Luttinger-compensated bipolarized magnetic semiconductor

Altermagnetic materials, with real-space antiferromagnetic arrangement and reciprocal-space anisotropic spin splitting, have attracted much attention. However, the spin splitting is small in most altermagnetic materials, which is a disadvantage to their application in electronic devices. In this study, based on symmetry analysis and the first-principles electronic structure calculations, we predict two Luttinger compensated bipolarized magnetic semiconductors $\mathrm{Mn}{(\mathrm{CN})}_{2}$ and $\mathrm{Co}{(\mathrm{CN})}_{2}$ with $s$-wave spin splitting as in the ferromagnetic materials. Our further analysis shows that the Luttinger compensated magnetism here depends not only on spin group symmetry, but also on the crystal field splitting and the number of $d$-orbital electrons. In addition, the polarized charge density indicates that both $\mathrm{Mn}{(\mathrm{CN})}_{2}$ and $\mathrm{Co}{(\mathrm{CN})}_{2}$ have the quasisymmetry $\mathrm{T}\ensuremath{\tau}$, resulting from the crystal field splitting and the number of $d$-orbital electrons. The Luttinger compensated magnetism not only has the zero total magnetic moment as the antiferromagnetism, but also has the $s$-wave spin splitting as the ferromagnetism, thus our work not only provides theoretical guidance for searching Luttinger compensated magnetic materials with distinctive properties, but also provides a material basis for the application in spintronic devices.