Valleytronics in two-dimensional magnetic materials

Abstract Valleytronics uses valleys, a novel quantum degree of freedom, to encode information. It combines other degrees of freedom, such as charge and spin, to produce a more comprehensive, stable, and efficient information processing system. Valleytronics has become an intriguing field in condensed matter physics due to the emergence of new two-dimensional materials in recent years. However, in nonmagnetic valleytronic materials, the valley polarization is transient and the depolarization occurs once the external excitation is withdrawn. Introduction of magnetic field is an effective approach to realizing the spontaneous valley polarization by breaking the time-reversal symmetry. In hexagonal magnetic valleytronic materials, the inequivalent valleys at the K and – K ( K ′) Dirac cones have asymmetric energy gaps and Berry curvatures. The time-reversal symmetry in nonmagnetic materials can be broken by applying an external magnetic field, adding a magnetic substrate or doping magnetic atoms. Recent theoretical studies have demonstrated that valleytronic materials with intrinsic ferromagnetism, now termed as ferrovalley materials, exhibit spontaneous valley polarization without the need for external fields to maintain the polarization. The coupling of the valley and spin degrees of freedom enables stable and unequal distribution of electrons in the two valleys and thus facilitating nonvolatile information storage. Hence, ferrovalley materials are promising materials for valleytronic devices. In this review, we first briefly overview valleytronics and its related properties, the ways to realize valley polarization in nonmagnetic valleytronic materials. Then we focus on the recent developments in two-dimensional ferrovalley materials, which can be classified according to their molecular formula and crystal structure: MX 2 ; M(XY) 2 , M(XY 2 ) and M(XYZ) 2 ; M 2 X 3 , M 3 X 8 and MNX 6 ; MNX 2 Y 2 , M 2 X 2 Y 6 and MNX 2 Y 6 ; and the Janus structure ferrovalley materials. In the inequivalent valleys, the Berry curvatures have opposite signs with unequal absolute values, leading to anomalous valley Hall effect. When the valley polarization is large, the ferrovalleys can be selectively excited even with unpolarized light. Intrinsic valley polarization in two-dimensional ferrovalley materials is of great importance. It opens a new avenue for information-related applications and hence is under rapid development.