Time-reversal symmetry breaking and spin-splitting phenomena, based exclusively on spin group symmetry, have been prominent topics in condensed matter physics. Until recently, magnetic materials have been classified into ferromagnetic and antiferromagnetic materials. Altermagnetism represents a newly discovered magnetic phase, characterized by zero net magnetization, similar to antiferromagnetic materials, and strong spin-dependent phenomena associated with ferromagnetic ones. The broken time-reversal symmetry in the altermagnets originates from crystal symmetries without requiring strong spin-orbit interaction. Lifting of spin degeneracy is a consequence of the preserved nonrelativistic spin group, defining the altermagnetic phase. A study of cobalt sulfide in NiAs and wurtzite phases reveals the spin momentum locked bands across off-symmetric regions in the Brillouin zone and transition temperature near room temperature. Another important consideration is the electronic correlation that influences both the electronic structure and the magnitude of spin splitting along the off-nodal lines in both atomic phases. Our findings demonstrate that CoS exhibits unconventional spin polarization order and altermagnetism phase indicating significant potential for broad theoretical and experimental research.

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• Crystal symmetry
• 3-dimensional systems
• Altermagnets
• Spin
• Density functional theory
• Hubbard model