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Magnetic damping is a key metric for emerging technologies based on magnetic nanoparticles, such as spin torque memory and high-resolution biomagnetic imaging. Despite its importance, understanding of magnetic dissipation in nanoscale ferromagnets remains elusive, and the damping is often treated as a phenomenological constant. Here, we report the discovery of a giant frequency-dependent nonlinear damping that strongly alters the response of a nanoscale ferromagnet to spin torque and microwave magnetic field. This damping mechanism originates from three-magnon scattering that is strongly enhanced by geometric confinement of magnons in the nanomagnet. We show that the giant nonlinear damping can invert the effect of spin torque on a nanomagnet, leading to an unexpected current-induced enhancement of damping by an antidamping torque. Our work advances the understanding of magnetic dynamics in nanoscale ferromagnets and spin torque devices.more » « less