Governing of the piezoelectric effect by external fields and strains

Piezoelectricity in quantum rare-earth metallic boron oxides with the coupling between magnetic, electric and elastic subsystem is studied theoretically. It is proved that the change of piezoelectric modules of the considered crystals are proportional to components of the quadrupole susceptibility, which determines the external magnetic and electric fields, strain and temperature dependences of that change. We show why holmium compounds manifest the strongest renormalization among other rare-earth ions in this family of crystals. The reason is in the structure of the low energy term of the electron configuration, depending on spins and orbital moments of 4f electrons.