  We determine the temperature profile in magnetic nanocontacts submitted to
the very large current densities that are commonly used for spin-torque
oscillator behavior. Experimentally, the quadratic current-induced increase of
the resistance through Joule heating is independent of the applied temperature
from 6 K to 300 K. The modeling of the experimental rate of the current-induced
nucleation of a vortex under the nanocontact, assuming a thermally-activated
process, is consistent with a local temperature increase between 150 K and 220
K. Simulations of heat generation and diffusion for the actual tridimensional
geometry were conducted. They indicate a temperature-independent efficiency of
the heat sinking from the electrodes, combined with a localized heating source
arising from a nanocontact resistance that is also essentially
temperature-independent. For practical currents, we conclude that the local
increase of temperature is typically 160 K and it extends 450 nm about the
nanocontact. Our findings imply that taking into account the current-induced
heating at the nanoscale is essential for the understanding of magnetization
dynamics in nanocontact systems.
