Effect of non-uniform exchange field in ferromagnetic graphene

We have presented here the consequences of the non-uniform exchange field on the spin transport issues in spin chiral configuration of ferromagnetic graphene. Taking resort to the spin-orbit coupling (SOC) term and non-uniform exchange coupling term we are successful to express the expression of Hall conductivity in terms of the exchange field and SOC parameters through the Kubo formula approach. However, for a specific configuration of the exchange parameter we have evaluated the Berry curvature of the system. We also have paid attention to the study of SU(2) gauge theory of ferromagnetic graphene. The generation of anti damping spin-orbit torque in spin chiral magnetic graphene is also briefly discussed.