Competing SDW phases and quantum oscillations in (TMTSF)$_2$ClO$_4$ in magnetic field

We propose a new approach for studying spin density waves (SDW) in the Bechgaard salt (TMTSF) 2 ClO 4 where lattice is dimerized in transverse direction due to anion ordering. The SDW response is calculated in the matrix formulation that rigorously treats the hybridization of inter-band and intra-band SDW correlations. Since the dimerization gap is large, of the order of transverse bandwidth, we also develop an exact treatment of magnetic breakdown in the external magnetic field. The obtained results agree with the experimental data on the fast magnetoresistance oscillations. Experimentally found 260T rapid oscillations and the characteristic T c dependance on magnetic field of relaxed material are fitted with our results for anion potential of the order of interchain hopping.