The $A$-site magnetic spinel ${\mathrm{Co}}_3{\mathrm{O}}_4$ exhibits a simple Néel-type collinear antiferromagnetic ordering below $T_N=30$ K, accompanied by a strong linear magnetoelectric effect. Here, we report magnetization and electric polarization measurements on single crystals of ${\mathrm{Co}}_3{\mathrm{O}}_4$ up to high magnetic fields. We show that the magnetoelectric polarization undergoes a crossover from linear to nonlinear behavior with increasing magnetic field, followed by complete suppression upon reaching the field-polarized ferromagnetic state, where inversion symmetry is recovered. Our microscopic spin model, reproducing the observed field evolution of the magnetoelectric response, evidences weak anisotropy that is crucial for the effective magnetoelectric control of the antiferromagnetic state [Phys. Rev. Lett. 135, 126704 (2025)].

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• Electric polarization
• High magnetic fields
• Magnetic order
• Magnetism
• Magnetoelectric effect
• Antiferromagnets
• Spinels
• Transition metal oxides
• Magnetization measurements