Exploration of surface oriented altermagnetic states in CrTe, FeSband MnO: a first-principles study.

The present work explores the influence of altermagnetism (AM) on the electronic structure of materials, specifically focusing on the emergence of non-relativistic spin splitting. We demonstrate that the-path dependence of altermagnetic spin splitting in the 3D Brillouin zone exhibits distinct altermagnetic surface states due to specific surface orientations. We considered three types of crystal systems (hexagonal, orthorhombic and tetragonal), to unveil the altermagnetic properties of these surface states. We calculated the two-dimensional projected Brillouin zones from the bulk and analyzed the interaction between these surface Brillouin zones and the k-dependent spin splitting. This analysis identifies the surfaces where opposite-sign spin splitting merges, nullifying AM and the surfaces where AM is preserved. Our investigation across the three principal surface orientations reveals that for several cases, two surfaces exhibit blindness to the AM, while the remaining surface retains altermagnetic properties. This dependence on surface orientation is further influenced by the specific magnetic order within the material. Finally, we demonstrate that the density of states of the majority and minority spins then governs the tunneling magnetoresistance. Additionally, we have calculated a anomalous Hall conductivity within density functional theory. Therefore, our work provides a framework for understanding and tailoring surface related AM, paving the way for potential applications in spintronics and modern quantum techniques.