Altermagnets and fully compensated ferrimagnets are two canonical classes of zero-net-moment magnets. An altermagnetic (AM) half-metal cannot exist due to its AM spin splitting, while a fully compensated ferrimagnetic (FC-FIM) metal seems impossible to realize because both spin channels remain gapless. Here, we propose that an FC-FIM metal can be realized by breaking the rotational or mirror symmetry that links two spin-opposite magnetic atoms in an AM metal. We further demonstrate that charge-carrier doping is fundamentally unable to generate a net magnetic moment in an altermagnet, whereas such a net moment can be readily induced in a fully compensated ferrimagnet. We use the AM monolayer ${\mathrm{Cr}}_2\mathrm{O}$ as a concrete example to validate our proposal. Either electric field or uniaxial strain can break the $S_{4z}$ symmetry of ${\mathrm{Cr}}_2\mathrm{O}$, thereby inducing a transition from an AM metal to an FC-FIM metal. Uniaxial strain plus carrier doping creates a net moment in an altermagnet, and the so-called piezomagnetism is essentially a strain-driven switch from altermagnetism to fully compensated ferrimagnetism. By analogy, we advance the concept of electromagnetism: an electric field drives the transition from altermagnetism to fully compensated ferrimagnetism, and subsequent charge-carrier doping stabilizes a net magnetization. Our work provides a roadmap for further exploring the connection and distinction between altermagnet and fully compensated ferrimagnet, and confirms the feasibility of FC-FIM metal.

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• Electronic structure
• Magnetism
• Altermagnets
• First-principles calculations