Influence of Current on Field-Driven Domain Wall Motion in Permalloy Nanowires from Time Resolved Measurements of Anisotropic Magnetoresistance

The motion of magnetic domain walls in permalloy nanowires is investigated by real-time resistance measurements. The domain wall velocity is measured as a function of the magnetic field in the presence of a current flowing through the nanowire. We show that the current can significantly increase or decrease the domain wall velocity, depending on its direction. These results are understood within a one-dimensional model of the domain wall dynamics which includes the spin transfer torque.

Figure 1

(a) SEM image of a permalloy nanowire and Rh contacts (A and B). A schematic drawing of the measurement circuit is also shown. (b), (c) Signal traces as a function of drive field ($H_{DR}$) for (b) negative current and (c) positive current. Field, current, and magnetization ($M$) directions are illustrated. The magnitude of the drive fields are indicated for each trace. Red solid lines are fits to a complementary error function. Note that in (c), we are not able to fit the traces for negative fields smaller than $\sim 25\mathrm{Oe}$, since the DW does not exit the nanowire within the time frame shown. The red solid lines for these traces are included only as a visual guide. Blue dotted lines indicate the time at which the input voltage pulse is injected.

Figure 2

(a) The signal trace is fitted with a complementary error function, $dV(t)=\frac{A}{2}\mathrm{Erfc}(\frac{t-t_{EXIT}}{\Delta \tau })$, which defines the time at which the DW exits the nanowire, $t_{EXIT}$, the fall time and the amplitude of the signal trace, $\Delta \tau$ and $A$, respectively. $t_{IN}$ is the time at which the curve reaches half of the total amplitude $A$. We define the time the DW spends in the nanowire as $\tau =t_{EXIT}-t_{IN}$. (b) $A$, (c) $\Delta \tau$, and (d) DW velocity are plotted as a function of the absolute drive field. The error bars in (d) take into account the measured distribution of $t_{IN}$. Circles and squares correspond to positive and negative currents, respectively.

Figure 3

(a) Drive field dependence of DW velocity in the low field regime for various applied currents. (b)–(d) DW velocities plotted at fixed drive fields as a function of current density. The zero velocity values indicated in (b) and (c) likely correspond to negative DW velocities. (e)–(g) Calculated DW velocity as a function of the drive field for current densities corresponding to those shown in (a). The parameters used in the calculation are $M_S=800\mathrm{emu}/{\mathrm{cm}}^3$, $\alpha =0.02$, $H_K=800\mathrm{Oe}$, $\Delta =25\mathrm{nm}$ [26], $P=1$ [27].