Phason modes in spin-density wave in the presence of long-range Coulomb interaction

We study the effect of long-range Coulomb interaction on the phason in spin-density wave (SDW) within mean field theory. In the longitudinal limit and in the absence of SDW pinning the phason is completely absorbed by the plasmon due to the Anderson-Higgs mechanism. In the presence of SDW pinning or when the wave vector {\bf q} is tilted from the chain direction, though the plasmon still almost exhausts the optical sum rule, another optical mode appears at $\omega < 2\Delta(T)$, with small optical weight. This low frequency mode below the SDW gap may be accessible to electron energy loss spectroscopy (EELS).