Interplay between altermagnetism and nonsymmorphic symmetries generating large anomalous Hall conductivity by semi-Dirac points induced anticrossings

We investigate the interplay between altermagnetic spin-splitting and nonsymmorphic symmetries using the space group No. 62 as a testbed. Studying different magnetic orders by means of first-principles calculations, we find that the altermagnetism (AM) is present in the $C$-type magnetic configuration while it is absent for the $G$-type and $A$-type configurations due to different magnetic space group types. The nonsymmorphic symmetries constrain the system to a fourfold degeneracy at the border of the Brillouin zone with semi-Dirac dispersion. In the case of large hybridization as for transition metal pnictides, the interplay between AM and nonsymmorphic symmetries generates an intricate network of several crossings and anticrossings that we describe in terms of semi-Dirac points and glide symmetries. When we add the spin-orbit coupling (SOC), we find a N\'eel-vector dependent spin-orbit splitting at the time-reversal invariant momenta points since the magnetic space groups depend on the N\'eel vector. The magnetic space group type I produces antiferromagnetic hourglass electrons that disappear in the type III. When the N\'eel vector is along $x$, we observe a glide-protected crossing that could generate a nodal line in the altermagnetic phase. The SOC splits the remaining band crossings and band anticrossings, producing a large anomalous Hall effect in all directions excluding the N\'eel-vector direction.