Diffusion equation and spin drag in spin-polarized transport

We study the role of electron-electron interactions for spin-polarized transport using the Boltzmann equation, and derive a set of coupled transport equations. For spin-polarized transport the electron-electron interactions are important, because they tend to equilibrate the momentum of the two-spin species. This “spin drag” effect enhances the resistivity of the system. The enhancement is stronger the lower the dimension is, and should be measurable in, for example, a two-dimensional electron gas with ferromagnetic contacts. We also include spin-flip scattering, which has two effects: it equilibrates the spin density imbalance and, provided it has a non-$s$-wave component, also a current imbalance.