Supercurrent-induced domain wall motion

We study the dynamics of a magnetic domain wall, inserted in, or juxtaposed to, a conventional superconductor, via the passage of a spin polarized current through a ferromagnet-superconductor-ferromagnet junction. Solving the Landau-Lifshitz-Gilbert equation of motion for the magnetic moments, we calculate the velocity of the domain wall and compare it with the case of a ferromagnet-normal-ferromagnet junction. We find that in several regimes the domain wall velocity is higher when it is driven by a supercurrent.

Figure 1

Evolution of $\langle s_z^l\rangle$ as a function of $J$. Various plateaus are obtained through quantum phase transitions.

Figure 2

Spatial variation of the gap function for different values of $J$ from $J=0.3,\dots ,2.5$. Note that the number of peaks increases by 1 as the average magnetization jumps from one plateau to the next.

Figure 3

Time evolution of a domain wall (DW) of 15 spins with parameters $J=1,J_{\mathrm{ex}}=0.5,V=1$. At the initial time ($t=0$) the DWl magnetic moments are contained in the $x$–$z$ plane. As time evolves the location of the center of the DW shifts to the right.

Figure 4

Time evolution of a domain wall of 41 spins with parameters $J=1,J_{\mathrm{ex}}=0.5,V=1$.

Figure 5

Time dependence of (a) the distance between the center of the domain wall, $x_{\mathrm{DW}}$, and the midpoint of the superconductor and (b) the velocity of the DW for different values of $J$ from $J=0.1,\dots ,2.5$. Solid (black) lines are the results for the superconductor; dashed (red) lines, the results for the normal system.

Figure 6

Dependence of the domain wall velocity with the various parameters. We consider the dependence with (a) the interface disorder, $U$, (b) the exchange between the spins $J_{\mathrm{ex}}$, and (c) the applied potential $V$. (d) Comparison of the velocity for the superconductor and the normal metal for the parameters $J=2$, $J_{\mathrm{ex}}=1.5$, $V=0.5$, and $\alpha =0.5$.

Figure 7

Time evolution of the domain wall (DW) of 15 spins and $J=1$, $J_{\mathrm{ex}}=0.5$, and $V=1$ for later times. For the parameters considered here the DW center point reaches the right-hand-side border and the remaining nonaligned magnetic moments move out of the $x$-$z$ plane. The boundary condition imposed by the right-hand-side ferromagnet fixes the orientation of the last magnetic moment ($t=1.25$). At later times $t=1.5$ and 1.75, the DW starts to distort and several spins rotate out of the original plane.

Figure 8

Time evolution of the domain wall (DW) of 15 spins and $J=2,J_{\mathrm{ex}}=1.5$, $V=0.5$, and $\alpha =0.5$. Increasing the couplings between the magnetic moments and their coupling to the electron spin density, and the Gilbert damping, the DW distortion is smaller, even though some spins start to move out of the initial plane when the center of the DW approaches the right-hand boundary ($t=1.65$).