  Coexistence of ferromagnetism, piezoelectricity and valley in two-dimensional
(2D) materials is crucial to advance multifunctional electronic technologies.
Here, Janus ScXY (X$\neq$Y=Cl, Br and I) monolayers are predicted to be
in-plane piezoelectric ferromagnetic (FM) semiconductors with dynamical,
mechanical and thermal stabilities. The predicted piezoelectric strain
coefficients $d_{11}$ and $d_{31}$ (absolute values) are higher than ones of
most 2D materials. Moreover, the $d_{31}$ (absolute value) of ScClI reaches up
to 1.14 pm/V, which is highly desirable for ultrathin piezoelectric device
application. To obtain spontaneous valley polarization, charge doping are
explored to tune the direction of magnetization of ScXY. By appropriate hole
doping, their easy magnetization axis can change from in-plane to out-of-plane,
resulting in spontaneous valley polarization. Taking ScBrI with 0.20 holes per
f.u. as a example, under the action of an in-plane electric field, the hole
carriers of K valley turn towards one edge of the sample, which will produce
anomalous valley Hall effect (AVHE), and the hole carriers of $\Gamma$ valley
move in a straight line. These findings could pave the way for designing
piezoelectric and valleytronic devices.
