  We theoretically investigate a nonlinear spin Hall effect in
$\mathcal{PT}$-symmetric antiferromagnetic metals, which serve as an efficient
spin current generator. We elucidate that an emergent spin-dependent Berry
curvature dipole is a microscopic origin of the nonlinear spin Hall effect,
which becomes nonzero with neither relativistic spin-orbit coupling, uniform
magnetization, nor spin-split band structure. By analyzing a microscopic
antiferromagnetic model without spin-orbit coupling for an intuitive
understanding of the phenomena, we elucidate essential hopping processes and a
condition to enhance the nonlinear spin Hall conductivity. We also provide a
complete table to include useful correspondence among the N\'eel vector,
odd-parity multipoles, nonlinear spin conductivity tensor, and candidate
materials in all the $\mathcal{PT}$-symmetric black-and-white magnetic point
groups.
