Magnetic geometry induced quantum geometry and nonlinear transports.

The combination of quantum geometry and magnetic geometry in magnets excites diverse phenomena, some critical for antiferromagnetic spintronics. However, very few material platforms have been predicted and experimentally verified to date, with the material pool restricted by the assumed need for strong spin-orbit coupling (SOC). Here, we bypass the need for SOC by considering magnetic order induced quantum geometry and corresponding nonlinear transports (NLTs) in antiferromagnets (AFMs). By integrating spin space group theory into the symmetry analysis, we find that collinear and coplanar magnetic geometries can only induce NLT driven by Berry curvature dipole, and noncoplanar ones may trigger NLT driven by dipoles of Berry curvature, inverse mass, and quantum metric. Using this approach, we establish a materials database of 260 AFMs with SOC-free NLT effects, and complement this with first-principles calculations on several prototypical material candidates. 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.