Spin transport from order to disorder

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.