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

The relation between the nonadiabaticity parameter $\beta$ and the damping parameter $\alpha$ is investigated in permalloy-based microdisks. In order to determine $\beta$, 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 $\beta =(0.29\pm 0.15)\times {10}^{-2}$ is determined for $1.73\%$ Dy doping, compared to $(0.067\pm 0.014)\times {10}^{-2}$ which is extracted for pure permalloy. This is supportive of a similar scaling of $\beta$ and $\alpha$ 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.

Figure 1

(a) Ferromagnetic resonance absorption spectra at an excitation frequency $f_{\text{FMR}}$ of $4.5\mathrm{GHz}$ for undoped Py (red) and two doped Py films ($1.73\%$; blue and black). The corresponding FWHM linewidths are $0.20\pm 0.01\mathrm{Oe}$ (red), $1.24\pm 0.15\mathrm{Oe}$ (blue), and $1.32\pm 0.15\mathrm{Oe}$ (black). The thin films were grown alongside the films used for structured samples. For the undoped films, the associated magnetic field dependence of the resonance frequency and the frequency evolution of the linewidth is shown in (b) and (c), respectively.

Figure 2

SEMPA images of the vortex-core displacement for magnetic vortex states of undoped disks with $p=+1$ and $c=+1$. (a),(b) The same disk with $j=+\text{/}-0.5\times {10}^{12}{\mathrm{Am}}^{-2}$. The black crosses mark the geometrical center of the disk where the vortex is located at zero current. (c) False-color scanning-electron-microscope image of a typical sample. The contact pads are shaded in yellow and the Py disk is shaded in blue. The substrate (gray) is naturally oxidized silicon. Here, the right-handed $x\text{−}y$ coordinate system is defined by the visible edges of the contacted disk structure with the $x$ axis being perpendicular to the edges of the contact pads and the $y$ axis being parallel to them. Thus, in this coordinate system, the electric current through the central region of the disk flows parallel to the $x$ axis.

Figure 3

(a) The extracted displacements for three different states of one disk, as indicated schematically, for varying current densities, plotted along the current direction $r_{\parallel }$ ($x$) and also perpendicular, $r_{\perp }$ ($y$). The error bars reflect the uncertainty in the determined vortex-core position as determined via a cross-correlation algorithm. Linear regressions were performed for the three states which show a significant difference in the slope, as shown by the highlighted $1\sigma$ environment. (b) Collected vortex-core positions for 27-nm-thick undoped Py disks. Magnetic states affected by pinning have been excluded from the plots using the approach pioneered in Ref. [5]. Red/blue corresponds to chirality $c=+/-1$, respectively. The superimposed black circles indicate the mean magnitude of displacement derived from the magnetic states under the influence of current densities of $0.0\times {10}^{11}{\mathrm{Am}}^{-2}$ (closed circles), $2.7\times {10}^{11}{\mathrm{Am}}^{-2}$ (closed squares), and $5.4\times {10}^{11}{\mathrm{Am}}^{-2}$ (stars). For some samples, additional displacements were observed for $4.5\times {10}^{11}{\mathrm{Am}}^{-2}$ (diamonds) and $8.1\times {10}^{11}{\mathrm{Am}}^{-2}$ (triangles) with the shaded regions being the associated $1\sigma$ areas. (c) The corresponding current-induced vortex-core displacement for the 26-nm-thick doped Py disks. Here, the solid circles indicate the mean magnitude of displacement for current densities of $0.9\times {10}^{11}{\mathrm{Am}}^{-2}$, $1.8\times {10}^{11}{\mathrm{Am}}^{-2}$, and $2.7\times {10}^{11}{\mathrm{Am}}^{-2}$ derived from the corresponding states indicated by closed rectangles, diamonds, and stars, respectively. For some samples, additional states have been measured at current densities of $0.0\times {10}^{11}{\mathrm{Am}}^{-2}$ (open circles) and $5.4\times {10}^{11}{\mathrm{Am}}^{-2}$ (open squares). The observed displacement of the vortex cores follows the predicted behavior [30] and thus the polarities $p$ can be inferred from the slope of the trajectories.