Collective modes in a system with two spin-density waves: the `Ribault' phase of quasi-one-dimensional organic conductors

TL;DR

This paper investigates the collective excitations in a complex magnetic phase of organic conductors with two coexisting spin-density waves, revealing unique modes and spectral properties linked to the phase's helicoidal structure.

Contribution

It introduces a theoretical analysis of collective modes in a two-SDW system, highlighting the existence of Goldstone and gapped modes and their spectral weight distribution, especially in the helicoidal phase.

Findings

Identified two Goldstone modes: out-of-phase and in-phase

Discovered two gapped modes with distinct spectral features

Spectral weight distribution depends on SDW amplitude ratio

Abstract

We study the long-wavelength collective modes in the magnetic-field-induced spin-density-wave (FISDW) phases experimentally observed in organic conductors of the Bechgaard salts family, focusing on phases that exhibit a sign reversal of the quantum Hall effect (Ribault anomaly). We have recently proposed that two SDW's coexist in the Ribault phase, as a result of Umklapp processes. When the latter are strong enough, the two SDW's become circularly polarized (helicoidal SDW's). In this paper, we study the collective modes which result from the presence of two SDW's. We find two Goldstone modes, an out-of-phase sliding mode and an in-phase spin-wave mode, and two gapped modes. The sliding Goldstone mode carries only a fraction of the total optical spectral weight, which is determined by the ratio of the amplitude of the two SDW's. In the helicoidal phase, all the spectral weight is pushed up above the SDW gap. We also point out similarities with phase modes in two-band or bilayer superconductors. We expect our conclusions to hold for generic two-SDW systems.