Direct Determination of Large Spin-Torque Nonadiabaticity in Vortex Core Dynamics

We use a pump-probe photoemission electron microscopy technique to image the displacement of vortex cores in Permalloy discs due to the spin-torque effect during current pulse injection. Exploiting the distinctly different symmetries of the spin torques and the Oersted-field torque with respect to the vortex spin structure we determine the torques unambiguously, and we quantify the amplitude of the strongly debated nonadiabatic spin torque. The nonadiabaticity parameter is found to be $\beta =0.15\pm 0.07$, which is more than an order of magnitude larger than the damping constant $\alpha$, pointing to strong nonadiabatic transport across the high magnetization gradient vortex spin structures.

Figure 1

Simulation and images of disks in a vortex state. (a) Simulation of a vortex structure. (b) Simulated current-induced VC displacement. The arrow points to the displaced VC and the angle of the VC displacement direction $\theta$ (angle subtended by the path of the vortex core displacement to the $y$ axis) is shown. (c) SEM image of the $6\mu \mathrm{m}$ wide and 30 nm thick Py disk with gold contacts (top and bottom bright contrast).

Figure 2

Pseudocolor images of current-induced VC displacements. (a) XMCD image of a centered clockwise vortex at zero current. (b) VC displacement for a current density of $j=0.8\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2$ with the electrons flowing upwards as indicated. (c) VC displacement for the opposite current direction. (d)–(f) show corresponding images for a VC with opposite chirality and polarity. The color bar indicates the direction of the magnetic contrast.

Figure 3

Systematic plot of VC displacements. The current-induced VC displacements are plotted for various combinations of polarity, chirality and current direction. The blue and red data points refer to combinations, where the difference in displacement direction is only due to the nonadiabatic spin-torque. Displacement to the lower and left parts of the disk are mirrored into the top right quarter appropriately to allow for an easy comparison between the VC displacements (the inset shows the original data). The value of the fitted slopes for the two chiralities is indicated. The error bars correspond to the accuracy in measuring the VC position. For the VC position in the $x$ direction the error bars are smaller than for the $y$ direction due to the better magnetic contrast in the $x$ direction.