Interplay of wave localization and turbulence in spin Seebeck effect

One of the most important discoveries in spintronics is the spin Seebeck effect (SSE), recently observed in both insulating and (semi)conducting magnets. However, the very existence of the effect in transverse configuration is still a subject of current debate. In this paper, motivated by the concept and the formulation of the mode- dependent magnon temperature introduced recently [Yan et al., Phys. Rev. B 95, 024417 (2017)], we develop a wave theory to explain the SSE by highlighting the interplay between wave localization and turbulence. We show that the emerging SSE with a sign change in the high/low-temperature regions is closely related to the extendedness of the spin wave that senses an average temperature of the system. On the one hand, ubiquitous disorders (or magnetic field gradients) can strongly suppress the transverse spin Seebeck effect (TSSE) due to the Anderson (or Wannier-Zeeman) spin-wave localization. On the other hand, the competing spin-wave turbulence from the magnetic anisotropy tends to delocalize the wave, and thus remarkably revives the TSSE before the magnon self-trapping. Our findings reveal the significant role of the magnetic anisotropy played in SSE and provide an appealing way to enhance the TSSE signal by choosing proper materials and sample shape.