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Spectral non-uniform temperature, non-local heat transfer, and the spin Seebeck effect

We present a theory of the spin Seebeck effect driven by subthermal non-local phonon heat transfer and spectral non-uniform temperature distribution. The theory explains the non-local behavior of the effect arising from the fact that phonons that store the energy (thermal) and the phonons that transfer it (subthermal) are located in different parts of the spectrum and have very different kinetics. This gives rise to a spectral phonon distribution function that deviates from local equilibrium along the substrate and is sensitive to boundary conditions. The theory also predicts a non-magnon origin of the effect in ferromagnetic metals in agreement with observations in recent experiments. Equilibration of the heat flow out of the substrate to the Pt probe and backwards leads to a measurable vertical spin-current produced by the spin polarized electrons dragged by the local thermal phonons. We predict specific sample length limits and other dependencies that can be probed experimentally, and obtain the correct magnitude of the effect.