Full quantum theory for magnon transport in two-sublattice magnetic insulators and magnon junctions

Magnon, as elementary excitation in magnetic systems, can carry and transfer angular momentum. Due to the absence of Joule heat during magnon transport, researches on magnon transport have gained considerable interests over the past decade. Recently, a full quantum theory has been employed to investigate magnon transport in ferromagnetic insulators (FMIs). However, the most commonly used magnetic insulating material in experiments, yttrium iron garnet (YIG), is a ferrimagnetic insulator (FIMI). Therefore, a full quantum theory for magnon transport in FIMI needs to be established. Here, we propose a Green's function formalism to compute the magnon bulk and interface current in both FIMIs and antiferromagnetic insulators (AFMIs). We investigate the spatial distribution and temperature dependence of magnon current in FIMIs and AFMIs generated by temperature or spin chemical potential step. In AFMIs, magnon currents generated by temperature step in the two sublattices cancel each other out. Subsequently, we numerically simulate the magnon junction effect using the Green's function formalism, and result shows near 100\% magnon junction ratio. This study demonstrates the potential for investigating magnon transport in specific magnonic devices using a full quantum theory.