Nonlinear spin Hall effect in PT-symmetric collinear magnets

We theoretically investigate a nonlinear spin Hall effect in 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 antifer-romagnetic 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??el vector, odd-parity multipoles, nonlinear spin conductivity tensor, and candidate materials in all the PT-symmetric black-and-white magnetic point groups