Million-atom molecular dynamics simulations of magnetic iron

Derlet, P. M.; Dudarev, S. L.

doi:10.1016/j.pmatsci.2006.10.011

Cited by 72 publications

(69 citation statements)

References 34 publications

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“…By explicitly incorporating a magnetic term in the functional form of the empirical many-body potential, Dudarev and Derlet [11][12][13] proposed the first magnetic potential for atomistic simulations at 0 K. The magnetic effect due to this potential stabilizes the dumbbell configuration so that the ground-state self-interstitial configuration in bcc iron is not the ͗111͘-crowdion but the ͗110͘-dumbbell, which is consistent with the ab initio calculations. 14,15 Recently, Ma et al 16,17 developed the spin-lattice dynamics ͑SLD͒ simulation scheme in which the coupled spin and lattice degrees of freedom are treated on equal footing in the equations of motion of the system.…”

Section: Introductionmentioning

confidence: 52%

Exchange interaction function for spin-lattice coupling in bcc iron

Wang

Woo

2010

Phys. Rev. B

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Functional representations of the spin polarization and the exchange interaction in terms of the lattice configuration is necessary to model the dynamics of the coupled spin and lattice subsystems in large-scale atomistic simulation of magnetic materials. Data needed for this purpose have only existed in the regime of small displacements from the equilibrium perfect lattice configurations. In this paper, we report and discuss the results of our first-principles calculations for bcc iron over a wide range of lattice constants using the magnetic force theorem and the one-electron Green's function. Despite the relatively complex functional form of the exchange interaction function for bcc iron our results show that it can be expressed as a superposition of Bethe-Slater-type curves representing interatomic exchange interaction of the 3d electrons.

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Section: Introductionmentioning

confidence: 52%

Exchange interaction function for spin-lattice coupling in bcc iron

Wang

Woo

2010

Phys. Rev. B

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“…where U DD is the "magnetic" embedded atom potential developed by Dudarev and Derlet [42,43], and E ground spin = − i<j J ij ({r k })|S i ||S j | is the energy contribution from a collinear spin state, subtracted out to eliminate the magnetic interaction energy that is implicitly contained in U DD . With the particular form of U ({r i }) given in Eq.…”

Section: Methodsmentioning

confidence: 99%

Collective dynamics in atomistic models with coupled translational and spin degrees of freedom

et al. 2017

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Using an atomistic model that simultaneously treats the dynamics of translational and spin degrees of freedom, we perform combined molecular and spin dynamics simulations to investigate the mutual influence of the phonons and magnons on their respective frequency spectra and lifetimes in ferromagnetic bcc iron. By calculating the Fourier transforms of the space-and time-displaced correlation functions, the characteristic frequencies and the linewidths of the vibrational and magnetic excitation modes were determined. Comparison of the results with that of the standalone molecular dynamics and spin dynamics simulations reveal that the dynamic interplay between the phonons and magnons leads to a shift in the respective frequency spectra and a decrease in the lifetimes. Moreover, in the presence of lattice vibrations, additional longitudinal magnetic excitations were observed with the same frequencies as the longitudinal phonons.

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“…Even in an MD simulation, magnetic interatomic potentials must include the interaction between neighboring spins, as discussed by Dudarev and Derlet 40,41 ͑DD͒ and by Ackland. 42 Nevertheless, the DD potential effectively treats magnetism as a 0 K phenomenon, assuming that the atomic spins are all aligned, and hence, the treatment of complex noncollinear spin configurations at a finite temperature remains outside its realm of applicability.…”

Section: B Molecular Dynamics For a Magnetic Materialsmentioning

confidence: 99%

“…The equations of motion for spins are derived from a generalized Heisenberg Hamiltonian where the exchange coupling function is fitted to the ab initio data and where the scalar part of the interatomic interaction is given by the magnetic DD potential. 40,41,43 These equations form the basis for the spin-lattice dynamics ͑SLD͒ algorithm. The SLD equations are integrated using the second-order Suzuki-Trotter decomposition ͑STD͒ ͑Refs.…”

Section: B Molecular Dynamics For a Magnetic Materialsmentioning

confidence: 99%

Large-scale simulation of the spin-lattice dynamics in ferromagnetic iron

2008

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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.

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Million-atom molecular dynamics simulations of magnetic iron

Cited by 72 publications

References 34 publications

Exchange interaction function for spin-lattice coupling in bcc iron

Exchange interaction function for spin-lattice coupling in bcc iron

Collective dynamics in atomistic models with coupled translational and spin degrees of freedom

Large-scale simulation of the spin-lattice dynamics in ferromagnetic iron

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