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A theoretical formulation for spin transport through an antiferromagnetic(AF) insulator is presented in the case driven/detected by direct/inverse spinHall effect in two heavy metal contacts. The spin signal is shown to betransferred by the ferromagnetic correlation function of the antiferromagnet,which is calculated based on a magnon representation. To cover high temperatureregimes, we include an auxiliary field representing short AF correlations and atemperature-dependent damping due to magnon scattering. The diffusion lengthfor spin is long close to the degeneracy of the two AF magnons, and has amaximum as function of temperature near the N\'eel transition.

Theory of spin transport through antiferromagnetic insulator