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Title: Large-scale simulation of the spin-lattice dynamics in ferromagnetic iron
Authors: Ma, PW
Woo, CH 
Dudarev, SL
Keywords: Curie temperature
Ferromagnetic materials
Heisenberg model
Magnetic domain walls
Spin dynamics
Spin fluctuations
Spin-lattice relaxation
Thermal expansion
Issue Date: 1-Jul-2008
Publisher: American Physical Society
Source: Physical review. B, Condensed matter and materials physics, 1 July 2008, v. 78, no. 2, 024434, p. 1-12 How to cite?
Journal: Physical review. B, Condensed matter and materials physics 
Abstract: 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.
ISSN: 1098-0121
EISSN: 1550-235X
DOI: 10.1103/PhysRevB.78.024434
Rights: Physical Review B © 2008 The American Physical Society. The Journal's web site is located at
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