with the available theoretical data. Our results are in good agreement with those previously reported in the literature. All the BiMO 3 oxides considered in the present work are semiconductors with an indirect band gap between the occupied O 2p and unoccupied Bi 6p states varying between 0.17 and 1.57 eV. Their electronic properties are determined mainly by Bi-O bonding, which, in turn, depends on the M -O bonding. Ferroelectric properties of these oxides come from the 6s 2 lone pair on the A-site Bi ion and is similarly affected by the M ions through their influence on the Bi-O bonding, as suggested by our calculations of density of state, Born effective charge, and soft modes. The existence of soft modes and eight ͓111͔ minima suggests that the phase transition in BiAlO 3 has a mixed displacive and order-disorder character. There is evidence that ferroelectricity is absent in BiGaO 3 . Our investigation suggests that the BiMO 3 oxides or their modified versions are promising ferroelectric, piezoelectric, multiferroic, and photocatalytic materials.

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