Abstract
The problem of determining the interaction of spin waves in the presence of a domain wall is examined. The Hamiltonian for a ferromagnet with a uniaxial anisotropy is rewritten in terms of harmonic oscillators with the use of the Holstein-Primakoff transformations. In the continuum limit a nonrelativistic scalar field theory is obtained. The equation of motion in three spatial dimensions admits domain-wall solutions. The Hamiltonian is expanded about the classical solution and the quadratic terms are used to generate the spin-wave spectrum. The results are shown to be consistent with other methods. The space of states and propagators are exhibited, and the extension to the higher-order terms governing spin-wave interactions is discussed.
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