  We develop a theory for spin transported by coherent Neel dynamics through an
antiferromagnetic insulator coupled to a ferromagnetic insulator on one side
and a current-carrying normal metal with strong spin-orbit coupling on the
other. The ferromagnet is considered within the mono-domain limit and we assume
its coupling to the local antiferromagnet Neel order at the
ferromagnet|antiferromagnet interface through exchange coupling. Coupling
between the charge current and the local Neel order at the other interface is
described using spin Hall phenomenology. Spin transport through the
antiferromagnet, assumed to possess an easy-axis magnetic anisotropy, is solved
within the adiabatic approximation and the effect of spin current flowing into
the ferromagnet on its resonance linewidth is evaluated. Onsager reciprocity is
used to evaluate the inverse spin Hall voltage generated across the metal by a
dynamic ferromagnet as a function the antiferromagnet thickness.
