Spin conductivity of gapped graphene

Spin conductivity of gapped graphene using Hubbard model is calculated. We obtain spin conductivity for two cases, the first we ignore coulomb interaction between electrons and the second in presence of coulomb interaction between electrons. It can be seen that for nonitercting case, by increasing the energy gap and magnetization, the spin conductivity in a constant frequency is increased. In interacting case plots of spin conductivity versus frequency have two peaks. One of them belongs to spin up electrons and the other belongs to spin down electrons. By increasing magnetization the peaks of spin up electrons will be shifted towards lower frequencies and the peaks of spin down electrons will be shifted towards higher frequencies. By increasing the repulsion coulomb interaction and the energy gap, spin up and spin down peaks will be shifted towards higher frequencies.