  We present a mechanism by which optically driven chiral phonon modes in
rare-earth trihalides generate giant effective magnetic fields acting on the
paramagnetic $4f$ spins. With cerium trichloride (CeCl$_3$) as our example
system, we calculate the coherent phonon dynamics in response to the excitation
by an ultrashort terahertz pulse using a combination of phenomenological
modeling and first-principles calculations. We find that effective magnetic
fields of over 100 tesla can possibly be generated that polarize the spins for
experimentally accessible pulse energies. The direction of induced
magnetization can be reversed by changing the handedness of circular
polarization of the laser pulse. The underlying process is a phonon analog of
the inverse Faraday effect in optics that has been described recently, and
which enables novel ways of achieving control over and switching of magnetic
order at terahertz frequencies.
