  The cross sections of elastic neutrino scattering on electrons and nuclei in
the regime of low-energy transfer are known to be very sensitive to neutrino
electromagnetic properties. In particular, the magnetic moment of the neutrino
can be effectively searched using liquid or solid detectors with a very low
energy threshold. We present the formalism that incorporates the neutrino
magnetic moment contribution in the theoretical treatment of the low-energy
elastic neutrino scattering on a condensed-matter target. The concept of the
dynamic structure factor is employed to describe the collective effects in the
target. The differential cross section for tritium antineutrino scattering on
the superfluid $^4$He is calculated numerically. We find that the neutrino
magnetic moment of the order of $10^{-11}\mu_B$ strongly affects the cross
section. Our results can be used in the search of neutrino magnetic moments in
future low-energy neutrino scattering experiments with liquid or solid targets.
