Altermagnetism and Weak Magnetism in the Insulating Distorted Perovskite Antiferromagnet NaOsO₃

The GdFeO₃-type perovskite antiferromagnet NaOsO₃, calculated here to be altermagnetic for all three typical collinear antiferromagnetic orders, was suggested early on to be a Slater-type insulator, due in large part to its continuous metal-insulator transition and its small energy gap. Below the Néel temperature, the gap opens along with ``weak magnetism'', accompanied by a discontinuity in the magnetic susceptibility. Most other properties remain continuous. Without explicit correlation in the band structure calculation, and neglecting spin-orbit coupling (SOC), already a gap opens. Inclusion of a modest on-site Coulomb repulsion (U~ 1 eV) is sufficient to eliminate a SOC-induced small band overlap, reproducing the experimentally observed gap of several tens meV as reported earlier. This evidence supports the viewpoint that NaOsO₃ lies in an unusual crossover region between Slater and Mott insulator. The unreported altermagnetism in NaOsO₃ is demonstrated and its consequences are considered. The origin of the very weak magnetism has been investigated using a combination of { ab initio} calculations and symmetry analysis of the magnetic space group, confirming the origin lying in the Dzyaloshinskii-Moriya spin-orbit coupling buttressed by altermagnetic order. After determining the easy axis, our calculation leads to an Os spin canting angle of about 3∘, accounting for the observed weak magnetism and the resulting discontinuity in the susceptibility. The altermagnetism spin-split bands (up to ~100 meV) result in a chiral-split magnon spectrum in both acoustic and optical modes in the THz range, and lead to significant anomalous Hall conductivity upon hole doping.