This paper presents minimal models for alternagnetism, a new class of magnetic order characterized by vanishing net magnetization and time-reversal symmetry breaking. Alternagnets exhibit momentum-dependent spin-split band structures and are distinct from both conventional ferromagnets and antiferromagnets. The authors construct tight-binding models for non-symmorphic space groups with a sublattice defined by two magnetic atoms, applicable to monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic materials. These models describe d-wave, g-wave, and i-wave alternagnetism and reveal alternagnetic ground states with Berry curvature linear in spin-orbit coupling. The models are applied to materials such as RuO₂, MnF₂, FeSb₂, κ-Cl, CrSb, and MnTe. The authors examine alternagnetic susceptibility and mean field instabilities within a Hubbard model, showing that these models yield alternagnetic ground states and a Berry curvature linear in spin-orbit coupling. The minimal models are shown to capture key properties of the band structure and magnetic spin splittings, and provide a general analytic expression for the SOC-derived Berry curvature. The models are applied to various materials, demonstrating their versatility in describing alternagnetism across different crystal structures and wave types. The paper also discusses the role of SOC in the Berry curvature and the crystal Hall effect, and highlights the importance of band degeneracies in stabilizing alternagnetism. The results suggest that alternagnetism can be stabilized by band engineering or optimization of the electromagnetic order parameter.This paper presents minimal models for alternagnetism, a new class of magnetic order characterized by vanishing net magnetization and time-reversal symmetry breaking. Alternagnets exhibit momentum-dependent spin-split band structures and are distinct from both conventional ferromagnets and antiferromagnets. The authors construct tight-binding models for non-symmorphic space groups with a sublattice defined by two magnetic atoms, applicable to monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic materials. These models describe d-wave, g-wave, and i-wave alternagnetism and reveal alternagnetic ground states with Berry curvature linear in spin-orbit coupling. The models are applied to materials such as RuO₂, MnF₂, FeSb₂, κ-Cl, CrSb, and MnTe. The authors examine alternagnetic susceptibility and mean field instabilities within a Hubbard model, showing that these models yield alternagnetic ground states and a Berry curvature linear in spin-orbit coupling. The minimal models are shown to capture key properties of the band structure and magnetic spin splittings, and provide a general analytic expression for the SOC-derived Berry curvature. The models are applied to various materials, demonstrating their versatility in describing alternagnetism across different crystal structures and wave types. The paper also discusses the role of SOC in the Berry curvature and the crystal Hall effect, and highlights the importance of band degeneracies in stabilizing alternagnetism. The results suggest that alternagnetism can be stabilized by band engineering or optimization of the electromagnetic order parameter.