Magnetostatic energy of stripe domain patterns

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The energy of an array of straight stripe magnetic domains, such as might be found in an epitaxial garnet (bubble) film, is examined theoretically by modifying and extending the results of Kooy and Enz. For a uniform pattern, the energy is conveniently expanded in a Taylor series, using variables which describe the relative widths of the stripe domains. The coefficients in the expansion are familiar transcendental functions of material and sample parameters. An immediate result is an expression for the linear susceptibility (to an applied field normal to the film plane) in terms of the sample thickness and zero-field domain width. The energies for non-uniform patterns, which are interpreted in terms of dispersion curves for waves of displacements of rigid walls from the zero-field positions, are calculated using two approaches. The results of a lattice dynamics model, in which the restoring forces are related to the expansion coefficients, are compared to the results of a model which uses an extension of Kooy and Enz’s result to general periodic domain patterns. The significant differences are attributed to the more accurate treatment by the second calculation of the long-range magnetostatic forces.