Quantum Theory of the Piezoelectric Effect in Rare-Earth Ferroborates

The piezoelectric effect theory is developed in rare-earth ferroborates. It is established that mainly single-ion mechanisms are responsible for the appearance of the effect: the existence of mechanical stresses leads to the induction in a crystal of dipole electric moments immediately in electron 4f shells of rare-earth ions, which leads to the crystal polarization. The effect is considered quantitatively for neodymium and samarium ferroborates; in particular, in the range from 0 K to 300 K, the temperature dependences of piezoelectric moduli have been obtained. In addition, it is shown that, at temperatures lower than the Neel point, the deformation of a crystal in magnetic field can lead to the appearance of the crystal polarization along crystallographic axis c. The temperature, field, and orientation dependences of the magnetically induced piezoelectric moduli are calculated.