Effect of the thermal conductivity of substrate on the temperature of nanowire for current induced domain wall motion

We investigate the Joule-heated nanowire temperature for current induced domain wall motion with a finite thickness insulator layer. The dependence of the temperature on the thermal conductivities of substrates and insulator layers, and the insulator layer thickness are studied by employing finite element method. We find that the increment of the temperature is roughly proportion to the inverse of thermal conductivity of the substrate and insulator layer. Furthermore, the increment of the temperature rises with the insulator thickness, and then saturates for the thick enough insulator layers. The results of the numerical calculations can be explained reasonably with the analytic solution for the Joule-heated nanowire temperature, even though it is valid only for the case without an insulator layer. Our results suggest appropriate guideline for the design of the experiments.