  We present a microscopic theory of magnon transport in ferromagnetic
insulators (FIs). Using magnon injection through microwave pumping, we propose
a way to generate magnon dc currents and show how to enhance their amplitudes
in hybrid ferromagnetic insulating junctions. To this end focusing on a single
FI, we first revisit microwave pumping at finite (room) temperature from the
microscopic viewpoint of magnon injection. Next, we apply it to two kinds of
hybrid ferromagnetic insulating junctions. The first is the junction between a
quasi-equilibrium magnon condensate and magnons being pumped by microwave,
while the second is the junction between such pumped magnons and noncondensed
magnons. We show that quasi-equilibrium magnon condensates generate ac and dc
magnon currents, while noncondensed magnons produce essentially a dc magnon
current. The ferromagnetic resonance (FMR) drastically increases the density of
the pumped magnons and enhances such magnon currents. Lastly, using microwave
pumping in a single FI, we discuss the possibility that a magnon current
through an Aharonov-Casher phase flows persistently even at finite temperature.
We show that such a magnon current arises even at finite temperature in the
presence of magnon-magnon interactions. Due to FMR, its amplitude becomes much
larger than the condensed magnon current.
