Fig. 1: Schematics of SSE and theoretical results.

a Process of conventional Seebeck effect where \(\nabla T\) and \({J}_{c}\) denote the temperature gradient and charge current, respectively. b Process of SSE in FM/NM structure where \(\nabla {T}_{z},\,M,\,{J}_{s}\), and \({{{{{\boldsymbol{\sigma }}}}}}\) denote the vertical temperature gradient, magnetization, spin current, and spin polarization vector, respectively. c Model structure where FM consists of two ferromagnetic layers with different exchange interaction \({J}_{{ex}}\). d Theoretical and numerical results of the ratio \({r}_{{{{{{\rm{SSE}}}}}}}\) (defined in the main text) as a function of \({J}_{{ex},2}/{J}_{{ex},1}\).