We first propose the nonlinear spin Hall effect of light (SHEL) and MOSHEL (magneto optic spin Hall effect of light) through a multilayer with graphene and nonlinear substrate (NLS) in terahertz region. The MO transfer matrix method is modified to calculate the SHEL shift in a nonlinear system. The NLS brings bistable characteristics for SHEL in which nonlinear splitting of left-handed circularly polarized (LHCP) and right-handed circularly polarized (RHCP) components can be observed. The Faraday rotation of light in terahertz region causes the asymmetrical SHEL shifts distribution of LHCP and RHCP components. Meanwhile the MO effect of graphene brings modulations for nonlinear SHEL and MOSHEL which provide us new and flexible methods to control spatial light field distribution. In addition, as the delay effect causes the chaos of bistable state system, the SHEL shift can be used as a quantum point for the chaos phenomenon.
