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

Altermagnetism, a new collinear magnetic state, has gained significant attention in the last few years, and the underlying mechanisms driving this quantum phase are still evolving. Going beyond the group theoretical analyses, which focus on providing a binary description of the presence or absence of the altermagnetic state, in this work, we explore the role of crystal chemical bonding. As the latter successfully integrates the crystal and orbital symmetries and is tunable, it provides a quantitative and realistic mechanism to explain the formation of altermagnetism. From the first principles calculations and tight-binding models within the framework of the linear combination of atomic orbitals on NiS, we establish a set of selection rules for the formation of altermagnetism in the NiAs prototype compounds (e.g. CrSb, MnTe, etc.). Broadly, if single orbitals from Ni and S sites are involved in the bonding, the second neighbor interaction between the nonmagnetic atoms is a must to modulate the intra-sublattice interactions differently for the opposite spin sublattices so that the antiferromagnetic sublattice band degeneracy is lifted and momentum-dependent altermagnetic spin split (AMSS) appears. However, when multiple orbitals are involved from the Ni and S sites in the chemical bonding, altermagnetism is naturally present. Together, they amplify the AMSS. Further, we propose twelve antinodal regions in the NiAs type hexagonal crystals, where AMSS split is maximum. Specific to NiS, AMSS increases with correlation, and for the edge valence and conduction bands, it can go beyond 1eV. The present study opens up new pathways to design chemical bonding driven selection rules in addition to the existing crystal symmetry criteria to tailor tunable altermagnetism.