Spin-density-wave instabilities in the organic conductor (TMTSF)_2ClO_4: Role of anion ordering

We study the spin-density-wave instabilities in the quasi-one-dimensional conductor (TMTSF)_2ClO_4. The orientational order of the anions ClO_4 doubles the unit cell and leads to the presence of two electrnic bands at the Fermi level. From the Ginzburg-Landau expansion of the free energy, we determine the low-temperature phase diagram as a function of the strength of the Coulomb potential due to the anions. Upon increasing the anion potential, we first find a SDW phase corresponding to an interband pairing. This SDW phase is rapidly supressed, the metallic phase being then stable down to zero temperature. The SDW instability is restored when the anion potential becomes of the order of the hopping amplitude. The metal-SDW transition corresponds to an intraband pairing which leaves half of the Fermi surface metallic. At lower temperature, a second transition, corresponding to the other intraband pairing, takes place and opens a gap on the whole Fermi surface. We discuss the consequences of our results for the experimental phase diagram of (TMTSF)_2ClO_4 at high magnetic field.Comment: 13 pages, 10 figures, Version 2 with minor correction