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Journal ArticleDOI

Langevin-dynamics study of the dynamical properties of small magnetic particles

J. L. García-Palacios, +1 more
- 01 Dec 1998 - 
- Vol. 58, Iss: 22, pp 14937-14958
TLDR
In this paper, the Langevin-dynamics approach was used to study the dynamics of magnetic nanoparticles, and the results were compared with different analytical expressions used to model the relaxation of nanoparticle ensembles, assessing their accuracy.
Abstract
The stochastic Landau-Lifshitz-Gilbert equation of motion for a classical magnetic moment is numerically solved (properly observing the customary interpretation of it as a Stratonovich stochastic differential equation), in order to study the dynamics of magnetic nanoparticles. The corresponding Langevin-dynamics approach allows for the study of the fluctuating trajectories of individual magnetic moments, where we have encountered remarkable phenomena in the overbarrier rotation process, such as crossing-back or multiple crossing of the potential barrier, rooted in the gyromagnetic nature of the system. Concerning averaged quantities, we study the linear dynamic response of the archetypal ensemble of noninteracting classical magnetic moments with axially symmetric magnetic anisotropy. The results are compared with different analytical expressions used to model the relaxation of nanoparticle ensembles, assessing their accuracy. It has been found that, among a number of heuristic expressions for the linear dynamic susceptibility, only the simple formula proposed by Shliomis and Stepanov matches the coarse features of the susceptibility reasonably. By comparing the numerical results with the asymptotic formula of Storonkin {Sov. Phys. Crystallogr. 30, 489 (1985) [Kristallografiya 30, 841 (1985)]}, the effects of the intra-potential-well relaxation modes on the low-temperature longitudinal dynamic response have been assessed, showing their relatively small reflection in the susceptibility curves but their dramatic influence on the phase shifts. Comparison of the numerical results with the exact zero-damping expression for the transverse susceptibility by Garanin, Ishchenko, and Panina {Theor. Math. Phys. (USSR) 82, 169 (1990) [Teor. Mat. Fiz. 82, 242 (1990)]}, reveals a sizable contribution of the spread of the precession frequencies of the magnetic moment in the anisotropy field to the dynamic response at intermediate-to-high temperatures.

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Citations
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Micromagnetic Simulation of Dynamic and Thermal Effects

TL;DR: In this paper, the authors used finite element micromagnetics to characterize the magnetization reversal mechanism of magnetic nanostructures and showed that the energy barrier for thermally activated switching decreases with decreasing particle volume, and thermal effects become important and may influence the switching time.
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Bayesian framework for modeling diffusion processes with nonlinear drift based on nonlinear and incomplete observations

TL;DR: A general Bayesian framework is proposed to model diffusion processes with nonlinear drift based on incomplete observations as generated by various types of experiments, and it is shown that trajectories, potentials, and diffusion constants can be efficiently and reliably estimated even in cases with little statistics or nonequilibrium measurement conditions.
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Noncollinear antiferromagnetic states in Ru-based Heusler compounds induced by biquadratic coupling

TL;DR: In this article, the authors derived the interatomic isotropic bilinear and biquadratic couplings between Mn atoms from the paramagnetic state, and showed that the frustrated coupling leads to non-collinear magnetic ground states in the compounds.
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Influence of field orientation on the magnetization dynamics of nanoparticles

TL;DR: Using the finite-temperature Landau-Lifshitz-Gilbert equation, this paper investigated the magnetization dynamics and its control of a monodomain ferromagnetic nanoparticle subjected to short magnetic-field pulses.
Journal ArticleDOI

Computational micromagnetics:: prediction of time dependent and thermal properties

TL;DR: In this paper, a finite element/boundary element micro-magnetics solver that combines a wavelet-based matrix compression technique for magnetostatic field calculations with a BDF/GMRES method for the time integration of the Gilbert equation of motion is presented.
References
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Book

Stochastic processes in physics and chemistry

TL;DR: In this article, the authors introduce the Fokker-planck equation, the Langevin approach, and the diffusion type of the master equation, as well as the statistics of jump events.

Stochastic Processes in Physics and Chemistry

Abstract: Preface to the first edition. Preface to the second edition. Abbreviated references. I. Stochastic variables. II. Random events. III. Stochastic processes. IV. Markov processes. V. The master equation. VI. One-step processes. VII. Chemical reactions. VIII. The Fokker-Planck equation. IX. The Langevin approach. X. The expansion of the master equation. XI. The diffusion type. XII. First-passage problems. XIII. Unstable systems. XIV. Fluctuations in continuous systems. XV. The statistics of jump events. XVI. Stochastic differential equations. XVII. Stochastic behavior of quantum systems.
Book

Numerical Solution of Stochastic Differential Equations

TL;DR: In this article, a time-discrete approximation of deterministic Differential Equations is proposed for the stochastic calculus, based on Strong Taylor Expansions and Strong Taylor Approximations.
Book

The Fokker-Planck equation

Hannes Risken