Variational Principle in Spin-Wave Theory: Application to the Theory of Magnetostatic Surface Waves

We have formulated a variational principle suitable for discussion of long-wavelength spin waves in ferromagnets. The form we discuss takes account of the fact that in the presence of magnetic dipole interactions an integral operator with a non-Hermitian kernel is encountered. We show that our form of the variational principle fully reproduces the bulk spin-wave dispersion relation and the magnetostatic surfacemode dispersion relation for a semi-infinite geometry, with magnetization parallel to the surface. We apply the variational principle to a discussion of the effect of exchange on the Damon-Eshbach magnetostatic surface modes. We find a new surface branch that lies between the bulk manifold and the Damon-Eshbach branch. The two branches intersect at a finite wave vector $k_c$ that depends strongly on the direction of propagation. For $k>\mathrm{}{k}_c$, we find no surface-mode solutions. The properties of the new lower branch are discussed in detail.