A wave-number-dependent dissipative term to magnetization dynamics, mirroring the conservative term associated with exchange, has been proposed recently for ferromagnetic metals. We present measurements of wave-number-($k$-)dependent Gilbert damping in three metallic ferromagnets, NiFe, Co, and CoFeB, using perpendicular spin wave resonance up to 26 GHz. In the thinnest films accessible, where classical eddy-current damping is negligible, size effects of Gilbert damping for the lowest and first excited modes support the existence of a $k^2$ term. The new term is clearly separable from interfacial damping typically attributed to spin pumping. Higher-order modes in thicker films do not show evidence of enhanced damping, attributed to a complicating role of conductivity and inhomogeneous broadening. Our extracted magnitude of the $k^2$ term, $\mathrm{\Delta }{\alpha }_{kE}^{*}=\mathrm{\Delta }{\alpha }_0^{*}+A_k^{*}{k}^2$, where $A_k^{*}=0.08–0.1{\mathrm{nm}}^2$ in the three materials, is an order of magnitude lower than that identified in prior experiments on patterned elements.

• Received 31 October 2013

DOI:https://doi.org/10.1103/PhysRevLett.116.117602