  Schwinger boson mean-field theory (SBMFT) is a non-perturbative approach
which treats ordered and disordered phases of magnetic systems on equal
footing. We leverage its versatility to evaluate the spin correlators which
determine thermally-induced spin transport (the spin Seebeck effect) in
Heisenberg ferromagnets (FMs) and antiferromagnets (AFs), at arbitrary
temperatures. In SBMFT, the spin current, $J_s$, is made up of
particle-hole-like excitations which carry integral spin angular momentum. Well
below the ordering temperature, $J_s$ is dominated by a magnonic contribution,
reproducing the behavior of a dilute-magnon gas. Near the transition
temperature, an additional, paramagnetic-like contribution becomes significant.
In the AF, the two contributions come with opposite signs, resulting in a
signature, rapid inversion of the spin Seebeck coefficient as a function of
temperature. Ultimately, at high temperatures, the low-field behavior of the
paramagnetic SSE reduces to Curie-Weiss physics. Analysis based on our theory
confirms that in recent experiments on gadolinium gallium garnet, the low-field
spin Seebeck coefficient $\mathcal{S}(T) \propto \chi(T)$, the spin
susceptibility, down to the Curie-Weiss temperature. At lower temperatures in
the disordered phase, our theory shows a deviation of $\mathcal{S}(T)$ relative
to $\chi(T)$ in both FMs and AFs, which increases with decreasing temperature
and arises due to a paramagnetic liquid phase in our theory. These results
demonstrate that the SSE can be a probe of the short-ranged magnetic
correlations in disordered correlated spin systems and spin liquids.
