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In a number of current experiments in the field of spin-caloritronics a temperature gradient across a nanostructured interface is applied and spin-dependent transport phenomena are observed. However, a lack in the interpretation and knowledge let it unclear how the temperature drop across a magnetic nanostructured interface looks like where both phonons and electrons may contribute to thermal transport. We answer this question for the case of a magnetic tunnel junction (MTJ) where the tunneling magneto Seebeck effect occurs. Nevertheless, our results can be extended to other nanostructured interfaces as well. Using an textit{ab initio} method we explicitly calculate phonon and electron thermal conductance across the Fe/MgO/Fe-MTJs by using Greens function method. Further, by estimating the electron-phonon interaction in the Fe leads we are able to calculate the electron and phonon temperature profile across the Fe/MgO/Fe-MTJ. Our results show that there is an electron-phonon temperature imbalance at the Fe-MgO interfaces. In consequence, a revision of the interpretation of current experimental measurements might be necessary.
Despite the ubiquity of applications of heat transport across nanoscale interfaces, including integrated circuits, thermoelectrics, and nanotheranostics, an accurate description of phonon transport in these systems remains elusive. Here we present a
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