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

Abstract

Altermagnets are collinear antiferromagnets with spin-split electronic states. We introduce Ruddlesden-Popper chromates Sr$_{n+1}$Cr$_n$O$_{3n+1}$ (including SrCrO$_3$) as candidate materials in which altermagnetism can emerge from spontaneous orbital ordering rather than crystal symmetry. First-principles calculations reveal a layer-dependent spin splitting: if the spin and orbital orders align in adjacent layers, the system exhibits non-relativistic spin splitting, and thus altermagnetism. In contrast, if either the spin or the orbital order is reversed in adjacent layers, we observe a layerwise uncompensated spin splitting, that is compensated in the adjacent layer, giving rise to the concept of anti-altermagnetism. In the RP series, odd $n$ members support coexistence of altermagnetism and anti-altermagnetism, whereas even $n$ and the perovskite limit are strictly anti-altermagnetic. In both cases, larger $n$ favors metallicity, and in odd $n$ compounds strain can further stabilize altermagnetism.