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Energetics and switching of quasi-uniform statesin small ferromagnetic particles

Published online by Cambridge University Press:  15 March 2004

François Alouges ,
Sergio Conti ,
Antonio DeSimone  and
Yvo Pokern
François Alouges
Affiliation:
Laboratoire de Mathématique, Université d'Orsay, 91405 Orsay Cedex, France, and Centre de Mathématiques et de Leurs Applications, École Normale Supérieure de Cachan, 61 avenue du Président Wilson, 94235 Cachan Cedex, France, [email protected].
Sergio Conti
Affiliation:
Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany, [email protected].
Antonio DeSimone
Affiliation:
SISSA, International School for Advanced Studies, Via Beirut 2-4, 34014 Trieste, Italy, [email protected].
Yvo Pokern
Affiliation:
Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK.
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Abstract

We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size.

Keywords

Micromagneticsfinite elements.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 2 , March 2004 , pp. 235 - 248
Copyright
© EDP Sciences, SMAI, 2004

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References

A. Aharoni, Introduction to the theory of ferromagnetism. Oxford Ed., Clarendon Press (1996).
A. Aharoni, Angular dependence of nucleation by curling in a prolate spheroid. J. Appl. Phys. 82 (1997) 1281–1287.
F. Alouges, A new algorithm for computing liquid crystal stable configurations: the harmonic mapping case. SIAM J. Numer. Anal. 34 (1997) 1708–1726.
Alouges, F., Computation of demagnetizing field in micromagnetics with the infinite elements method. ESAIM: COCV 6 (2001) 629–647. CrossRef
A. Bagnérés-Viallix, P. Baras and J.B. Albertini, 2d and 3d calculations of micromagnetic wall structures using finite elements. IEEE Trans. Magn. 27 (1991) 3819–3822.
G. Bertotti, Hysteresis in magnetism. Academic Press, San Diego (1998).
E. Bonet, W. Wernsdorfer, B. Barbara, A. Benoît, D. Mailly and A. Thiaville, Three-dimensional magnetization reversal measurements in nanoparticles. Phys. Rev. Lett. 83 (1999) 4188–4191.
Brown, W.F., Criterion for uniform micromagnetization. Phys. Rev. 105 (1957) 1479–1482. CrossRef
T. Chang, J.-G. Zhu and J.H. Judy, Method for investigating the reversal properties of isolated barium ferrite fine particles utilizing magnetic force microscopy (mfm). J. Appl. Phys. 73 (1993) 6716–6718.
W. Chen, D.R. Fredkin and T.R. Koehler, A new finite element method in micromagnetics. IEEE Trans. Magn. 29 (1993) 2124–2128.
Y.M. Chen, The weak solutions to the evolution problems of harmonic maps. Math. Z. 201 (1989) 69–74.
DeSimone, A., Hysteresis and imperfection sensitivity in small ferromagnetic particles. Meccanica 30 (1995) 591–603. CrossRef
D.R. Fredkin and T.R. Koehler, Finite element methods for micromagnetics. IEEE Trans. Magn. 28 (1992) 1239–1244.
E.H. Frei, S. Shtrikman and D. Treves, Critical size and nucleation field of ideal ferromagnetic particles. Phys. Rev. 106 (1957) 446–454.
R. Hertel and H. Kronmüller, Finite element calculations on the single-domain limit of a ferromagnetic cube – a solution to µmag standard problem no. 3. J. Magn. Magn. Mat. 238 (2002) 185–199.
A. Hubert and R. Schäfer, Magnetic domains. Springer, Berlin (1998).
Y. Ishii, Magnetization curling in an infinite cylinder with a uniaxial magnetocrystalline anisotropy. J. Appl. Phys. 70 (1991) 3765–3769.
R.D. McMichael, Standard problem number 3, problem specification and reported solutions, Micromagnetic Modeling Activity Group, www.crcms.nist.gov/~rdm/mumag.html (1998).
A.J. Newell and R.T. Merrill, The curling nucleation mode in a ferromagnetic cube. J. Appl. Phys. 84 (1998) 4394–4402.
R. O'Barr, M. Lederman, S. Schultz, W. Xu, A. Scherer and R.J. Tonucci, Preparation and quantitative magnetic studies of single-domain nickel cylinders. J. Appl. Phys. 79 (1996) 5303–5305.
W. Rave, K. Fabian and A. Hubert, Magnetic states of small cubic particles with uniaxial anisotropy. J. Magn. Magn. Mat. 190 (1998) 332–348.
F. Rogier, S. Labbé and P.Y. Bertin, Schéma en temps et calcul du champ démagnétisant pour le micromagnétisme. NUMELEC'97, École Centrale de Lyon (1997).
M.E. Schabes and H.N. Bertram, Magnetization processes in ferromagnetic cubes. J. Appl. Phys. 64 (1988) 1347–1357.
E.C. Stoner and E.P. Wohlfarth, A mechanism of magnetic hysteresis in heterogeneous alloys. Phil. Trans. R. Soc. London Ser. A 240 (1948) 599–642.
Thiaville, A., Coherent rotation of magnetization in three dimensions: a geometrical approach. Phys. Rev. B 61 (2000) 12221. CrossRef
L.A. Ying, Infinite elements method. Beijing University Press (1995).