Joule heating in ferromagnetic nanowires: Prediction and observation

We present an analytic theory of the Joule heating in metallic nanowires. The steady state is calculated for heat conduction through the insulation layer and then the transient state is considered from the thermodynamics law. The temperature is predicted to exhibit a quick exponential decay to a steady state within a few tens of nanoseconds. The decay time is linearly dependent on the temperature coefficient and both increase to saturation values with the increasing wire width. The validity of the theory is experimentally confirmed by the in situ measurement of the temperature-dependent electric resistance.