Governing of the piezoelectric effect by external fields and strains

Abstract

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.Magneto-electric, piezoelectric and magneto-mechanic effects attract much attention of researchers. The interest to the studies of such effects is stimulated by two reasons. First, these effects are interesting of their own as the manifestation of the interaction between several degrees of freedom in physical systems. Second, maybe more important, these effects are used in a number of practical applications in the modern technique, where it is often necessary to govern some properties of devices by changing various external parameters. Piezoelectricity is one of the most known and developed branches of physics, where electric and elastic degrees of freedom are strongly inter-related. Piezoelectric materials are used in a number of applications, e.g., in the production of piezosensors, transducers, relaxators, piezoelectric cables, filters, actuators, generators, stabilizators, transformators, motors, etc. Last decades piezoelectricity is widely used in microelectronics, in particular in microelectromechanical systems, including biomedical ones. The most popular subjects for the manifestation of magneto-electro-mechanic effects are so-called multiferroics, which reveal both magnetic and ferroelectric properties see, e.g., [1][2][3][4][5] . Notice that multiferroics are magnetically and electrically ordered systems. However, it is clear from general grounds that similar effects can exist in magnetic systems without magnetic and electric ordering, i.e., in quantum paramagnets. The effects of interaction of magnetic degrees of freedom and piezoelectricity in quantum systems with localized energy levels can be useful for the modern laser technique and for the regulation of quantum computers.The goal of the present study is to find the effect of the renormalization of piezoelectric characteristics due to the coupling between the electric, magnetic and elastic subsystem of the quantum paramagnetic compound. Namely, we investigate the rare-earth based trigonal crystals with non-centersymmetric symmetry of the lattice. Such a symmetry permits piezoelectricity in the system. On the other hand, non-magnetic surrounding of magnetic ions determines the crystalline electric field, which acts on the latter, and, together with the spin-orbit interaction, affects the spin subsystem. This way the interaction between the spin, charge and elastic subsystems of the cryst...