Mode- and size-dependent Landau-Lifshitz damping in magnetic nanostructures: evidence for nonlocal damping

We demonstrate a strong dependence of the effective damping on the nanomagnet size and the particular spin-wave mode that can be explained by the theory of intralayer transverse-spin pumping. The effective Landau-Lifshitz damping is measured optically in individual, isolated nanomagnets as small as 100 nm. The measurements are accomplished by use of a novel heterodyne magneto-optical microwave microscope with unprecedented sensitivity. Experimental data reveal multiple standing spin-wave modes that we identify by use of micromagnetic modeling as having either localized or delocalized character, described generically as end and center modes. The damping parameter of the two modes depends on both the size of the nanomagnet as well as the particular spin-wave mode that is excited, with values that are enhanced by as much as 40% relative to that measured for an extended film. Contrary to expectations based on the ad hoc consideration of lithography-induced edge damage, the damping for the end mode decreases as the size of the nanomagnet decreases. The data agree with the theory for damping caused by the flow of intralayer transverse spin currents driven by the magnetization curvature. These results have serious implications for the performance of nanoscale spintronic devices such as spin-torque-transfer magnetic random access memory.