Magnetism and Transport for Two-Dimensional Electrons: Absence of Stoner Ferromagnetism and Positive In-Plane Magnetoresistance in the Metallic Phase

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We calculate the interaction kernel K for two-dimensional diffusive electrons. The screening of the Coulomb interaction together with the Fermi statistics induces a spin selection rule for electron-electron scattering so that in leading order in the inverse conductance only pairs of electrons with antiparallel spins do scatter. At low temperature, this results in a larger coherence length for fully polarized electrons and thus in a positive in-plane magnetoresistance. An applied in-plane magnetic field also induces a nonmonotonous behavior of K at finite temperature. Alternatively, the vanishing of the scattering in the triplet channel strongly reduces ferromagnetism deep in the metallic regime. These effects weaken as the density of charge carriers is reduced.