Numerical solution of Fokker-Planck equation for single domain particles

The Fokker-Planck equation proposed by Brown to describe the evolution of the probability distribution density of the orientation of the magnetic moment of a single-domain particle is usually solved by expanding the unknown function in a series of spherical harmonics. In this paper, we use a differe...

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Bibliographic Details
Published in:Physica. B, Condensed matter Condensed matter, 2019-10, Vol.571, p.142-148
Main Authors: Peskov, N.V., Semendyaeva, N.L.
Format: Article
Language:English
Subjects:
Anisotropy
Density
Dynamic hysteresis
Finite element method
Finite element solution
Fokker-Planck equation
Harmonic analysis
Hysteresis
Magnetic moments
Magnetism
Numerical analysis
Probability distribution
Single domain particles
Spherical harmonics
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Summary:The Fokker-Planck equation proposed by Brown to describe the evolution of the probability distribution density of the orientation of the magnetic moment of a single-domain particle is usually solved by expanding the unknown function in a series of spherical harmonics. In this paper, we use a different method to solve the Fokker-Planck equation, namely, the finite element method. We describe the procedure for constructing a triangular grid on the surface of a sphere and give formulas for calculating the coefficients of the equations for the probability density values at the grid nodes. As an example, the results of calculating the dynamic magnetic hysteresis for particles with cubic anisotropy are demonstrated. •The numerical solution of Brown's Fokker-Planck equation is obtained by the finite element method.•FEM implementation details are described.•The dynamic magnetic hysteresis of particles with cubic anisotropy is calculated by solving the Fokker-Planck equation.
ISSN:0921-4526
1873-2135
DOI:10.1016/j.physb.2019.07.004