Theory of spin-anisotropic electron-electron interactions in quasi-one-dimensional metals

We construct a theoretical model for one-dimensional conductors taking into account the effects of spin-dependent interactions due to spin-orbit or electronic dipole-dipole couplings. We show that a new type of interaction which does not conserve the z-component of the spin is generated, and that in the presence of time-reversal and inversion symmetry four different coupling constants are necessary to describe the most general case. The spin-dependence of the interactions is computed for spin-orbit and dipolar coupling. The use of bosonization and a renormalization group calculation allow us to obtain the correlation functions and the zero-temperature phase diagram of a strictly one-dimensional system. There is a gap in the spin excitations in the whole phase diagram which leads to fully anisotropic spin-density wave phases. The behaviour under a magnetic field is studied and we find a spin-flop transition. In order to describe quasi-one-dimensional systems we introduce an effective interchain coupling and treat it in the mean-field approximation. The phase diagram is qualitatively different in the cases of weak and strong anisotropy. We discuss possible experimental implications of our results. In particular, spin-orbit coupling leads to an easy axis parallel to the conducting chains, whereas for dipole-dipole interactions the easy axis is perpendicular to the chains.