Susceptibility and surface magnetostatic modes for the spiral and cone states of rare-earth magnets

Spiral states (in which the equilibrium spin vector rotates uniformly at right angles to a helical axis) and cone states (in which the spin vector rotates at an angle θ≠90° to the helical axis) are observed in various rare-earth magnets within some temperature interval. The spin-wave spectrum ω(k) is rederived, and the magnetic-susceptibility tensor is found, for the cone state; expressions for the spiral state are given as special cases. In the cone state, the susceptibility tensor has a gyromagnetic form, and has poles at the spin-wave frequencies ω(±${\mathbf{k}}_0$), where ${\mathbf{k}}_0$ is the wave vector of the equilibrium helix; in the spiral state, the susceptibility tensor is diagonal, with a single pole at ω(${\mathbf{k}}_0$), since the frequencies ω(±${\mathbf{k}}_0$) are degenerate in the spiral. The results are applied to a calculation of the magnetostatic-surface-mode spectrum for the geometry in which the helical axis lies in the surface. In the cone state, propagation is nonreciprocal, but due to the existence of two poles, two surface-mode branches occur, with different ranges of allowed propagation directions; in the spiral state, propagation is reciprocal. The implications of the results for Brillouin scattering and attenuated total reflection are discussed, and a wide range of possible extensions of the calculations is outlined.