Nonadiabatic spin-transfer torque of magnetic vortex structures in a permalloy square

Abstract

The stationary displacement of a magnetic vortex core in a permalloy square caused by an ultrahigh direct current has been measured utilizing scanning electron microscopy with polarization analysis. Data have been analyzed for three different generic states of the Landau structure and up to a current density of $3\ifmmode\times\else\texttimes\fi{}{10}^{11}\mathrm{A}/{\mathrm{m}}^{2}$. This procedure allows for separating the effects caused by the Oersted field, the nonadiabatic, and the adiabatic spin-transfer torque. In addition, the spin polarization of the driving current $P=(65\ifmmode\pm\else\textpm\fi{}4)%$ is independently determined from the spin drift velocity of ${v}_{j}=(4.79\ifmmode\pm\else\textpm\fi{}0.26)$ m/s at $j=1\ifmmode\times\else\texttimes\fi{}{10}^{11}\mathrm{A}/\mathrm{m}$. Ferromagnetic resonance measurements have been conducted to complete the set of parameters for our film system ($\ensuremath{\alpha},g,{M}_{\mathrm{S}}$). The full set of parameters allows for a direct comparison of the nonadiabatic spin-transfer torque with previously published results. In contrast to published values in the range of the damping parameter, a strongly increased value of $\ensuremath{\beta}=0.119\ifmmode\pm\else\textpm\fi{}0.022$ as a parameter of nonadiabaticity is found, which supports recent theoretical predictions of an additional nonlocal spin-transfer torque contribution effective at the vortex structure.