Ferromagnetic correlations in quasi-one-dimensional conducting channels

We propose a model that explains the experimental observation of spontaneous spin polarization of conducting electrons in quasi-one-dimensional ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}/\mathrm{GaAs}$ channels [K. J. Thomas, J. T. Nicholls, M. Y. Simmons, M. Pepper, D. R. Mace, and D. A. Ritchie, Phys. Rev. Lett. 77, 135 (1996); K. J. Thomas, J. T. Nicholls, M. J. Appeyard, M. Y. Simmons, M. Pepper, D. R. Mace, W. R. Tribe, and D. A. Ritchie, Phys. Rev. B 58, 4846 (1998)]. We show that a ferromagnetic order is a generic property of a quasi-one-dimensional conducting channel embedded in a Wigner crystal. We also discuss gate voltage, magnetic field, and temperature dependences of the channel's conductance.