Realizing spontaneous valley polarization and topological phase transitions in monolayer ScX2 (X = Cl, Br, I)

Manipulating the valley degree of freedom besides the charge and spin has attracted increasing interest in fundamental sciences and emerging applications. In this study, the monolayer ScX ₂ (X = Cl, Br, I) magnetic semiconductors are reported by varying halide elements. Unexpectedly, monolayer ScCl ₂ is none of ferrovalley property, but both monolayer ScBr ₂ and ScI ₂ show obvious valley polarization owing to the joint effects of magnetic exchange interaction and spin–orbit coupling. However, both monolayer ScBr ₂ and ScI ₂ show an in-plane easy axis of magnetization, leading to lose spontaneous valley polarization. Herein, two means of tensile strain and charge doping are explored to obtain spontaneous valley polarization by regulating ferrovalley property and the direction of magnetization axis in monolayer ScBr ₂ and ScI ₂ . Interestingly, topological phase transitions from ferrovalley, half-valley metals to quantum anomalous Hall effect states appear with the increase of strain in monolayer ScBr ₂ and ScI ₂. The topologically nontrivial band gap of monolayer ScI ₂ is larger than that of monolayer ScBr ₂. After hole doping, the easy magnetization axis turns out-of-plane and the ferrovalley characteristic remains in the monolayer ScI ₂, thereby resulting in spontaneous valley polarization. Notably, 0.1 holes per f.u. doping in the present monolayer ScI ₂ corresponds to the carrier doping density is around 1.44 × 10 ¹⁴ cm ⁻², which can be achieved in Hall devices through available gate techniques.