Symmetry-guided Design Principles for Spin Splitting and Hall Transport in Orthorhombic Altermagnetic Perovskites
Magnetic symmetry can generate momentum-dependent spin-split electronic bands even in the absence of spin-orbit coupling (SOC), giving rise to the recently discovered class of altermagnets. Here, we establish a unified symmetry framework for collinear antiferromagnets in orthorhombic Pbnm perovskites by combining spin and magnetic group theory with first-principles calculations. We show that the irreducible representation of the magnetic order uniquely determines the momentum-space planes supporting altermagnetic spin splitting, the form of the effective low-energy Hamiltonian, the orientation of SOC-induced weak ferromagnetic canting, and the allowed anomalous Hall conductivity (AHC) tensor components. These predictions are validated in eight experimentally realized orthorhombic perovskite oxides spanning both insulating and metallic regimes. In particular, LaTiO3 and CaCrO3 exhibit sizable anomalous Hall conductivities of approximately 38 and 205 S/cm, respectively, despite nearly vanishing net magnetization. We further show that SOC gaps symmetry-protected altermagnetic band crossings, generating large Berry curvature, while the Hall response is fundamentally rooted in the underlying non-relativistic spin splitting. Our work establishes a predictive symmetry-based framework for discovering and engineering altermagnetic materials with tunable spin-dependent electronic and transport properties.