Beating the Walker Limit with Massless Domain Walls in Cylindrical Nanowires

We present a micromagnetic study on the current-induced domain-wall motion in cylindrical Permalloy nanowires with diameters below 50 nm. The transverse domain walls forming in such thin, round wires are found to differ significantly from those known from flat nanostrips. In particular, we show that these domain walls are zero-mass micromagnetic objects. As a consequence, they display outstanding dynamic properties, most importantly the absence of a breakdown velocity generally known as the Walker limit. Our simulation data are confirmed by an analytic model which provides a detailed physical understanding. We further predict that a particular effect of the current-induced dynamics of these domain walls could be exploited to measure the nonadiabatic spin-transfer torque coefficient.

Figure 1

A transverse DW formed in a 10 nm diameter cylindrical Py wire compared to a transverse wall in a 100 nm wide strip of 10 nm thickness (up-right). The Cartesian coordinate system and the spherical coordinate system used for the analytic study are shown on the lower left.

Figure 2

Schematic illustration of the current-driven DW motion. The cross sections indicate the position of the wall plane at successive moments in time, while the arrows represent the orientation of the transverse magnetization. The gray spiral illustrates the precessional motion of the wall.

Figure 3

(a) Simulated DW velocity as a function of the current density $j$ for four different values of $\beta$ in the case of a 10 nm round Py wire ($\alpha =0.02$). Inset ($a_1$): Simulated DW dynamics in a 100 nm wide and 10 nm thick strip. (b) DW displacement as a function of time for three different values of $j$. (c) Comparison of the DW speed between the 10 and the 40 nm wire. The lines in (a), ($a_2$) and (c) are analytical values of $u$ according to Eq. (2), while the lines in the inset ($a_1$) are guides to the eye. Excellent agreement with the analytic model is obtained, especially for lower values of the current density as shown in inset ($a_2$).

Figure 4

Simulated angular DW velocity as a function of $j$ for $\alpha =0.02$ and three values of $\beta$ in a round 10 nm Py wire. The lines represent analytic values (see text). Inset: Comparison between the angular DW velocity in the 10 and the 40 nm wire. The lines are guides to the eye.