Antiferromagnetic states which break inversion symmetry are able to host odd-parity spin splittings, in analogy to altermagnets. Here we study the emergence of these inversion-asymmetric antiferromagnet (IA AFM) states via an itinerant mechanism in nonsymmorphic systems with two magnetic ions per unit cell. We identify the symmetries that allow mixed-parity irreducible representations for commensurate ordering vectors, and hence permit a continuous transition into the IA AFM. The Landau free energy which describes the transition is derived from a general microscopic model, from which we establish conditions favorable to the appearance of the IA AFM: inversion is not a site symmetry of a magnetic ion, and the nesting involves different bands. Moreover, the odd-parity spin splitting is negatively correlated with the stability of the IA AFM. We illustrate our conclusions with specific examples. The insight into the IA AFM provided by our work can guide the identification of candidate materials.

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• Antiferromagnetism
• Hubbard model
• Tight-binding model