  We analytically investigate the Fano-type optical response and four-wave
mixing (FWM) process by exploiting the magnetoelasticity of a ferromagnetic
material. The deformation of the ferromagnetic material plays the role of
mechanical displacement, which is simultaneously coupled to both optical and
magnon modes. We report that the magnetostrictively induced displacement
demonstrates Fano profiles, in the output field, which is well-tuned by
adjusting the system parameters, like effective magnomechanical coupling,
magnon detuning, and cavity detuning. It is found that the magnetoelastic
interaction also gives rise to the FWM phenomenon. The number of the FWM
signals mainly depends upon the effective magnomechanical coupling and the
magnon detuning. Moreover, the FWM spectrum exhibits suppressive behavior upon
increasing (decreasing) the magnon (cavity) decay rate. The present scheme will
open new perspectives in highly sensitive detection and quantum information
processing.
