Electric-field-induced fully-compensated ferrimagnetism in experimentally synthesized monolayer MnSe

Owing to their inherent characteristics of zero stray field and terahertz dynamics, two-dimensional (2D) zero-net-magnetization magnets demonstrate the potential for miniaturization, ultradensity and ultrafast performance. Recently, fully-compensated ferrimagnet of 2D zero-net-magnetization magnets has already attracted attention, as it can exhibit global spin-splitting, magneto-optical response and anomalous Hall effect [\textcolor[rgb]{0.00,0.00,1.00}{Phys. Rev. Lett. 134, 116703 (2025)}]. Therefore, it is very important to provide experimentally feasible strategies and materials to achieve fully-compensated ferrimagnets. Here, we use the experimentally synthesized A-type $PT$-antiferromagnet (the joint symmetry ($PT$) of space inversion symmetry ($P$) and time-reversal symmetry ($T$)) MnSe as the parent material to induce fully-compensated ferrimagnetism through an out-of-plane electric field. This electric field can remove the $P$ symmetry of the lattice, thereby breaking the $PT$ symmetry and inducing spin-splitting. When considering spin-orbital coupling (SOC), MnSe with an out-of-plane magnetization can achieve the anomalous valley Hall effect (AVHE). In addition, we also discuss inducing fully-compensated ferromagnetism via Se vacancies and Janus engineering. Our works can promote the further development of 2D fully-compensated ferrimagnets both theoretically and experimentally.