Following recent intensive studies on altermagnetism (ALM) characterized by nonrelativistic even-parity spin splitting, realizing unconventional odd-parity magnetism has also attracted increasing interest. Here, using symmetry arguments based on spin-group analyses, we elucidate necessary conditions for the emergence of odd-parity spin splitting in collinear antiferromagnetic systems, which is further established as the standard odd-parity ALM. It is derived that the odd-parity ALM arises from the following criteria: (i) the breaking nonmagnetic time reversal symmetry (TRS), i.e., the breaking real-space TRS; (ii) the long-range collinear compensated magnetism; (iii) the symmetry $\left[C_2\right|\left|\overline{E}\right]$ or $\left[C_2\right|\left|M\right]$ connecting opposite-spin sublattices, where $C_2, \overline{E}$, and $M$, respectively, represent a ${180}^{\circ }$ rotation around the axis perpendicular to spins, the inversion, and the mirror reflection separating opposite-spin sublattices, directly reflecting the high-order harmonic ($l\ge 3$) and the $p$-wave ($l=1$) odd-parity ALM, respectively. Moreover, we utilize the well-known Haldane-Hubbard model to identify odd-parity spin splitting in the collinear ALM ground state, where (i) the nonmagnetic TRS is broken by opposite sublattice currents coming from the Haldane hopping; (ii) the symmetry $\left[C_2\right|\left|\overline{E}\right]$ is ensured because the currents flowing on opposite-spin sublattices are reversed.

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• Magnetism
• Altermagnets
• Magnetic systems
• Two-dimensional electron system
• Approximation methods for many-body systems
• Electron-correlation calculations
• Many-body techniques