  Silicene is a competitive and promising 2D material, possessing interesting
topological, electronic and optical properties. The presence of strong spin
orbit interaction in silicene and its analogues, germanene and tinene, leads to
the opening of a gap in the energy spectrum and spin-splitting of the bands in
each valley. We develop a general method to determine the magneto-optic
response of silicene, when a Gaussian beam is incident on silicene grown on a
dielectric substrate in the presence of a static magnetic field. We use a
semiclassical treatment of silicene monolayer to describe the Faraday rotation
(FR) and Magneto-optical Kerr effect (MOKE) using a general model for beam
propagation. The response can be modulated both electrically and magnetically.
We derive analytic expressions for valley and spin polarized FR and MOKE for
arbitrary polarization of incident light in the terahertz regime. We
demonstrate that large FR and MOKE can be achieved by tuning the electric
field, magnetic fields and chemical potential in these fascinating 2D
materials. Implications for novel valleytronic experiments are also discussed.
