  The valley degrees of freedom of carriers in crystals is useful to process
information and perform logic operations, and it is a key factor for valley
application to realize the valley polarization. Here, we propose a model that
the valley polarization transition at different valley points (-K and K points)
is produced by biaxial strain. By the first-principle calculations, we
illustrate our idea with a concrete example of Janus $\mathrm{GdClF}$
monolayer. The predicted $\mathrm{GdClF}$ monolayer is dynamically,
mechanically and thermally stable, and is a ferromagnetic (FM) semiconductor
with perpendicular magnetic anisotropy (PMA), valence band maximum (VBM) at
valley points and high Curie temperature ($T_C$). Due to its intrinsic
ferromagnetism and spin orbital coupling (SOC), a spontaneous valley
polarization will be induced, but the valley splitting is only -3.1 meV, which
provides an opportunity to achieve valley polarization transition at different
valley points by strain. In considered strain range ($a/a_0$: 0.94$\sim$1.06),
the strained GdClF monolayer has always energy bandgap, strong FM coupling and
PMA. The compressive strain is in favour of -K valley polarization, while the
tensile strain makes for K valley polarization. The corresponding valley
splitting at 0.96 and 1.04 strain are -44.5 meV and 29.4 meV, which are higher
than the thermal energy of room temperature (25 meV). Due to special Janus
structure, both in-plane and out-of-plane piezoelectric polarizations can be
observed. It is found that the direction of in-plane piezoelectric
polarizations can be overturned by strain, and the $d_{11}$ at 0.96 and 1.04
strain are -1.37 pm/V and 2.05 pm/V. Our works pave the way to design the
ferrovalley material as multifunctional valleytronics and piezoelectric devices
by strain.
