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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Journal ArticleDOI
Magnetic field threshold for nucleation and depinning of domain walls in the neodymium permanent magnet Nd 2 Fe 14 B
TL;DR: Mohakud et al. as discussed by the authors investigated the difference in the nucleation and pinning fields between the Bloch and N\'eel DWs and found that the thermal fluctuation effect affects the threshold fields in the Nd magnet model more significantly than those in the simple anisotropic Heisenberg model.
Journal ArticleDOI
Fast switching behaviour of nanoscopic NiFe- and Co-elements
TL;DR: In this article, three-dimensional micromagnetic simulations were performed to study the magnetisation reversal processes of granular nanoelements using a hybrid finite element/boundary element model.
Journal ArticleDOI
Temperature dependence of spontaneous magnetization using a continuous model
TL;DR: In this article, the temperature dependence of spontaneous magnetization of a cubic nanoparticle of nickel has been studied and both a micromagnetic continuous and classical Heisenberg models have been used.
Journal ArticleDOI
Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution
TL;DR: In this paper, the authors studied the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution.
DissertationDOI
Circuit Simulation of All-Spin Logic
TL;DR: In this paper, an improved stochastic magnetization dynamics/time-dependent spin transport model based on a finite-difference scheme of both the temporal and spatial derivatives is proposed.
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.