Finite element solution of the Fokker–Planck equation for single domain particles

The Fokker–Planck equation derived by Brown for the probability density function of the orientation of the magnetic moment of single domain particles is one of the basic equations in the theory of superparamagnetism. Brown’s equation has an analytical solution, which is represented as a series in sp...

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Vydané v:Physica. B, Condensed matter Ročník 599; s. 412535
Hlavný autor: Peskov, N.V.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 15.12.2020
Elsevier BV
Predmet:
Algorithms
Anisotropy
Exact solutions
Finite element method
Finite element solution
Fokker-Planck equation
Magnetic anisotropy
Magnetic domains
Magnetic fields
Magnetic moments
Magnetism
Probability density functions
Single domain particles
Spherical harmonics
Temperature
Temperature dependence
Time dependence
Fokker–Planck equation
Finite element solution
Single domain particles
ISSN:0921-4526, 1873-2135
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Shrnutí:The Fokker–Planck equation derived by Brown for the probability density function of the orientation of the magnetic moment of single domain particles is one of the basic equations in the theory of superparamagnetism. Brown’s equation has an analytical solution, which is represented as a series in spherical harmonics with time-dependent coefficients. This analytical solution is commonly used when studying problems related to Brown’s equation. However, for particles with complex magnetic anisotropy, calculating the coefficients of the analytical solution can be a rather difficult task. In this paper, we propose an algorithm for the numerical solution of Brown’s equation based on the finite element method. The algorithm allows numerically solving Brown’s equation for particles with anisotropy of a fairly general form for constant and variable magnetic fields and with time-dependent temperature and other model parameters. In particular, an example of the numerical solution of an equation for particles with cubic anisotropy accounting two anisotropy constants and variable temperature is presented. •The Fokker–Planck equation is solved numerically using FEM.•The efficient way to create a triangular grid on the sphere surface is described.•Numerical examples regarded to magnetization and demagnetization under heating are presented.
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content type line 14
ISSN:0921-4526
1873-2135
DOI:10.1016/j.physb.2020.412535