Giant phonon-induced effective magnetic fields in $4f$ paramagnets

We present a mechanism by which circularly driven phonon modes in the 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 inverted by reversing the polarization of the laser pulse. The underlying mechanism is a phonon analog to the inverse Faraday effect in optics and enables novel ways of achieving control over and switching of magnetic order at terahertz frequencies.