Tunable abundant valley Hall effect and chiral spin–valley locking in Janus monolayer VCGeN ₄

It is both conceptually and practically fascinating to explore fundamental research studies and practical applications of two-dimensional systems with the tunable abundant valley Hall effect. In this work, based on first-principles calculations, the tunable abundant valley Hall effect is proved to appear in Janus monolayer VCGeN₄. When the magnetization is along the out-of-plane direction, VCGeN₄ is an intrinsic ferromagnetic semiconductor with a valley feature. The intriguing spontaneous valley polarization exists in VCGeN₄ due to the common influence of broken inversion and time-reversal symmetries, which makes it easier to realize the anomalous valley Hall effect. Furthermore, we observe that the valley-non-equilibrium quantum anomalous Hall effect is driven by external strain, which is located between two half-valley-metal states. When reversing the magnetization, the spin flipping makes the position of the edge state to change from one valley to another valley, demonstrating an intriguing behavior known as chiral spin-valley locking. Although the easy magnetic axis orientation is along the in-plane direction, we can utilize an external magnetic field to transform the magnetic axis orientation. Moreover, it is found that the valley state, electronic and magnetic properties can be well regulated by the electric field. Our works explore the mechanism of the tunable abundant valley Hall effect by applying an external strain and electric field, which provides a perfect platform to investigate the spin, valley, and topology.