Nonlinear spin Hall effect in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math> -symmetric collinear magnets

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