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 (SiO 2 ). 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.

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In this work we study the influence of the thermal contact resistance on the temperature of a typical nanostripe used in current induced magnetic domain wall movement or depinning. The thermal contact resistance arises from an imperfect heat transport across the interface between the metallic ferromagnetic nanostripe and the substrate. We show that this parameter, which is likely nonzero in any experimental device, increases the temperature in the nanostripe considerably. When the current is injected in the nanostripe in nanosecond long pulses, the larger temperature also implies a reduction of the effective current density delivered by the pulse generator. Both, the thermal contact resistance and the dynamic response of the pulse generator, are usually neglected in theoretical estimations of the influence of spin transfer torque on domain wall displacement and depinning. Here we show that only if the thermal contact resistance and the electric resistivity of the ferromagnetic nanostripe are optimized to the best values reported in the bibliography, the Joule heating may not be so crucial for current densities of the order of 10 8 A/cm 2 . Also, the use of physical constrictions (notch) to pin the magnetic domain wall may complicate the interpretation of the results as they always come together with relevant thermal gradients.