  Valley-related multiple Hall effect in two-dimensional lattice is of notable
interest both for its fundamental physics and for its potential applications.
In this work, by means of a low energy kp model analysis, a mechanism of
producing valley-related multiple Hall effect in hexagonal lattice via strain
engineering is proposed, and a general picture of valley-contrasted band
inversion is developed. Through first-principles calculations, this mechanism
is further established in a ferromagnetic hexagonal lattice of single-layer
ScI2. Single-layer ScI2 prefers in-plane magnetization and exhibits neither
anomalous valley Hall effect nor valley-polarized quantum anomalous Hall effect
in nature. Remarkably, these two Hall effects emerge simultaneously in this
system under 4.705% tensile strain and disappear simultaneously when further
increasing strain, suggesting the exotic valley-related multiple Hall effect.
The underlying physical mechanism is revealed using a model analysis and is
generally applicable. Our work greatly enriches the valley-related physics.
