  We study the nonequilibrium transport for the asymmetric and negative
differential magnon tunneling driven by temperature bias. We demonstrate that
the many-body magnon interaction that makes the magnonic spectrum
temperature-dependent is the crucial factor for the emergence of rectification
and negative differential spin Seebeck effects in magnon tunneling junctions.
When magnonic junctions have temperature-dependent density of states, reversing
the temperature bias is able to give asymmetric spin currents and increasing
temperature bias could give an anomalously decreasing magnonic spin current. We
show that these properties are relevant for building spin Seebeck diodes and
transistors, which could play important roles in controlling information and
energy in magnonics and spin caloritronics.
