# Energetics and switching of quasi-uniform states in small ferromagnetic particles

François Alouges; Sergio Conti; Antonio DeSimone; Yvo Pokern

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 38, Issue: 2, page 235-248
- ISSN: 0764-583X

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topAlouges, François, et al. "Energetics and switching of quasi-uniform states in small ferromagnetic particles." ESAIM: Mathematical Modelling and Numerical Analysis 38.2 (2010): 235-248. <http://eudml.org/doc/194212>.

@article{Alouges2010,

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.
},

author = {Alouges, François, Conti, Sergio, DeSimone, Antonio, Pokern, Yvo},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Micromagnetics; finite elements.; small ferromagnetic particles; micromagnetic equilibrium; flower-vortex transition; finite-element computations},

language = {eng},

month = {3},

number = {2},

pages = {235-248},

publisher = {EDP Sciences},

title = {Energetics and switching of quasi-uniform states in small ferromagnetic particles},

url = {http://eudml.org/doc/194212},

volume = {38},

year = {2010},

}

TY - JOUR

AU - Alouges, François

AU - Conti, Sergio

AU - DeSimone, Antonio

AU - Pokern, Yvo

TI - Energetics and switching of quasi-uniform states in small ferromagnetic particles

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 38

IS - 2

SP - 235

EP - 248

AB -
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.

LA - eng

KW - Micromagnetics; finite elements.; small ferromagnetic particles; micromagnetic equilibrium; flower-vortex transition; finite-element computations

UR - http://eudml.org/doc/194212

ER -

## References

top- 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. Zbl0886.35010
- F. Alouges, Computation of demagnetizing field in micromagnetics with the infinite elements method. ESAIM: COCV6 (2001) 629–647. Zbl0992.78007
- 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.
- W.F. Brown, Criterion for uniform micromagnetization. Phys. Rev.105 (1957) 1479–1482.
- 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. Zbl0685.58015
- A. DeSimone, Hysteresis and imperfection sensitivity in small ferromagnetic particles. Meccanica30 (1995) 591–603. Zbl0836.73060
- 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. Zbl0078.23307
- 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. Zbl0031.38003
- A. Thiaville, Coherent rotation of magnetization in three dimensions: a geometrical approach. Phys. Rev. B61 (2000) 12221.
- L.A. Ying, Infinite elements method. Beijing University Press (1995).

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