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Modelling of the Peltier effect in magnetic multilayers

We model the charge, spin, and heat currents in ferromagnetic metal$|$normal metal$|$normal metal trilayer structures in the two current model, taking into account bulk and interface thermoelectric properties as well as Joule heating. Results include the temperature distribution as well as resistance-current curves that reproduce the observed shifted parabolic characteristics. Thin tunneling barriers can enhance the apparent Peltier cooling. The model agrees with experimental results for wide multilayer pillars, but the giant effects observed for diameters $\lesssim 100\,$nm are still under discussion.