Spin-dependent scattering in magnetized Luttinger liquids

For a magnetized one-dimensional Luttinger liquid (LL) we study the influence of spin-dependent scattering from a localized magnetization inhomogeneity caused, e.g. by a local external magnetic field. Two cases are considered: (i) a uniformly magnetized LL close to an external magnetic tip that scatters the electrons and (ii) a LL with two domains, one paramagnetic and the other ferromagnetic. A renormalization group treatment of electron interactions yields scaling equations for the transmission and reflection amplitudes. For repulsive interactions we find two possible zero temperature insulator fixed points: one in which the carriers are reflected in the same spin channel and another where the electron spin is reversed upon reflection, leading to a finite spin current and vanishing charge current under a small voltage bias. In case (ii) we find the “spin–flip-insulating” regime to be stabilized by a pure potential scattering as caused, e.g. by impurities.