Frequency dependence of the longitudinal spin Seebeck effect

The spin Seebeck effect provides an easy way to create and manipulate spin current. Schreier et al. experimentally observed a decrease of spin Seebeck voltage at high frequencies in the yttrium iron garnet/Pt system [Phys. Rev. B 93, 224430 (2016)]. The frequency dependence was attributed to the magnon spectrum. Here we provide a different explanation using the frequency dependence of the ac spin current. By combining a phenomenological two-temperature model with the ac- temperature method, our calculation shows that the frequency dependence of the spin current is determined by the thermal wavelength and the thermal boundary conditions of the phonons and the magnons.