Quantum Geometric Engineering of Dual Hall Effects in 2D Antiferromagnetic Bilayers via Interlayer Magnetic Coupling

The interplay between quantum geometry and magnetic order offers a novel strategy for designing next-generation nanodevices. Here, we demonstrate that interlayer magnetic coupling in two-dimensional (2D) CoPSe3 bilayers enables precise control over quantum geometric mechanisms, unlocking dual intrinsic Hall effects. Our first-principles calculations reveal that the altermagnetic (AM) phase exhibits a giant anisotropic anomalous Hall effect (AHE) ($\sigma_{xy}$ is approximately 46 S/cm) driven by Berry curvature localized at generic k-points, while the PT-symmetric antiferromagnetic (AFM) phase hosts an intrinsic second-order nonlinear anomalous Hall effect (NAHE) ($\chi_{xyy}$ is approximately 160 ${\mu}$S/V) originating from quantum metric accumulation at high-symmetry k-points. By tuning interlayer magnetic couplings, we achieve reversible switching between these phases, leveraging their distinct band structures and symmetry constraints. The Neel-vector-dependent AHE in the AM phase and the symmetry-protected NAHE in the AFM phase highlight quantum geometry as a versatile tool for manipulating transport properties. Our work establishes 2D antiferromagnets as a promising platform for multifunctional device architectures, bridging linear and nonlinear magnetoelectric responses through tailored quantum geometric engineering.