Altermagnetism, an unconventional 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 intrasublattice interactions differently for the opposite spin sublattices so 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 12 antinodal regions in the NiAs type hexagonal crystals, where AMSS is maximum. The electron correlation can tune the AMSS. Specific to NiS, for the edge valence band, the AMSS increases with correlation and can go beyond 1eV. The present study opens pathways to design chemical bonding driven selection rules in addition to the existing crystal symmetry criteria to tailor tunable altermagnetism.

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• Altermagnetism
• Electronic structure
• Density functional calculations
• Tight-binding model