Altermagnetism in the orthorhombic Pnma structure through group theory and DFT calculations

Antiferromagnetism, initially considered interesting but useless, recently emerged as one of the most promising magnetic phases for technology. Recently, a low-symmetry antiferromagnetic phase, known as altermagnetic phase, has been discovered, where no time-reversal $(\mathcal{T})$ symmetry is observed in spite of a vanishing net magnetization, leading to nondegenerate bands from the opposite magnetic sublattices. In this work, we consider two representatives of orthorhombic $Pnma$ space group, namely, ${\mathrm{BiFeO}}_{3}$ and ${\mathrm{CaMnO}}_{3}$, and find the altermagnetic lowest-energy phase in both from our density functional theory calculations. We find a substantial spin-splitting in both systems along a high-symmetry path in the Brillouin zone without considering the spin-orbit interaction (SOI). Detailed features of the band dispersion obtained from our calculation confirm the lifting of sublattice spin degeneracy only in the ${k}_{x}=0$ plane while preserving the spin degeneracy in the other planes of the Brillouin zone. We provide a comprehensive symmetry analysis based on the magnetic space group (MSG) to explain our DFT findings and an insightful symmetry-allowed model Hamiltonian, which qualitatively agrees with our results. Additionally, we extend our symmetry analysis to encompass two other potential MSGs within the $Pnma$ space group that may host the spin-splitting phenomenon without considering SOI and the likely form of their Hamiltonian. Our calculations considering SOI reveal weak ferromagnetism in both systems. The detailed studies presented here pave the way for a deeper understanding of the spin-splitting phenomena within the $Pnma$ space group, offering insights into the intricate interplay between symmetry and electronic as well as magnetic properties.