  The two-dimensional (2D) multiferroic materials have widespread of
application prospects in facilitating the integration and miniaturization of
nanodevices. However, it is rarely coupling between the magnetic,
ferroelectric, and ferrovalley in one 2D material. Here, we propose a mechanism
for manipulating magnetism, ferroelectric, and valley polarization by
interlayer sliding in 2D bilayer material. Monolayer GdI2 exhibits a
ferromagnetic semiconductor with the valley polarization up to 155.5 meV. More
interestingly, the magnetism and valley polarization of bilayer GdI2 can be
strongly coupled by sliding ferroelectricity, appearing these tunable and
reversible. In addition, we uncover the microscopic mechanism of magnetic phase
transition by spin Hamiltonian and electron hopping between layers. Our
findings offer a new direction for investigating 2D multiferroic in the
implication for next-generation electronic, valleytronic, and spintronic
devices.
