PT-Symmetric Antiferromagnets as Building Blocks for Anomalous Transport.

Antiferromagnets with space-time inversion symmetry inherently suppress Berry curvature and the anomalous Hall effect (AHE), greatly limiting their use in spintronic applications. Here, we propose a symmetry-guided design strategy that employs monolayer -symmetric antiferromagnets as fundamental building blocks to induce AHE. We establish screening criteria to identify magnetic layer groups capable of yielding AHE when stacked via interlayer mirror symmetry. The resulting bilayers remain magnetically compensated and constitute a type IV class of magnets, distinct from ferromagnets, antiferromagnets, and altermagnets. A tight-binding model demonstrates the feasibility of this approach, showing that such stacked structures can host AHE and even realize its quantized form. First-principles calculations on bilayer MnPSe further corroborate the design framework and reveal a symmetry-enforced layer-constructive Hall effect. Our work highlights symmetry-controlled stacking as a practical route for engineering unconventional magnetic materials and realizing AHE within them.