Dissipative dynamics of magnetic solitons in metals

Soliton dynamics in spin-textured metals generate electrical currents, which produce backaction through spin torques. We modify the Landau-Lifshitz-Gilbert equation and the corresponding solitonic equations of motion to include such higher-order texture effects. We also find a quasistatic equation for the induced electrochemical potential, which needs to be solved for self-consistently, in the incompressible limit. As an example, we consider the gyration of a vortex in a point-contact spin valve and discuss modifications of orbit radius, frequency, and dissipation power.

Figure 1

(Color online) Left panel: energy density Eq. (13) of the vortex texture $\mathbf{m}$ (red dotted arrows) due to the Oersted field $\mathbf{H}$ (green solid arrows), in the $xy$ plane centered at the point contact, with unit length $a$. The arrows depict a crude model of the vortex as four domains separated by $\pi /2$ walls emanating from the vortex center. On the gray scale, higher-energy density corresponds with lighter shade. One clearly sees a region of high energy that scales linearly with the separation distance between the vortex and the point contact, resulting in a linear attractive potential. The inset shows a side-view schematic of the magnetic bilayer in the $z$ direction. Right panel: a plot of the charge current due to each term in the spin-force field Eq. (19) in a region of $3\lambda \times 3\lambda$ centered at the vortex core. The contribution collinear with the Magnus force is shown with thick red arrows. The viscous $O\left(\beta \right)$ terms are indicated by blue arrows and have been magnified by setting $\beta \sim 1$. The long black arrows indicate the direction of each term in Eq. (15), labeled by their respective couplings.