  Magnetoelectric (ME) effect refers to the coupling between electric and
magnetic fields in a medium resulting in electric polarization induced by
magnetic fields and magnetization induced by electric fields. The linear ME
effect in certain magnetoelectric materials such as multiferroics has been of
great interest due to its application in the fabrication of spintronics
devices, memories, and magnetic sensors. However, the exclusive studies on the
nonlinear ME effect are mostly centered on the investigation of second-harmonic
generation in chiral materials. Here, we report the demonstration of nonlinear
wave mixing of optical electric fields and radio-frequency (rf) magnetic fields
in thermal atomic vapor, which is the consequence of the higher-order nonlinear
ME effect in the medium. The experimental results are explained by comparing
with density matrix calculations of the system. We also experimentally verify
the expected dependence of the generated field amplitudes on the rf field
magnitude as evidence of the magnetoelectric effect. This study can open up the
possibility for precision rf-magnetometry due to its advantage in terms of
larger dynamic range and arbitrary frequency resolution.
