Nonlinear Magnetoelectric Edelstein Effect.

The generation of spin magnetization by linear and nonlinear Edelstein effects has so far relied solely on electric fields. Here, we propose a distinct mechanism, the nonlinear magnetoelectric Edelstein effect (NMEE), in which electric and magnetic fields act cooperatively to produce spin magnetization. The NMEE comprises intrinsic and extrinsic components, both of quantum geometric origin, arising, respectively, from the spin-space Berry curvature dipole and the spin-space quantum metric dipole. Through symmetry analysis, we demonstrate that these two components play complementary roles: the intrinsic NMEE induces a Néel spin-orbit torque, whereas the extrinsic NMEE enables detection of Néel-vector reversal in PT-symmetric antiferromagnets, exemplified by CuMnAs. Moreover, the intrinsic NMEE persists even in insulating systems, as shown in the Kane-Mele model. Our findings establish a quantum-geometric route to manipulate and probe magnetic order, opening new directions for antiferromagnetic spintronics.