  We investigate spin transport by thermally excited spin waves in an
antiferromagnetic insulator. Starting from a stochastic Landau-Lifshitz-Gilbert
phenomenology, we obtain the out-of-equilibrium spin-wave properties. In linear
response to spin biasing and a temperature gradient, we compute the spin
transport through a normal metal$|$antiferromagnet$|$normal metal
heterostructure. We show that the spin conductance diverges as one approaches
the spin-flop transition; this enhancement of the conductance should be readily
observable by sweeping the magnetic field across the spin-flop transition. The
results from such experiments may, on the one hand, enhance our understanding
of spin transport near a phase transition, and on the other be useful for
applications that require a large degree of tunability of spin currents. In
contrast, the spin Seebeck coefficient does not diverge at the spin-flop
transition. Furthermore, the spin Seebeck coefficient is finite even at zero
magnetic field, provided that the normal metal contacts break the symmetry
between the antiferromagnetic sublattices.
