Spinor Boltzmann equation with Berry curvature

In this paper, we study the influence of Berry curvature on spin-dependent transport in the system with spin-orbit coupling. The interaction of spin-orbit coupling in ferromagnets will induce a non-zero Berry curvature by breaking the time-reversal symmetry, which has effect on both charge and spin transport processes. We introduce the Berry curvature into spinor Boltzmann equation by modifying the effective velocity of electron, then derive the Berry curvature-concerned expressions for spin accumulation, spin current, and charge current, and investigate the influence of Berry curvature on the transport process. Comparisons are also made with the spinor Boltzmann equations which includes Rashba spin-orbit coupling but without Berry curvature.