Since electrons have an internal degree of freedom, spin, they are characterized not only by charge density and electric current, but also by spin density and spin current. The spin current is described by a tensor$$q:{ij}$$, where the first index indicates the direction of flow, while the second one says which component of the spin is flowing.
CITATION STYLE
Dyakonov, M. I., & Khaetskii, A. V. (2017). Spin Hall Effect. In Springer Series in Solid-State Sciences (Vol. 157, pp. 241–280). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-319-65436-2_8
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