Deterministic role of chemical bonding in the formation of altermagnetism: Reflection from correlated electron system NiS

Altermagnetism, a new collinear magnetic state that has traits of both ferromagnetism and antiferromagnetism, has gained significant attention in the last few years and the underlying mechanisms driving this quantum phase are still evolving. Going beyond the phenomenological models and group theoretical analyses, which focus on providing a binary explanation of the presence or absence of the altermagnetic state, in this work, we explored the role of crystal chemical bonding. As the latter successfully integrates the crystal and orbital symmetries and is tunable, it provides a quantitative and more realistic mechanism to explain the formation of altermagnetism. From the first principle calculations and tight-binding models within the framework of the linear combination of atomic orbitals on NiS, belonging to the hexagonal NiAs family (e.g. CrSb, MnTe, etc.), we reveal that the second neighbor interaction between the orbitals of the non-magnetic atoms is the most deterministic in inducing altermagnetism. These second-neighbor bondings modulate the intra-sublattice interactions differently for the opposite spin sublattices. As a consequence, the antiferromagnetic sublattice band degeneracy is lifted and it results in momentum dependent altermagnetic spin split (ASS). We further reveal that the strong altermagnetism is observed in these materials due to the participation of multiple and selective orbitals, both from Ni and S, in the chemical bonding. We proposed twelve antinodal regions in the NiAs type hexagonal crystals, where ASS split is maximum. Specific to NiS, ASS increases with correlation, and for the edge valence and conduction bands it can go beyond 1eV, which makes this compound ideal for carrying out altermagnetic experiments and for exploring non-trivial quantum transport through electron and hole doping. The present study opens up new pathways to tailor tunable altermagnetism.