  We demonstrate the emergence of collective spin modes with hyperbolic
dispersion in three-dimensional spin-orbit coupled polar metals magnetized by
intrinsic ordering or applied fields. These particle-hole bound states exist
for arbitrarily weak repulsive interactions; they are optically accessible and
can be used to generate pure spin current when magnetization is tilted away
from the polar axis. We suggest material hosts for these excitations and
discuss their potential relevance to nanoscale spintronic and polaritonic
applications.
