Dipole-exchange modes in thin ferromagnetic films with strong out-of-plane anisotropies

Dipole-exchange modes are calculated for ultrathin ferromagnetic films with strong out-of-plane surface anisotropies large enough to force the magnetization out of plane. The direction of the magnetization is controlled by an in-plane static applied field. It is shown that dipolar-dominated spin-wave modes go soft for applied field strengths near where the magnetization begins to turn out of plane. For ultrathin films, however, the surface mode may contain a significant exchange energy that results in a nonzero minimum frequency at the applied field where the magnetization begins to turn out of plane. A potentially useful finding is a sensitive dependence of this minimum frequency on the exchange constant of the material.