We develop the theory of spin light of neutrino in matter ($SL\nu$) and
include the effect of plasma influence on the emitted photon. We use the
special technique based on exact solutions of particles wave equations in
matter to perform all the relevant calculations, and track how the plasmon mass
enters the process characteristics including the neutrino energy spectrum,
$SL\nu$ rate and power. The new feature it induces is the existence of the
process threshold for which we have found the exact expression and the
dependence of the rate and power on this threshold condition. The $SL\nu$
spatial distribution accounting for the above effects has been also obtained.
These results might be of interest in connection with the recently reported
hints of ultra-high energy neutrinos $E = 1 \div 10$ PeV observed by IceCube.Comment: 8 pages, 2 figures, v2: typos corrected, discussions adde