(Anti-)Altermagnetism from Orbital Ordering in the Ruddlesden-Popper Chromates Sr$_{n+1}$Cr$_n$O$_{3n+1}$

Abstract: Altermagnets form a subclass of collinear antiferromagnets with spin-split electronic states. Here, we introduce the Ruddlesden-Popper chromates Sr${n+1}$Cr$_n$O${3n+1}$ (including the perovskite SrCrO$_3$) as candidates for antiferromagnetic materials in which altermagnetism emerges from spontaneous orbital ordering, rather than crystal symmetry. Using first-principles calculations, we identify a layer-dependent spin splitting of the electronic states, driven by the interplay between spin and orbital order. We show that if the spin and orbital orders align in adjacent layers, the system exhibits a net spin splitting, and thus altermagnetism. In contrast, if either the spin or the orbital order is reversed in adjacent layers, we observe an anti-altermagnetic state where layerwise compensation leads to net zero spin splitting. We find that for odd $n$, altermagnetic and anti-altermagnetic phases can coexist, whereas for even $n$ and in the perovskite limit, the system remains strictly anti-altermagnetic. In both cases, increasing $n$ favors metallicity. Finally, we indicate that in odd $n$ compounds, epitaxial strain can promote the altermagnetic phase.