Since its discovery, yttrium iron garnet (YIG) has been object of great interest because of its peculiarly low magnetic damping. Magnetic materials with reduced damping promote microwave power efficiency, longer magnon lifetime and longer spin-wave propagation. Owing to research on charge-to-spin current conversion, the control of magnetic damping in ferromagnetic thin films has recently been achieved by inducing charge current on adjacent metal layer with strong spin-orbit coupling (SOC). We report damping reduction in metallized YIG thin films (YIG/Ag/Ni) without the need of applied charge current and suggest that the origin of this unexpected effect is a strengthening of the FMR uniform mode in the YIG layer, due to frequency- and phase-locking that result from self-synchronization mediated by nonzero spin densities transiting the metallic layers.