  We measure the magnetic damping parameter a in thin film CoFeB and permalloy
(Py) nanomagnets at room temperature using ferromagnetic resonance driven by
microwave frequency spin-transfer torque. We obtain $\alpha_{CoFeB} = 0.014 \pm
0.003$ and $\alpha_{Py}=0.010 \pm 0.002$, values comparable to measurements for
extended thin films, but significantly less than the effective damping
determined previously for similar nanomagnets by fits to time-domain studies of
large-angle magnetic excitations and magnetic reversal. The greater damping
found for the large amplitude nanomagnet dynamics is attributed to the
nonlinear excitation of non-uniform magnetic modes.
