Theory of spin polarization in mesoscopic spin–orbit coupling systems

We establish a general formalism of the bulk spin polarization (BSP) and the current-based spin polarization (CSP) for mesoscopic ferromagnetic and spin–orbit interaction (SOI) semiconducting systems. Based on this formalism, we reveal the basic properties of BSP and CSP and their relationships. The BSP describes the intrinsic spin polarized properties of devices. The CSP depends on both intrinsic parameters of device and the incident current. For the non-spin-polarized incident current with the in-phase spin-phase coherence, CSP equals to BSP. We give analytically the BSP and CSP of several typical nanodevice models, ferromagnetic nanowire, Rashba nanowire and rings. These results provide basic physical behaviors of BSP and CSP and their relationships.