An interplay between an applied strain and the Berry curvature reconstruction in the uniaxially strained monolayer MoS2 is explored that leads to the unbalanced Berry curvatures centered at K and -K points and, eventually, the valley magnetization under an external electric field. This is shown to explain a recent experimental observation of the valley magnetoelectric effect and develop a novel concept of the valley magnetic domain (VMD), i.e., a real-space homogeneous distribution of the valley magnetization. A realization of VMD guarantees a sufficient number of stable valley-polarized carriers, one of the most essential prerequisites of the valleytronics. Furthermore, we discover the anomalous electron dynamics through the VMD activation and achieve a manipulation of the anomalous transverse current perpendicular to the electric field, directly accessible to the signal processing [for instance, the current modulation under the VMD (i.e., the VMD wall) moving and the terahertz current rectification under the VMD switching]. This suggests a concept of VMD for use in providing new physical insight into the valleytronic functionality and its manipulation as a key ingredient of potential device applications.
Keywords: Valley magnetoelectric effect; anomalous transverse current; symmetry-broken transverse diode; valley Hall effect; valley magnetic domain.