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Zbl 1085.82015
Alouges, François; Conti, Sergio; DeSimone, Antonio; Pokern, Yvo
Energetics and switching of quasi-uniform states in small ferromagnetic particles. (English)
[J] M2AN, Math. Model. Numer. Anal. 38, No. 2, 235-248 (2004). ISSN 0764-583X; ISSN 1290-3841/e

This paper presents a finite-element algorithm to solve the micromagnetic equations. Computing micromagnetic equilibria amounts to solving a non-local constrained minimization problem. The demagnetization field is computed on a homothetic-lower decomposition of a finite portion of the outer space, whose mesh is generated by scaling the surface mesh of body. The nonlinear update of the magnetization is obtained by minimization on the manifold tangent to the constraint. The computations estimate the deviations from the Stoner-Wohlfarth (SW) model for small particles, assuming uniform magnetization inside the particle. The algorithm used consists of a building of the magnetizations sequence satisfying the non-convex constraint. The iterative construction includes a computation of a descent direction and fulfillment of the magnetization update. \par As a first application of the numerical method, it is considered the Micromagnetic Standard Problem 3, estimating the size of a cube, at which the ground state changes from a quasi-uniform (flower) to a vortex state, in the presence of uniaxial anisotropy. Two cases are considered, namely the flower-vortex and the twisted flower-vortex transitions. The last is a modification of the symmetric flower breaking inversion symmetry with lower energy than the flower in the region of interest. As a second application, it is considered a switching of small particles. The numerical results for particles of cubic or almost-cubic shape within the single-domain regime illustrate the leading corrections to the SW model with increasing particle size. For small sizes critical fields reproduce the SW results. However, larger particles have shape-dependent critical fields with a non-monotone dependence on size and with a complex angular dependence, which cannot be reproduced assimilating the particle to an ellipsoid.
[I. A. Parinov (Rostov-na-Donu)]

MSC 2000:: *82D40 Magnetic materials
65N30 Finite numerical methods (BVP of PDE)
78M10 Finite element methods (optics)

Keywords: small ferromagnetic particles; micromagnetic equilibrium; flower-vortex transition; finite-element computations

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