$d$-Wave Surface Altermagnetism in Centrosymmetric Collinear Antiferromagnets

Abstract: Broken inversion symmetry at the surfaces of centrosymmetric collinear antiferromagnets lifts the combined inversion and time-reversal symmetry ($PT$) and can generate nonrelativistic d-wave spin splitting, termed surface altermagnetism. Combining symmetry analysis with first-principles calculations, we show that surface inversion breaking, while necessary, is not sufficient for this effect. Surface altermagnetism emerges only when the surface termination simultaneously breaks both $PT$ and translation--time-reversal symmetry ($tT$), thereby inducing magnetic sublattice inequivalence between antiferromagnetically coupled surface moments. We demonstrate this mechanism explicitly for the G-type antiferromagnets V$_3$Al and BaMn$_2$Sb$_2$, and show that the same symmetry criterion applies broadly across distinct structural families of centrosymmetric antiferromagnets. These results establish a general, symmetry-based route to realizing robust, exchange-driven spin polarization at antiferromagnetic surfaces and interfaces.