We investigate spin currents in microstructured permalloy/platinum bilayers that are excited via magnetic high-frequency fields. Due to this excitation spin pumping occurs at the permalloy/platinum interface and a spin current is injected into the platinum layer. The spin current is detected as a voltage via the inverse spin-Hall effect. We find two regimes reflected by a nonlinear, abrupt voltage surge, which is reproducibly observed at distinct excitation field strengths. Micromagnetic simulations suggest that the surge is caused by excitation of a spin-wave-like mode. The comparatively large voltages reveal a highly efficient spin-current generation method in a mesoscopic spintronic device.