Current Driven Domain Wall Velocities Exceeding the Spin Angular Momentum Transfer Rate in Permalloy Nanowires

The velocity of domain walls driven by current in zero magnetic field is measured in permalloy nanowires using real-time resistance measurements. The domain wall velocity increases with increasing current density, reaching a maximum velocity of $\sim 110\mathrm{m}/\mathrm{s}$ when the current density in the nanowire reaches $\sim 1.5\times {10}^8\mathrm{A}/{\mathrm{cm}}^2$. Such high current driven domain wall velocities exceed the estimated rate at which spin angular momentum is transferred to the domain wall from the flow of spin polarized conduction electrons, suggesting that other driving mechanisms, such as linear momentum transfer, need to be taken into account.

Figure 1

(a),(b) SEM images of the device with illustrations of the measurement circuit. Labels $c_1$, $c_2$, and $c_3$ indicate the contact lines. The box labeled dc includes both a current source and a voltmeter connected in parallel. Solid arrows represent the portion of the permalloy nanowire across which the resistance is measured: (a) $c_1\mathrm{\text{−}}{c}_2$ and (b) $c_2\mathrm{\text{−}}{c}_3$. (c)–(f) Upper images: SEM images with overlays of the magnetization configuration (solid arrows) and the current path (dotted arrows). Lower panels: Probability of finding a DW in section $c_1\mathrm{\text{−}}{c}_2$ ($P_{12}$, black squares) and $c_2\mathrm{\text{−}}{c}_3$ ($P_{23}$, red circles), plotted as a function of the applied field. A 100 ns long voltage pulse is used in each case.

Figure 2

(a),(b) Examples of injection of transverse and vortex DWs into section $c_1\mathrm{\text{−}}{c}_2$ of the nanowire using $-1.8$ (a) and $-2.8\mathrm{V}$ (b) voltage pulses (1–20 ns long), respectively. Corresponding histograms of $\Delta R$ are shown. (c),(d) Injection probability ($P_{12}$) maps for HH (c) transverse and (d) vortex DWs. The color scale represents the probability. The applied magnetic field is zero. (e),(f) Profiles of the probability at $-2.0$, $-2.8$, and $-3.5\mathrm{V}$ for (e) transverse and (f) vortex DWs. (g),(h) Vortex DW velocities for (g) HH and (h) TT DWs plotted against the voltage pulse amplitude and the corresponding current density that flows into the nanowire. The solid (open) symbols represent data where the averaged probability of a vortex wall found in section $c_1\mathrm{\text{−}}{c}_2$ is higher (lower) than 50%.

Figure 3

(a) Typical signal traces $\Delta V(t)$ for the fields indicated in each panel. The voltage pulse is injected at $t=0$. A voltage pulse, $-2.8\mathrm{V}$ and 100 ns long, is used to inject a HH DW. The corresponding current density that flows into the permalloy nanowire is $-1.4\times {10}^8\mathrm{A}/{\mathrm{cm}}^2$. Solid red lines are fits using an error function [7]. (b) Amplitudes $A_1$ and $A_2$, defined in (a), plotted as a function of the applied field. A $-2.8\mathrm{V}$, 100 ns long voltage pulse is used to inject a HH DW. (c),(d) DW velocity near zero field plotted versus the current density. Velocities of (c) HH and (d) TT DWs are shown. The solid (open) symbols represent data where the averaged probability of a DW exiting section $c_1\mathrm{\text{−}}{c}_2$ is higher (lower) than 50%. Error bars correspond to $\frac{\Delta \tau }{\tau }v$, where $\Delta \tau$ and $v$ represent the fall time of $\Delta V(t)$ and the velocity, respectively.