Unidirectional Thermal Effects in Current-Induced Domain Wall Motion

We report experimental evidence of thermal effects on the displacement of vortex walls in NiFe nanostrips. With the use of nanosecond current pulses, a unidirectional motion of the magnetic domain walls towards the hotter part of the nanostrips is observed, in addition to current-induced domain wall motion. By tuning the heat dissipation in the samples and modeling the heat diffusion, we conclude that this unidirectional motion can only be explained by the presence of a temperature profile along the nanostrip. A quantitative analysis of the experiments shows that, on top of the classical thermodynamic pressure on the domain wall, another force, probably the magnonic spin Seebeck effect, is displacing the domain walls.

Figure 1

Schematic of the experiment and sample structures. (a) SEM image of a single-curve sample, in which one DW is nucleated at the center by a transverse field $H_n$. (b) In the double-curve case, this procedure creates two DWs at $1/4$ and $3/4$ of the length. (c) Optical image of the coplanar waveguide by which the sample is connected, with a schematic of the electronics.

Figure 2

VW motion observed by MFM in a nanostrip with double curvature, 450 nm wide and $12\mu \mathrm{m}$ long. The upper (lower) VW corresponds to the tail to tail (head to head) configuration (green arrows with dotted-line tails schematize the magnetization orientation). Current pulses of 2 ns duration and $3\mathrm{TA}/{\mathrm{m}}^2$ amplitude (open arrows display the electrons’ motion) are applied between consecutive MFM images. The temperature gradient, indicated by red full arrows, is towards the center (red dashed line). Typical results for a nanostrip grown on a 100 nm oxide layer are shown as follows: (a1) electrons injected from bottom, motion of lower VW by 400 nm; (a2) electrons injected from the top, motion of upper VW by 800 nm; (a3) rarely observed motion of both VW, but still with a larger displacement towards the center. For an identical sample with native silicon oxide (b), symmetrical motion in both directions is observed (3 ns pulses).

Figure 3

Histogram of measured nonzero VW displacements, $q$, for a nanostrip of width $w=450\mathrm{nm}$ grown on thick silicon oxide. Positive (negative) values correspond to the propagation towards the center of nanostrip (resp. ends). As there are 20 trials for each current pulse category and polarity, the number of no-motion results, not shown at $q=0$, can be obtained by difference.

Figure 4

(a) Measured VW displacement as a function of initial position ($x_0$), after injecting a current pulse, 2 ns long and with $2\mathrm{TA}/{\mathrm{m}}^2$ amplitude, for single curvature nanostrips 400 nm wide and $6\mu \mathrm{m}$ long. Positive displacement refers to motion towards the nanostrip center, and open (full) symbols correspond to STT driving the VW to the center (resp. end). The curves show the values calculated using a 1D model with two collective coordinates, including STT and the thermodynamic effective field, for a damping constant $\alpha =0.01$. (b) Normalized temperature increase $T^{\prime }=T-T_0$ profiles computed for times 0, 5, 10, 20, 30, and 48 ns after the current pulse end (arrow shows the effect of time increase). The decrease of central temperature $T(0,t)$ with time $t$ is shown in inset. See Supplemental Material [22] for parameters.