Magnon diffusion theory for the spin Seebeck effect in ferromagnetic and antiferromagnetic insulators

In magnetic insulators, spin currents are carried by the elementary excitations of the magnetization: spin waves or magnons. In simple ferromagnetic insulators there is only one magnon mode, while in two-sublattice antiferromagnetic insulators (AFIs) there are two modes, which carry spin currents in opposite directions. Here we present a theory for the diffusive magnonic spin current generated in a magnetic insulator layer by a thermal gradient in the spin Seebeck effect. We show that the formulations describing magnonic perturbation using a position-dependent chemical potential and those using a magnon accumulation are completely equivalent. Then we develop a drift-diffusion formulation for magnonic spin transport treating the magnon accumulation governed by the Boltzmann transport and diffusion equations and considering the full boundary conditions at the surfaces and interfaces of an AFI/normal metal bilayer. The theory is applied to the ferrimagnetic yttrium iron garnet and to the AFIs MnF2 and NiO, providing good quantitative agreement with experimental data.