Finite Element Micromagnetics

  • Thomas Schrefl
  • Dieter Suess
  • Werner Scholz
  • Hermann Forster
  • Vassilios Tsiantos
  • Josef Fidler
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 28)


The development of advanced magnetic materials such as magnetic sensors, recording heads, and magneto-mechanic devices requires a precise understanding of the magnetic behavior. As the size of the magnetic components approach the nanometer regime, detailed predictions of the magnetic properties becomes possible using micromagnetic simulations. Micromagnetics combines Maxwell’s equations for the magnetic field with an equation of motion describing the time evolution of the magnetization. The local arrangement of the magnetic moments follows from the complex interaction between intrinsic magnetic properties such as the magnetocrystalline anisotropy and the physical/chemical microstructure of the material.

This paper reviews the basic numerical methods used in finite element micromagnetic simulations and presents numerical examples in the field of soft magnetic sensor elements, polycrystalline thin film elements, and magnetic nanowires.


Domain Wall Finite Element Mesh Magnetic Body Magnetostatic Interaction Domain Wall Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Aharoni A. (1996) Introduction to the Theory of Ferromagnetism. Oxford University Press, New YorkGoogle Scholar
  2. 2.
    Dahlberg, E. D., Zhu, J. G. (1995) Micromagnetic Microscopy and Modeling. Physics Today 48, 34–40CrossRefGoogle Scholar
  3. 3.
    Schabes, M. E., Fullerton, E. E., Margulies, D. T. (2001) Theory of Antiferromagnetically Coupled Magnetic Recording Media. J. Appl. Phys., in pressGoogle Scholar
  4. 4.
    Johnson, M. (2000) Magnetoelectronic memories last and last …. IEEE Spectrum 37, 33–40CrossRefGoogle Scholar
  5. 5.
    Brown Jr., W. F. (1963) Micromagnetics, Interscience, New YorkGoogle Scholar
  6. 6.
    Kinderlehrer, D., Ma, L. (1994) Computational Hysteresis in Modeling Magnetic Systems. IEEE Trans. Magn. 30, 4380–4382CrossRefGoogle Scholar
  7. 7.
    He L., Doyle W. D. et al. (1996) High-speed switching in magnetic recording media. J. Magn. Magn. Mat. 155, 6–12CrossRefGoogle Scholar
  8. 8.
    Akagi F., Nakamura A. et al. (2000) Computer Simulation of Magnetization Switching Behavior in High-Data-Rate Hard-Disk Media Masukazu Igarashi, IEEE. Trans. Magn. 36, 154–158CrossRefGoogle Scholar
  9. 9.
    Harrell, R. W. (2001) Orientation dependence of the dynamic coercivity of Stoner-Wohlfarth particles. IEEE Trans. Magn. 37, 533–537CrossRefGoogle Scholar
  10. 10.
    Gilbert, T. L. (1955) A Lagrangian formulation of gyromagnetic equation of the magnetization field, Phys. Rev. 100, 1243Google Scholar
  11. 11.
    Chen, Q., Konrad, A. (1997) A review of finite element open boundary techniques for static and quasi-static electromagnetic field problems. IEEE Trans. Magn. 33, 663–676CrossRefGoogle Scholar
  12. 12.
    Fredkin, D. R., Koehler, T. R. (1990) Hybrid method for computing demagnetizing fields. IEEE Trans. Magn. 26, 415–417CrossRefGoogle Scholar
  13. 13.
    Bruaset, A. M. (1997) Krylov subspace iterations for sparse linear systems. In: Morten Daehlen, M., Tveito, A. (Eds.) Numerical Meth and Software Tools in Industrial Mathematics. Birkhauser, Boston, 21 Google Scholar
  14. 14.
    Gadbois, J., and Zhu, J. G. (1995) Effect of Edge Roughness in Nano-Scale Magnetic Bar Switching. IEEE Trans. Magn. 31, 3802–3804CrossRefGoogle Scholar
  15. 15.
    Toussaint, J. C., Kevorkian, B., Givord, D., and Rossignol, M. F. (1996) Micromagnetic Modeling of Magnetization Reversal in Permanent Magnets. In: Proceedings of the 9th International Symposium Magnetic Anisotropy and Coercivity In Rare-Earth Transition Metal Alloys, World Scientific, Singapore, 59–68Google Scholar
  16. 16.
    Yang, B., Fredkin, D.R. (1998) Dynamical micromagnetics by the finite element method. IEEE Trans. Magn. 34, 3842–3852CrossRefGoogle Scholar
  17. 17.
    Cohen, S. D., and Hindmarsh, A. C. (1996) CVODE, A Stiff/Nonstiff ODE Solver in C. Computers in Physics, 10 138–143.Google Scholar
  18. 18.
    Saad, Y. (1996) Iterative methods for sparse linear systems, PWS Publishing Company, BostonzbMATHGoogle Scholar
  19. 19.
    Kirk, K. J., Chapman, J. N., Wilkinson, C. D. W. (1997) Switching fields and magnetostatic interactions of thin film magnetic nanoelements. Appl. Phys. Lett. 71, 539–541CrossRefGoogle Scholar
  20. 20.
    Rave, W., Ramstock, K., Hubert, A. (1998) Corners and Nucleation in Micromagnetics. J. Magn. Magn. Mater. 183, 329–333CrossRefGoogle Scholar
  21. 21.
    Hertel, R., Kronmuller, H. (1998) Adaptive finite element mesh refinement techniques in three-dimensional micromagnetic modeling. IEEE Trans. Magn. 34, 3922–3930CrossRefGoogle Scholar
  22. 22.
    Schrefl T., Forster H. et al. (2001) Micromagnetic Simulation of Switching Events, In: Kramer, B. (Ed.) Advances in Solid State Physics 41. Springer, Berlin Heidelberg, 623–635CrossRefGoogle Scholar
  23. 23.
    Cowburn, R. P., Welland, M. E. (2000) Room temperature magnetic quantum cellular automata, Science 287, 1466–1468CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Thomas Schrefl
    • 1
  • Dieter Suess
    • 1
  • Werner Scholz
    • 1
  • Hermann Forster
    • 1
  • Vassilios Tsiantos
    • 1
  • Josef Fidler
    • 1
  1. 1.Institute of Applied and Technical PhysicsVienna University of TechnologyViennaAustria

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