Inertial terms to magnetization dynamics in ferromagnetic thin films

Inertial magnetization dynamics have been predicted at ultrahigh speeds, or frequencies approaching the energy relaxation scale of electrons, in ferromagnetic metals. Here we identify inertial terms to magnetization dynamics in thin Ni${}_{79}$Fe${}_{21}$ and Co films near room temperature. Effective magnetic fields measured in high-frequency ferromagnetic resonance (115-345 GHz) show an additional stiffening term which is quadratic in frequency and $\sim$ 80 mT at the high frequency limit of our experiment. Our results extend understanding of magnetization dynamics at sub-picosecond time scales.