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Inertia effects in magnetization dynamics are theoretically shown to resultin a different type of spin waves, i.e. nutation surface spin waves, whichpropagate at terahertz frequencies in in-plane magnetized ferromagnetic thinfilms. Considering the magnetostatic limit, i.e. neglecting exchange coupling,we calculate dispersion relation and group velocity, which we find to be slowerthan the velocity of conventional (precession) spin waves. In addition, we findthat the nutation surface spin waves are backward spin waves. Furthermore, weshow that inertia causes a decrease of the frequency of the precession spinwaves, namely magnetostatic surface spin waves and backward volumemagnetostatic spin waves. The magnitude of the decrease depends on the magneticproperties of the film and its geometry.

Dispersion relation of nutation surface spin waves in ferromagnets