Paraelectrical Resonance

the resonance absorption of radio-frequency waves by a substance associated with the orientation of the electric dipole moments of the particles (ions or molecules) composing the substance in an external electric field. The spectrometer used to observe paraelectrical resonance is similar to an electron paramagnetic resonance spectrometer.

Paraelectrical resonance is possible if the orientation of the electric dipole moment with respect to an external electric field is not arbitrary but assumes a number of discrete values. Then the energy of the particle’s interaction with the field also assumes discrete values. Such discrete orientations of the dipole moment occur if (1) the particle rotates freely in the external electric field or (2) a particle located in an intracrystalline electric field has several equivalent equilibrium positions that differ in the direction of the dipole moment and are separated by energy barriers that are not too large and allow reorientation of the particle by tunneling. In the first case, the discreteness of the orientation of the electric dipole moment is due to the quantization of the projection m of the angular momentum of the rotating particle on the direction of the external field. Paraelectrical resonance spectra are observed in gases containing molecules with an electric dipole moment. The second case occurs in certain alkali-halide single crystals containing an ionic impurity with an electric dipole moment at temperatures below 10°K. An example is a crystal of KC1 with an impurity of OH^- or CN^- ions, which replace CI^- ions in the crystal lattice of KC1 and have six equivalent equilibrium directions for the orientation of their intrinsic dipole moment with respect to the crystallographic axes. “Tunneling rotations,” which connect the equilibrium positions, correspond energetically to frequencies in the SHF region. A constant external electric field displaces and splits these levels, thus altering the frequency of transitions between them.

Paraelectrical resonance is possible not only when the impurity particle has an intrinsic dipole moment but also when it has no intrinsic moment but is displaced with respect to the center of the cavity it occupies in the crystal lattice. For example, when a Li⁺ ion replaces a larger K⁺ ion in a crystal of KC1, it is displaced into one of eight equilibrium positions and, together with the negative “hole,” forms a dipole whose orientation changes when tunneling occurs from one position to another.