We utilized Brillouin light-scattering spectroscopy to study the magnetization dynamics in nanoscale permalloy elements driven by a large microwave magnetic field. We demonstrate that at large precession angles, the magnons excited by the microwaves scatter into the lowest-frequency state by a process similar to the scattering that leads to the Bose-Einstein condensation of magnons in the low-loss garnet films. The discovered effect is important for understanding the nonlinear processes in

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... gly driven nanomagnetic devices such as spin-torque nano-oscillators and magnetic memory.