We have investigated the magnetic damping of precessional spin dynamics in defect-controlled epitaxial grown Fe$_3$O$_4$(111)/Yttria-stabilized Zirconia (YSZ) nanoscale films by all-optical pump-probe measurements. The intrinsic damping constant of the defect-free Fe$_3$O$_4$ film is found to be strikingly larger than that of the as-grown Fe$_3$O$_4$ film with structural defects. We demonstrate that the population of the first-order perpendicular standing spin wave (PSSW) mode, which is exclusively observed in the defect-free film under sufficiently high external magnetic fields, leads to the enhancement of the magnetic damping of the uniform precession (Kittel) mode. We propose a physical picture in which the PSSW mode acts as an additional channel for the extra energy dissipation of the Kittel mode. The energy transfer from Kittel mode to PSSW mode increases as in-plane magnetization precession becomes more uniform, resulting in the unique intrinsic magnetic damping enhancement in the defect-free Fe$_3$O$_4$ film.
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