  Light fields at THz and mid-infrared frequencies allow for the direct
excitation of collective modes in condensed matter, which can be driven to
large amplitudes. For example, excitation of the crystal lattice, has been
shown to stimulate insulator-metal transitions, melt magnetic order, or enhance
superconductivity. Here, we generalize these ideas and explore the simultaneous
excitation of more than one lattice mode, which are driven with controlled
relative phases. This nonlinear mode mixing drives rotations as well as
displacements of the crystal-field atoms, mimicking the application of a
magnetic field and resulting in the excitation of spin precession in the
rare-earth orthoferrite $ErFeO_3$. Coherent control of lattice rotations may
become applicable to other interesting problems in materials research, for
example as a way to affect the topology of electronic phases.
