Direct observation of spin diffusion enhanced nonadiabatic spin torque effects in rare-earth-doped permalloy

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The relation between the nonadiabaticity parameter $\ensuremath{\beta}$ and the damping parameter $\ensuremath{\alpha}$ is investigated in permalloy-based microdisks. In order to determine $\ensuremath{\beta}$, high-resolution imaging of the current-induced vortex-core displacement is performed using scanning electron microscopy with polarization analysis. The materials properties of the films are varied via rare-earth Dy doping, leading to a greatly enhanced damping, while retaining the same spin configuration for the confined vortex state. A clear trend to much higher nonadiabaticity values is seen for the higher doping levels and an averaged value of $\ensuremath{\beta}=(0.29\ifmmode\pm\else\textpm\fi{}0.15)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ is determined for $1.73%$ Dy doping, compared to $(0.067\ifmmode\pm\else\textpm\fi{}0.014)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ which is extracted for pure permalloy. This is supportive of a similar scaling of $\ensuremath{\beta}$ and $\ensuremath{\alpha}$ in this system, pointing to a common origin of the spin relaxation which is at the heart of nonadiabatic transport and the dissipation of angular momentum that provides damping, in line with theoretical calculations.