Linewidth and Dispersion of the Virtual Magnon Surface State in Thick Ferromagnetic Films

The magnetostatic surface state in thick ferromagnetic films with an applied magnetic field $H$ parallel to the surface is shown to be a virtual surface state when both exchange and dipolar interactions are included. Simple expressions for the frequency as a function of the wave vector parallel to the surface $\Omega \left(k_y\right)$ and the effective linewidth $\Delta H$ (due to decay into bulk magnons) of the virtual surface state are calculated by power-series expansion of the exact eigenvalue equation. The width $\Delta H$ increases with increasing applied field $H$ and is proportional to $k_y^3$. For an yttrium iron garnet film with $H$ on the order of ${10}^3$Oe, $\Delta H\lesssim 40$ Oe for $k_y\le {10}^5$ ${\mathrm{cm}}^{-1\mathrm{}}$. For $k_y\sim {10}^6$ ${\mathrm{cm}}^{-1\mathrm{}}$, $\Delta H$ becomes too large to employ the employ the virtual-state concept and no well-defined surface state exists.