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One of the most important discoveries in spintronics is the spin Seebeckeffect (SSE) recently observed in both insulating and (semi-)conductingmagnets. However, the very existence of the effect in transverse configurationis still a subject of current debates, due to conflicting results reported indifferent experiments. Present understanding of the SSE is mainly based on aparticle-like picture with the local equilibrium approximation (LEA), i.e.,spatially resolved temperature-field assumed to describe the system. In thiswork, we abandon the LEA to some extent and develop a wave theory to explainthe SSE, by highlighting the interplay between wave localization andturbulence. We show that the emerging SSE with a sign change in thehigh/low-temperature regions is closely related to the extendedness of the spinwave that senses an average temperature of the system. On the one hand,ubiquitous disorders (or magnetic field gradients) can strongly suppress thetransverse spin Seebeck effect (TSSE) due to Anderson (or Wannier-Zeeman)spin-wave localization. On the other hand, the competing wave turbulence ofinteracting magnons tends to delocalize the wave, and thus remarkably revivesthe TSSE before the magnon self-trapping. Our theory provides a promising routeto resolve the heated debate on TSSE with a clear experiment scheme to test itin future spin caloritronic devices.

Interplay of Wave Localization and Turbulence in Spin Seebeck Effect