Joule heating in ferromagnetic nanostripes with a notch

The temperature in a ferromagnetic nanostripe with a notch subject to Joule heating has been studied in detail. We first performed an experimental real-time calibration of the temperature versus time as a 100 ns current pulse was injected into a Permalloy nanostripe. This calibration was repeated for different pulse amplitudes and stripe dimensions and the set of experimental curves were fitted with a computer simulation using the Fourier thermal conduction equation. The best fit of these experimental curves was obtained by including the temperature-dependent behavior of the electrical resistivity of the Permalloy and of the thermal conductivity of the substrate $\left(\mathrm{Si}{\mathrm{O}}_2\right)$. Notably, a nonzero interface thermal resistance between the metallic nanostripe and the substrate was also necessary to fit the experimental curves. We found this parameter pivotal to understand our results and the results from previous works. The higher current density in the notch, together with the interface thermal resistance, allows a considerable increase of the temperature in the notch, creating a large horizontal thermal gradient. This gradient, together with the high temperature in the notch and the larger current density close to the edges of the notch, can be very influential in experiments studying the current assisted domain wall motion.