Exploring Altermagnetism in Orthorhombic PnmaPnma 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, have been discovered, where no time reversal ($\mathcal{T}$) symmetry is observed in spite of a vanishing net magnetization, leading to non-degenerate bands from the opposite magnetic sublattices. In this work, we consider two representatives of orthorhombic $Pnma$ space group, namely, BiFeO$_3$ and CaMnO$_3$ and find 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 $k_y$-$k_z$ 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. These detailed studies 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.Comment: 10 pages, 6 figure

Antiferromagnetism, spin splitting, and spin-orbit interaction in MnTe

Hexagonal MnTe emerges as a critical component in designing magnetic quantum heterostructures, calling for a detailed study. After finding a suitable combination of exchange-correlation functional and corrections, our study within {\em ab initio} density functional theory uncovers an insulating state with a preferred antiferromagnetic order. We compute the exchange interaction strengths to estimate the antiferromagnetic ordering temperature via Monte Carlo calculations. Our calculations and symmetry analysis reveal a large spin splitting in the system due to the antiferromagnetic order without considering spin-orbit interaction, except in the $k_x$-$k_y$ plane. Critically examining the band dispersion and spin textures obtained from our calculations and comparing them with an insightful symmetry analysis and analytical model, we confirm a combined Rashba-Dresselhaus interaction in the $k_x$-$k_y$ plane, around the K point of the system. Finally, we find ferroelectricity in the system for a higher energy magnetic configuration. Our results and insights would help design heterostructures of MnTe for technological applications.Comment: 10 pages, 6 figure