  Nonlinear transports (NLTs) have garnered broad attention based on their
topological origin in quantum geometry. When quantum geometry meets magnetic
geometry in magnets, their crossover excites diverse phenomena particularly
related to antiferromagnetic spintronics. However, very few material platforms
have been predicted and experimentally verified to date, where spin-orbit
coupling (SOC) plays an indispensable role in generating NLTs. Therefore, to
boost antiferromagnetic spintronics affected by the dual effect of quantum
geometry and magnetic geometry, a material database of antiferromagnets (AFMs)
with magnetic geometry driven quantum geometry and more significant NLT effects
is urgently needed. Here, we integrate the state-of-the-art spin space group
theory into the symmetry analysis of NLT tensors. By completely disentangling
SOC effects, we find that collinear and coplanar magnetic geometry can only
induce NLT driven by Berry curvature dipole, and noncoplanar one may trigger
NLT driven by dipoles of Berry curvature, inverse mass, and quantum metric.
Remarkably, a materials database of 260 AFMs with SOC-free NLT effects is
established. Several prototypical material candidates are presented by
first-principle calculations, including collinear AFM VNb$_{3}$S$_{6}$ with NLT
driven by Berry curvature dipole, and a room-temperature noncoplanar AFM CrSe
with NLTs driven by quantum metric dipole. Our work not only provides a
universal theoretical framework for studying various magnetism-driven transport
effects, but also predicts broad, experimentally accessible material platforms
for antiferromagnetic spintronics.
