  We investigate the antiferromagnetic spin Seebeck effect across the spin-flop
transition in a numerical simulation based on the time-dependent
Ginzburg-Landau equation for a bilayer of a uniaxial insulating antiferromagnet
and an adjacent metal. By directly simulating the rate of change of the
conduction-electron spin density ${\bf s}$ in the adjacent metal layer, we
demonstrate that a sign reversal of the antiferromagnetic spin Seebeck effect
across the spin-flop transition occurs when the interfacial coupling of ${\bf
s}$ to the staggered magnetization ${\bf n}$ of the antiferromagnet dominates,
whereas no sign reversal appears when the interfacial coupling of ${\bf s}$ to
the magnetization ${\bf m}$ dominates. Moreover, we show that the sign reversal
is influenced by the degree of spin dephasing in the metal layer. Our result
indicates that the sign reversal is not a generic property of a simple uniaxial
antiferromagnet, but controlled by microscopic details of the exchange coupling
at the interface and the spin dephasing in the metal layer.
