Effect of paramagnon drag on thermoelectric transport properties: Linear response theory

It has been proposed that paramagnetic materials exhibit a unique thermoelectric effect near the ferromagnetic transition point due to spin fluctuations. This phenomenon is often referred to as paramagnon drag. We calculate the contribution of this paramagnon drag to the Seebeck coefficient microscopically on the basis of the linear response theory. This leed to a general formula for the contribution to the Seebeck coefficient due to the paramagnon drag, and we clarify the conditions in which the Seebeck coefficient enhances near the ferromagnetic transition point for a single-band and isotropic system. Moreover, we calculate the Seebeck coefficients for a band $\varepsilon \propto k^n$ and a mixture of free-electron-like and flat bands.