Spin Hall effect of spin-texture origin is explored theoretically for antiferromagnetic (AF) metals. Based on the observation that a scalar spin chirality formed by the Néel vector is not a physically well-defined quantity, it is found that a vector chirality formed by the Néel vector gives rise to a topological spin Hall effect. This is topological since it is proportional to the winding number counted by in-plane vector chirality along the sample edge, which corresponds to a homotopy class ${\pi }_1\left(S^1\right)$, instead of ${\pi }_2\left(S^2\right)$ of scalar chirality, and can be nonvanishing for AF merons but not for AF skyrmions. The effect is enhanced when the Fermi level lies near the AF gap, and, surprisingly, at weak coupling with a small AF gap. These features are confirmed numerically based on the Landauer-Büttiker formula. Important roles played by nonadiabatic processes and spin dephasing are pointed out.

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• Skyrmions
• Spin Hall effect
• Antiferromagnets
• Feynman diagrams
• Gauge theory techniques
• Tight-binding model