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Verification of the Thomson-Onsager reciprocity relation for spin caloritronics

We investigate the Thomson-Onsager relation between the spin-dependent Seebeck and spin-dependent Peltier effect. To maintain identical device and measurement conditions we measure both effects in a single Ni$_{80}$Fe$_{20}$/Cu/Ni$_{80}$Fe$_{20}$ nanopillar spin valve device subjected to either an electrical or a thermal bias. In the low bias regime, we observe similar spin signals as well as background responses, as required by the Onsager reciprocity relation. However, at large biases, deviation from reciprocity occurs due to dominant nonlinear contribution of the temperature dependent transport coefficients. By systematic modeling of these nonlinear thermoelectric effects and measuring higher order thermoelectric responses for different applied biases, we identify the transition between the two regimes as the point at which Joule heating start to dominate over Peltier heating. Our results signify the importance of local equilibrium for the validity of this phenomenological reciprocity relation.