VARIATIONAL PRINCIPLE IN SPIN-WAVE THEORY . APPLICATION TO 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 kc that depends strongly on the direction of propagation. For k>kc, we find no surface-mode solutions. The properties of the new lower branch are discussed in detail. © 1969 The American Physical Society.