Spin Seebeck effect (SSE) holds promise for new spintronic devices with low-energy consumption. The underlying physics, essential for a further progress, is yet to be fully clarified. This study of the time resolved longitudinal SSE in the magnetic insulator yttrium iron garnet (YIG) concludes that a substantial contribution to the spin current stems from small wave-vector subthermal exchange magnons. Our finding is in line with the recent experiment by S. R. Boona and J. P. Heremans, Phys. Rev. B 90, 064421 (2014). Technically, the spin-current dynamics is treated based on the Landau-Lifshitz-Gilbert (LLG) equation also including magnons back-action on thermal bath, while the formation of the time dependent thermal gradient is described self-consistently via the heat equation coupled to the magnetization dynamics
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