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Another Thin-Film Limit of Micromagnetics

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Abstract.

We consider the variational problem of micromagnetics for soft, relatively small thin films with no applied magnetic field. In terms of the film thickness t, the diameter l and the magnetic exchange length w, we study the asymptotic behavior in the small-aspect-ratio limit t/l→0, when either (a) w2/l2≫(t/l)| log (t/l)| or (b) w2/l2∼(t/l)| log (t/l)|. Our analysis builds on prior work by Gioia & James and Carbou. The limiting variational problem is much simpler than 3D micromagnetics; in particular it is two-dimensional and local, with no small parameters. The contribution of shape anisotropy reduces, in this limit, to a constant times the boundary integral of (m·n)2.

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References

  1. Aharoni, A.: Introduction to the Theory of Ferromagnetism. Oxford Univ. Press, 1996

  2. Aharoni, A.: Energy of one dimensional domain walls in ferromagnetic films. J. Appl. Phys. 37(8), 3271–3279 (1966)

    Article  Google Scholar 

  3. Alouges, F., Riviére, T., Serfaty, S.: Neel and cross-tie wall energies for planar micromagnetic configurations. ESAIM Control Optim. Calc. Var. 8, 31–68 (2002)

    Article  Google Scholar 

  4. Ammari, H., Halpern, L., Hamdache, K.: Asymptotic behavior of thin ferromagnetic films. Asymptotic Analysis 24, 277–294 (2000)

    Google Scholar 

  5. Carbou, G.: Thin layers in micromagnetism. Math. Models and Methods in Appl. Sciences 11, N9 1529–1546 (2001)

    Google Scholar 

  6. Cowburn, R.P., Adeyeye, A.O., Welland, M.E.: Configurational anisotropy in nanomagnets. Phys.Rev. Lett. 81, 5414–5417 (1999)

    Article  Google Scholar 

  7. DeSimone, A.: Hysteresis and imperfection sensitivity in small ferromagnetic particles. Meccanica 30, 591–603 (1995)

    Article  Google Scholar 

  8. DeSimone, A., Kohn, R.V., Müller, S., Otto, F.: A reduced theory for thin film micromagnetics. Comm. Pure Appl. Math. 55, 1408–1460 (2002)

    Article  Google Scholar 

  9. Garcia-Cervera, C.J.: One-dimensional magnetic domain walls. To appear in Euro. J. Appl. Math.

  10. Gioia, G., James, R.D.: Micromagnetics of very thin films. Proc. Roy. Soc. London A 453, 213–223 (1997)

    Google Scholar 

  11. Hubert, A., Schäfer, R.: Magnetic Domains: The Analysis of Magnetic Microstructures. Springer-Verlag, 1998

  12. Kurzke, M.: Boundary vortices in thin magnetic films. To appear in Calc. Var. Part. Diff. Equat.

  13. Kurzke, M.: A nonlocal singular perturbation problem with periodic well potential. MPI Preprint 106, (2003)

  14. Moser, R.: Boundary vortices for thin ferromagnetic films. Arch. Ration. Mech. Anal. 174, 267–300 (2004)

    Article  MathSciNet  Google Scholar 

  15. Moser, R.: Ginzburg-Landau vortices for thin ferromagnetic films. AMRX Appl. Math. Res. Express 1, 1–32 (2003)

    Article  Google Scholar 

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Authors and Affiliations

  1. Courant Institute, 251 Mercer Street, New York, NY, 10012

    Robert V. Kohn & Valeriy V. Slastikov

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  1. Robert V. Kohn
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  2. Valeriy V. Slastikov
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Correspondence to Robert V. Kohn.

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Communicated by F. Otto

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Kohn, R., Slastikov, V. Another Thin-Film Limit of Micromagnetics. Arch. Rational Mech. Anal. 178, 227–245 (2005). https://doi.org/10.1007/s00205-005-0372-7

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  • DOI: https://doi.org/10.1007/s00205-005-0372-7

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