External-field-induced transition from altermagnetic metal to fully-compensated ferrimagnetic metal in monolayer $\mathrm{Cr_2O}$

Abstract: 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 $\mathrm{Cr_2O}$ as a concrete example to validate our proposal. Either electric field or uniaxial strain can break the $S_{4z}$ symmetry of $\mathrm{Cr_2O}$, 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.