  In the absence of an external magnetic field and a spin-polarized charge
current, an antiferromagnetic system supports two degenerate magnon modes. An
applied thermal bias activates the magnetic dynamics, leading to a magnon flow
from the hot to the cold edge (magnonic spin Seebeck current). Both degenerate
bands contribute to the magnon current but the orientations of the magnetic
moments underlying the magnons are opposite in different bands. Therefore,
while the magnon current is nonzero, the net spin current is zero.
