  New terms to the dynamical equation of magnetization motion, associated with
spin transport, have been reported over the past several years. Each newly
identified term is thought to possess both a real and an imaginary effective
field leading to fieldlike and dampinglike torques on magnetization. Here we
show that three metallic ferromagnets possess an imaginary effective-field term
which mirrors the well-known real effective-field term associated with exchange
in spin waves. Using perpendicular standing spin wave resonance between 2-26
GHz, we evaluate the magnitude of the finite-wavenumber ($k$) dependent Gilbert
damping $\alpha$ in three typical device ferromagnets, Ni$_{79}$Fe$_{21}$, Co,
and Co$_{40}$Fe$_{40}$B$_{20}$, and demonstrate for the first time the presence
of a $k^2$ term as $\Delta\alpha=\Delta\alpha_0+A_{k}\cdot k^2$ in all three
metals. We interpret the new term as the continuum analog of spin pumping,
predicted recently, and show that its magnitude, $A_{k}$=0.07-0.1 nm$^2$, is
consistent with transverse spin relaxation lengths as measured by conventional
(interlayer) spin pumping.
