  In metals in the vicinity of a polar transition, interactions between
electrons and soft phonon modes remain to be determined. Here we explore the
consequences of spin-orbit assisted electron-phonon coupling on the collective
modes of such nearly polar metals in the presense of magnetic field. We find
that the soft polar phonon hybridizes with spin-flip electronic excitations of
the Zeeman-split bands leading to an anticrossing. The associated energy
splitting allows for an unambiguous determination of the strength of the
spin-orbit mediated coupling to soft modes in polar metals by spectroscopic
experiments. The approach to the polar transition is reflected by the softening
of the effective g-factor of the hybridized spin-flip mode. Analyzing the
static limit, we find that the polar order parameter can be oriented by
magnetic field. This provides possibilities for new switching protocols in
polar metallic materials. We demonstrate that the effects we predict can be
observed with current experimental techniques and discuss promising material
candidates.
