  We propose an intrinsic nonlinear spin Hall effect, which enables the
generation of collinearly-polarized spin current in a large class of
nonmagnetic materials with the corresponding linear response being
symmetry-forbidden. This opens a new avenue for field-free switching of
perpendicular magnetization, which is required for the next-generation
information storage technology. We develop the microscopic theory of this
effect, and clarify its quantum origin in band geometric quantities which can
be enhanced by topological nodal features. Combined with first-principles
calculations, we predict pronounced effects at room temperature in topological
metals $\mathrm{PbTaSe_{2}}$ and PdGa. Our work establishes a fundamental
nonlinear response in spin transport, and opens the door to exploring
spintronic applications based on nonlinear spin Hall effect.
