Temperature Dependence of the Spin Torque Effect in Current-Induced Domain Wall Motion

We present an experimental study of domain wall motion induced by current pulses as well as by conventional magnetic fields at temperatures between 2 and 300 K in a 110 nm wide and 34 nm thick ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ ring. We observe that, in contrast with field-induced domain wall motion, which is a thermally activated process, the critical current density for current-induced domain wall motion increases with increasing temperature, which implies a reduction of the spin torque efficiency. The effect of Joule heating due to the current pulses is measured and taken into account to obtain critical fields and current densities at constant sample temperatures. This allows for a comparison of our results with theory.

Figure 1

(a) SEM image of the ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ ring investigated (34 nm thick, 110 nm wide, $1\mu \mathrm{m}$ diameter) with the numbered contacts and the polar angles indicated. (b) OOMMF simulation of a vortex wall in a ring with the sample geometry. (c) Resistance of the ring area between contacts 2 and 3 as a function of the wall position (schematically shown) at $T_{\mathrm{cryo}}=100\mathrm{K}$.

Figure 2

Domain wall depinning at the temperatures $T_{\mathrm{cryo}}$ indicated in the legend for (a) current and field parallel and (b) current and field antiparallel. All lines are guides to the eye. The statistical errors of the critical fields are of the order of $\pm 0.5$ to 1 mT. For values above the lines, the domain wall is displaced, below it remains pinned. Open symbols in (a) show the splitting of the boundary for high temperatures as explained in the text. The inset of (a) shows the critical field as function of the temperature for zero current (black squares) and for $j=2.07\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2$ (red triangles).

Figure 3

(a) Temperature increase due to Joule heating as a function of current density for $T_{\mathrm{cryo}}=4\mathrm{K}$ (red squares) and 200 K (blue circles). (b) Domain wall depinning for a sample temperature of $100\pm 5\mathrm{K}$ with current and field parallel. Black squares indicate measured values, red circles are interpolated. (c) Critical current density as function of the temperature. Black squares refer to the cryostat temperature $T_{\mathrm{cryo}}$, red circles to real temperatures $T_{\mathrm{real}}$ corrected for the effect of Joule heating. Open symbols indicate maximum values of the current density injected during the sample lifetime and are therefore lower limits for the critical current density.