Valley Hall Effect and Magnetic Moment in Magnetized Silicene

We investigate the physical properties of silicene with both staggered sublattice potential and magnetization by using Kubo formalism, the latter arises from the magnetic proximity effect by depositing Fe atoms to silicene or depositing silicene on an appropriate ferromagnetic insulator. Based on the low-energy continuum model of the system where inversion symmetry is broken, we show that the system exhibits spin half metal state when staggered sublattice potential is in the same magnitude with mean and staggered magnetization. Besides, Hall conductivity and magnetic moment are all valley dependent, so we investigate the valley Hall effect of the system further by considering magnetization exclusively. This means carriers in different valleys turning into opposite directions transverse to an in-plane electric field. At last, we prove these results by investigating Berry curvature that characterizing Hall transport, which is also valley dependent. These effects can be used to generate valley-polarized currents solely by magnetization, forming the basis for the valley-based electronics applications.