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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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Journal ArticleDOI

Effective Néel relaxation time constant and intrinsic dipolar magnetism in a multicore magnetic nanoparticle system

TL;DR: In this article, the frequency-dependent complex magnetic susceptibility of water-dispersed magnetic nanoclusters at very low field amplitude was evaluated by using spectroscopic susceptometry.

Atomistic spin dynamics and relativistic effects in chiral nanomagnets

TL;DR: In this paper, studies based on magnetization dynamics on atomic length scales are presented for a number of magnetic systems, where Dzyaloshinskii-Moriya (DM) interaction is present.
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Finite temperature micromagnetics and magnetic measurements of submicron patterned permalloy thin films

TL;DR: In this article, the second-order Heun scheme was used to predict the coercivity of submicron patterned permalloy thin films with simulation, which was shown to be adequate for this purpose.
Journal ArticleDOI

Langevin micromagnetics of recording media using subgrain discretization

TL;DR: In this paper, a finite element based micromagnetic magnetization was applied to study thermally assisted switching of thin film media in the high speed regime, where the space discretization leads to a system of stochastic differential equations with multiplicative noise, interpreted as Stratonovich and solved using the method of Heun.
Journal ArticleDOI

On the superparamagnetic size limit of nanoparticles on a ferroelectric substrate

TL;DR: In this article, the authors theoretically investigate how a magnetoelectric coupling to a ferroelectric substrate modifies the superparamagnetic limit, with a special focus on the possible realization of substantially smaller multiferroic clusters with thermally stable magnetization.
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.
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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.
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The Fokker-Planck equation

Hannes Risken