Electro-phononic and magneto-phononic frequency conversion

Nonlinear frequency conversion by optical rectification, as well as difference- and sum-frequency generation are fundamental processes for producing electromagnetic radiation at different frequencies. Here, we demonstrate that coherently excited infrared-active phonons can be used as transducers for generating nonlinear electric polarizations and magnetizations via phonon-phonon and phonon-magnon interactions, in a way similar to nonlinear optical frequency conversion. We derive analytical solutions for the time-dependent polarizations and magnetizations for the second-order response to the electric field component of an ultrashort laser pulse. These allow us to define second-order nonlinear electric and magneto-electric susceptibilities that capture the rectification, as well as the impulsive and sum-frequency excitation of coherent phonons and magnons. Our theoretical framework naturally incorporates existing mechanisms and further leads to the prediction of a hybrid magneto-opto-phononic inverse Faraday effect involving photon-phonon-magnon scattering. Our work demonstrates nonlinear phononics as a pathway to controlling the electric polarization and magnetization in solids.