A functional calculus for the magnetization dynamics

Tranchida, Julien; Thibaudeau, Pascal; Nicolis, Stam

doi:10.48550/arxiv.1606.02137

Cited by 2 publications

(2 citation statements)

References 57 publications

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“…This methodology, which is special case of spin-lattice simulations, proved to be an efficient way to study many magnetic phenomena, such as ultrafast magnetization reversal [13], or the configuration of topological spin structures like skyrmions [14]. In addition, this approach can be used to obtain statistical averages over a large number of spins [15] to generate effective magnetization dynamics.…”

Section: Introductionmentioning

confidence: 99%

Massively parallel symplectic algorithm for coupled magnetic spin dynamics and molecular dynamics

Tranchida

Plimpton

Thibaudeau

et al. 2018

Journal of Computational Physics

107

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A parallel implementation of coupled spin-lattice dynamics in the LAMMPS molecular dynamics package is presented. The equations of motion for both spin only and coupled spin-lattice dynamics are first reviewed, including a detailed account of how magneto-mechanical potentials can be used to perform a proper coupling between spin and lattice degrees of freedom. A symplectic numerical integration algorithm is then presented which combines the Suzuki-Trotter decomposition for non-commuting variables and conserves the geometric properties of the equations of motion. The numerical accuracy of the serial implementation was assessed by verifying that it conserves the total energy and the norm of the total magnetization up to second order in the timestep size. Finally, a very general parallel algorithm is proposed that allows large spin-lattice systems to be efficiently simulated on large numbers of processors without degrading its mathematical accuracy. Its correctness as well as scaling efficiency were tested for realistic coupled spin-lattice systems, confirming that the new parallel algorithm is both accurate and efficient.

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Section: Introductionmentioning

confidence: 99%

Massively parallel symplectic algorithm for coupled magnetic spin dynamics and molecular dynamics

Tranchida

Plimpton

Thibaudeau

et al. 2018

Journal of Computational Physics

107

View full text Add to dashboard Cite

show abstract

“…In the most general situation, the functional derivatives δs i (t) δη j (t ′ ) can be calculated [26], and eq. ( 23) admits simplifications in the white noise limit.…”

Section: Additive Noisementioning

confidence: 99%

Nambu mechanics for stochastic magnetization dynamics

Thibaudeau

Nussle

2017

Journal of Magnetism and Magnetic Materials

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The Landau-Lifshitz-Gilbert (LLG) equation describes the dynamics of a damped magnetization vector that can be understood as a generalization of Larmor spin precession. The LLG equation cannot be deduced from the Hamiltonian framework, by introducing a coupling to a usual bath, but requires the introduction of additional constraints. It is shown that these constraints can be formulated elegantly and consistently in the framework of dissipative Nambu mechanics. This has many consequences for both the variational principle and for topological aspects of hidden symmetries that control conserved quantities. We particularly study how the damping terms of dissipative Nambu mechanics affect the consistent interaction of magnetic systems with stochastic reservoirs and derive a master equation for the magnetization. The proposals are supported by numerical studies using symplectic integrators that preserve the topological structure of Nambu equations. These results are compared to computations performed by direct sampling of the stochastic equations and by using closure assumptions for the moment equations, deduced from the master equation.

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A functional calculus for the magnetization dynamics

Cited by 2 publications

References 57 publications

Massively parallel symplectic algorithm for coupled magnetic spin dynamics and molecular dynamics

Massively parallel symplectic algorithm for coupled magnetic spin dynamics and molecular dynamics

Nambu mechanics for stochastic magnetization dynamics

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