Collective modes in an ultraquantum crystal: Field-induced spin-density-wave phases. II. Coupling between longitudinal and transverse fluctuations

It is well known that a two-dimensional anisotropic electron gas with an open Fermi surface is unstable at low temperature under the application of a uniform magnetic field perpendicular to the conducting plane. In a previous paper we have studied the collective modes of the field-induced density-wave phases within an approximation which neglects the coupling between spin-density fluctuations and charge-density fluctuations. We have found that the spin-wave mode and the phase mode were degenerate. In this paper we have taken into account the coupling between fluctuations transverse and parallel to the applied magnetic field. Our new results confirm the structure found previously, and describe the small perturbations on the rotonlike modes due to the longitudinal-transverse coupling. We find that both spin-wave and phase-fluctuation modes still exhibit, besides the trivial Goldstone bosons, a series of rotonlike modes for wave vectors of the order of the inverse magnetic length, but the degeneracy of the rotonlike energy minima is weakly lifted: the spin-wave-like modes decrease their energy slightly, while the phasonlike ones are practically unaffected, at least at their minima. The theory applies to Bechgaard salts. © 1988 The American Physical Society.