Journal ArticleDOI
Langevin-dynamics study of the dynamical properties of small magnetic particles
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.read more
Citations
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Colossal spin transfer torque effect on skyrmion along the edge.
TL;DR: By the micromagnetic simulations the skyrmion motion along the edge driven by the current transverse to it is studied and it is found that the velocity is enhanced by the factor of ∼ 1/α (α: the Gilbert damping) with the maximum value determined only by the confining force from the edge.
Journal ArticleDOI
Low frequency hysteresis loops of superparamagnetic nanoparticles with uniaxial anisotropy
TL;DR: In this article, the low frequency hysteresis loops of superparamagnetic nanoparticles with uniaxial anisotropy are calculated as a function of the particle diameter, alternating magnetic field amplitude H 0, frequency, and particle magnetic parameters both for oriented and nonoriented assemblies.
Journal ArticleDOI
Fast micromagnetic simulations on GPU—recent advances made with $\mathsf{mumax}^3$
Jonathan Leliaert,Mykola Dvornik,Jeroen Mulkers,J. De Clercq,Milorad V. Milošević,B. Van Waeyenberge +5 more
TL;DR: This topical review of micromagnetic modeling gives an overview of this modeling approach and shows how it has contributed to the forefront of current magnetism research.
Journal ArticleDOI
Memory functions of magnetic skyrmions
Wataru Koshibae,Yoshio Kaneko,Junichi Iwasaki,Masashi Kawasaki,Masashi Kawasaki,Yoshinori Tokura,Yoshinori Tokura,Naoto Nagaosa,Naoto Nagaosa +8 more
TL;DR: In this paper, the elementary functions of skyrmions are demonstrated aiming at the design principles of SKyrmionic memory devices by numerical simulations of the Landau-Lifshitz-Gilbert equation, and they are shown to be advantageous for high-density data storage, nonvolatile memory, and ultra-low current and energy cost manipulation.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
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
Peter E. Kloeden,Eckhard Platen +1 more
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.