Analytic expression for the temperature of the current-heated nanowire for the current-induced domain wall motion

The authors find a simple analytic expression for the temperature of Joule heated nanowire by current pulse, which is important in the study of the current induced domain wall motion. Since the effect of spin transfer torque depends on the thermal energy of the system, the temperature of the nanowire is a vital information. Even though the numerical solution of the heat conduction equation is well established, not only does it require a lot of numerical effort, but neither does it give any physical insight. With appropriate assumptions and Green's function method, the author derive a simple expression for the temperature of the nanowire as a function of the current density, sample geometry, and thermal properties of the substrate. The authors confirm the validity of their analytic expression by the comparison between the results of a simple expression and a commercial finite element method.