The classification of collinear magnetic phases in analogy with atomic orbitals and superconducting pairings has long lacked a collinear $p$-wave counterpart—systems exhibiting linear-in-$k$ spin splitting (SS) without net magnetization or spin-orbit coupling. Here, we resolve this gap by identifying a class of compensated magnets, in which antiparallel spins occupy symmetry-inequivalent sites related by a mirror operation. We show that electric dipoles constrained by mirror symmetry enable a magnetoelectric coupling that produces $p$-wave off-centered Fermi surfaces. This mechanism also gives rise to an intrinsic spin and crystal Hall effects as well as directional anomalous Hall response, locked by symmetry to the mirror plane. We derive the enabling symmetry conditions, establish a hierarchy of electric multipolar contributions, and identify by inverse design five prototypical candidates, including the high-pressure triple perovskite ${\mathrm{Mn}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$ verified via first-principles calculations as a prototypical collinear $p$-wave magnet. Our results unify $s$-, $d$-, and $p$-wave collinear magnets and reveal mirror symmetry as a key ingredient for engineering SS in antiferromagnets.

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• Anomalous Hall effect
• Antiferromagnetism
• Magnetic order
• Magnetic texture
• Magnetoelectric effect
• Spin Hall effect
• Spintronics
• p-wave
• Altermagnets
• Antiferromagnets
• Spin