In the absence of spin-orbit coupling, collinear magnets are classified as even-wave magnets, i.e., either ferromagnets, antiferromagnets, or altermagnets. It is based on the belief that collinear magnets always feature an inversion-symmetric band structure, which forbids odd-parity magnetism. Here, we show that collinear magnets, which break time-reversal symmetry in the nonmagnetic sector, e.g., through loop currents, can have an inversion-symmetry-broken band structure and lead to unconventional types of collinear magnets. Hence, collinear odd-parity magnets do exist, and we explain that a magnetic field-induced Edelstein effect is their unique signature. We propose minimal models based on the coexistence of antiferromagnet order with compensated loop current orders for all types of collinear magnets. Our Letter provides a new perspective on collinear magnets and the spin-space group classification.

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• Fermi surface
• Magnetism
• Spin accumulation
• Spin current
• Spintronics
• Altermagnets
• Antiferromagnets
• Ferrimagnets
• Ferromagnets
• Magnetic systems
• Band structure methods
• Bloch wave theory
• Tight-binding model