Spin Waves pp 203-222 | Cite as

Variational Formulation for Magnetostatic Modes

  • Daniel D Stancil
  • Anil Prabhakar

In Chapter 5, we solved for the magnetostatic modes in a variety of geometries. These geometries were characterized by simple boundary shapes, uniform bias fields, and uniform materials. In some cases, however, material and field non-uniformities may be needed to control the dispersion or to guide and localize the magnetostatic mode energy. In other cases, the effects of undesired inhomogeneities need to be assessed. Such problems are not easily attacked by the classical boundary value techniques used in Chapter 5. Consequently, this chapter is devoted to a variational approach capable of treating arbitrary inhomogeneities in a relatively simple and elegant way.


Variational Formulation Ground Plane Lagrangian Density Volume Wave Natural Boundary Condition 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    W. F. Brown Jr., Micromagnetics, ser. Interscience Tracts on Physics and Astronomy. New York: Interscience Publishers, 1963, vol. 18.Google Scholar
  2. [2]
    D. D. Stancil, ‘‘Variational formulation of magnetostatic wave dispersion relations,’ IEEE Trans. Magn., vol. 19, p. 1865, 1983.CrossRefGoogle Scholar
  3. [3]
    N. E. Buris and D. D. Stancil, ‘‘Magnetostatic surface-wave propagation in ferrite thin films with arbitrary variations of the magnetization through the film thickness,’ IEEE Trans. Microwave Theory Tech., vol. MTT-33, p. 484, 1985.CrossRefGoogle Scholar
  4. [4]
    N. E. Buris and D. D. Stancil, ‘‘Magnetostatic volume modes of ferrite thin films with magnetization inhomogeneities through the film thickness,’ IEEE Trans. Microwave Theory Tech., vol. MTT-33, p. 1089, 1985.CrossRefGoogle Scholar
  5. [5]
    N. E. Buris and D. D. Stancil, ‘‘Magnetostatic backward waves in low dose ion implanted YIG films,’ IEEE Trans. Magn., vol. 22, p. 859, 1986.CrossRefGoogle Scholar
  6. [6]
    M. Tsutsumi, Y. Masaoka, T. Ohira, and N. Kumagai, ‘A new technique for magnetostatic wave delay lines,’ IEEE Trans. Microwave Theory Tech., vol. 29, p. 583, 1981.CrossRefGoogle Scholar
  7. [7]
    E. Sawado and N. S. Chang, ‘Variational approach to analysis of propagation of magnetostatic waves in highly inhomogeneously magnetized media,’ J. Appl. Phys., vol. 55, p. 1062, 1984.CrossRefGoogle Scholar
  8. [8]
    J. Matthews and R. L. Walker, Mathematical Methods of Physics. Menlo Park, CA: W. A. Benjamin Inc., 1970.Google Scholar
  9. [9]
    H. Goldstein, C. P. Poole, and J. L. Safko, Classical Mechanics, 3rd ed. Cambridge, MA: Addison-Wesley, 2001.Google Scholar
  10. [10]
    D. A. Fishman and F. R. Morgenthaler, ‘Investigation of the velocity of energy circulation of magnetostatic modes in ferrites,’ J. Appl. Phys., vol. 54, p. 3387, 1983.CrossRefGoogle Scholar
  11. [11]
    F. R. Morgenthaler, ‘Dynamic magnetoelastic coupling in ferromagnets and antiferromagnets,’ IEEE Trans. Magn., vol. 8, p. 130, 1972.CrossRefGoogle Scholar
  12. [12]
    F. R. Morgenthaler, ‘Control of magnetostatic waves in thin films by means of spatially nonuniform bias fields,’ Circ. Syst. Signal Pr., vol. 4, p. 63, 1985.MATHCrossRefGoogle Scholar
  13. [13]
    R. Courant, ‘Variational methods for the solution of problems of equilibrium and vibrations,’ Bull. Amer. Math. Soc., vol. 49, p. 123, 1943.CrossRefMathSciNetGoogle Scholar
  14. [14]
    Y. Long, M. Koshiba, and M. Suzuki, ‘Finite-element solution of planar inhomogeneous waveguides for magnetostatic waves,’ IEEE Trans. Microwave Theory Tech., vol. 35, p. 731, 1987.CrossRefGoogle Scholar
  15. [15]
    M. Koshiba and Y. Long, ‘Finite-element analysis of magnetostatic wave propagation in a YIG film of finite dimensions,’ IEEE Trans. Microwave Theory Tech., vol. 37, p. 1768, 1989.CrossRefGoogle Scholar
  16. [16]
    T. Ueda, Y. Ueda, H. Shimasaki, and M. Tsutsumi, ‘Numerical analysis of nonlinear magnetostatic wave propagation by finite-element method,’ IEEE Trans. Mag., vol. 39, pp. 3157–3159, 2003.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Carnegie Mellon UniversityPittsburghUSA
  2. 2.Indian Institute of TechnologyChennaiIndia

Personalised recommendations