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

Abstract

top
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.

How to cite

top

Alouges, 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
  1. A. Aharoni, Introduction to the theory of ferromagnetism. Oxford Ed., Clarendon Press (1996).  
  2. A. Aharoni, Angular dependence of nucleation by curling in a prolate spheroid. J. Appl. Phys. 82 (1997) 1281–1287.  
  3. F. Alouges, A new algorithm for computing liquid crystal stable configurations: the harmonic mapping case. SIAM J. Numer. Anal. 34 (1997) 1708–1726.  
  4. F. Alouges, Computation of demagnetizing field in micromagnetics with the infinite elements method. ESAIM: COCV6 (2001) 629–647.  
  5. 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.  
  6. G. Bertotti, Hysteresis in magnetism. Academic Press, San Diego (1998).  
  7. 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.  
  8. W.F. Brown, Criterion for uniform micromagnetization. Phys. Rev.105 (1957) 1479–1482.  
  9. 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.  
  10. W. Chen, D.R. Fredkin and T.R. Koehler, A new finite element method in micromagnetics. IEEE Trans. Magn. 29 (1993) 2124–2128.  
  11. Y.M. Chen, The weak solutions to the evolution problems of harmonic maps. Math. Z. 201 (1989) 69–74.  
  12. A. DeSimone, Hysteresis and imperfection sensitivity in small ferromagnetic particles. Meccanica30 (1995) 591–603.  
  13. D.R. Fredkin and T.R. Koehler, Finite element methods for micromagnetics. IEEE Trans. Magn. 28 (1992) 1239–1244.  
  14. E.H. Frei, S. Shtrikman and D. Treves, Critical size and nucleation field of ideal ferromagnetic particles. Phys. Rev. 106 (1957) 446–454.  
  15. 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.  
  16. A. Hubert and R. Schäfer, Magnetic domains. Springer, Berlin (1998).  
  17. Y. Ishii, Magnetization curling in an infinite cylinder with a uniaxial magnetocrystalline anisotropy. J. Appl. Phys. 70 (1991) 3765–3769.  
  18. R.D. McMichael, Standard problem number 3, problem specification and reported solutions, Micromagnetic Modeling Activity Group, www.crcms.nist.gov/~rdm/mumag.html (1998).  
  19. A.J. Newell and R.T. Merrill, The curling nucleation mode in a ferromagnetic cube. J. Appl. Phys. 84 (1998) 4394–4402.  
  20. 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.  
  21. W. Rave, K. Fabian and A. Hubert, Magnetic states of small cubic particles with uniaxial anisotropy. J. Magn. Magn. Mat. 190 (1998) 332–348.  
  22. 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).  
  23. M.E. Schabes and H.N. Bertram, Magnetization processes in ferromagnetic cubes. J. Appl. Phys. 64 (1988) 1347–1357.  
  24. 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.  
  25. A. Thiaville, Coherent rotation of magnetization in three dimensions: a geometrical approach. Phys. Rev. B61 (2000) 12221.  
  26. L.A. Ying, Infinite elements method. Beijing University Press (1995).  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.