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, it is demonstrated that interlayer magnetic coupling in two-dimensional (2D) CoPSe₃ bilayers enables precise control over quantum geometric mechanisms, unlocking dual intrinsic Hall effects. The first-principles calculations reveal that the altermagnetic (AM) phase exhibits a giant anisotropic anomalous Hall effect (AHE) (σ_xy ≈46 S cm^-1) driven by Berry curvature localized at generic k-points, while the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>P</mml:mi> <mml:mi>T</mml:mi></mml:mrow> <mml:annotation>$\mathcal{P}\mathcal{T}$</mml:annotation></mml:semantics> </mml:math> -symmetric antiferromagnetic (AFM) phase hosts an intrinsic second-order nonlinear anomalous Hall effect (NAHE) (χ_xyy ≈ 160 µS V^-1) originating from quantum metric accumulation at high-symmetry k-points. By tuning interlayer magnetic couplings, reversible switching between these phases is achieved, leveraging their distinct band structures and symmetry constraints. The Néel-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. This work establishes 2D antiferromagnets as a promising platform for multifunctional device architectures, bridging linear and nonlinear magnetoelectric responses through tailored quantum geometric engineering.