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A new approach is introduced to obtain information about the adiabatic potential energy surface of the Jahn-Teller (JT) complexes subject to theT⊗e+t2problem in doped crystals. It employs simulation of the contribution of the JT sub-system to ultrasonic attenuation with account of three mechanisms of relaxation and subsequent comparison with the experimental data on temperature dependence of the attenuation obtained with the use of doped crystal and nominally pure one. The approach has been applied to the CaF 2 crystal doped with chromium. The experiment has been carried out at the frequencies of (13-158) × 10 6 Hz at low temperatures (4-170 K). Peak for all the ultrasonic normal modes propagating along the [110] axis has been observed at about 8 K. It has been considered as the JT effect manifestation by the sub-system of Cr 2+ F8-complexes. Symmetry properties of the global minima and saddle points have been identified, the JT stabilization energies and coordinates of the extrema points in the five-dimensional space of symmetrized displacements have been evaluated. Besides, a broad shoulder has been found at 15-40 K and attributed to contribution of the Cr 3+ F8-sub-system., (© 2022 IOP Publishing Ltd.)

A novel type of sub-lattice of the Jahn-Teller (JT) centers was arranged in Ti-doped barium hexaferrite BaFe 12 O 19 . In the un-doped crystal all iron ions, sitting in five different crystallographic positions, are Fe 3+ in the high-spin configuration (S = 5/2) and have a non-degenerate ground state. We show that the electron-donor Ti substitution converts the ions to Fe 2+ predominantly in tetrahedral coordination, resulting in doubly-degenerate states subject to the [Formula: see text] problem of the JT effect. The arranged JT complexes, Fe 2+ O 4 , their adiabatic potential energy, non-linear and quantum dynamics, have been studied by means of ultrasound and terahertz-infrared spectroscopies. The JT complexes are sensitive to external stress and applied magnetic field. For that reason, the properties of the doped crystal can be controlled by the amount and state of the JT complexes.

A method is constructed that uses ultrasonic experiments to evaluate the parameters of the Jahn-Teller (JT) effect in impurity centers in crystals. The method is based on measurements of temperature dependent attenuation and phase velocity and does not require assumptions about mechanisms of relaxation. The results are illustrated by measurements performed on the impurity system ZnSe:Cr(2+), in which the Cr(2+) ion has a threefold degenerate T term in the ground state, subject to the [Formula: see text] JT problem. Ultrasound propagation anomalies show that the main JT distortions of the tetrahedral environment of the Cr(2+) ion are of tetragonal E type and hence the lowest branch of the adiabatic potential energy surface (APES) is formed in accordance with the [Formula: see text] problem. With dopant concentration 3.8 × 10(18) cm(-3) the modulus of the constant of linear vibronic coupling to tetragonal E type vibrations is determined by two independent experiments: |F(E)| = 5.49 × 10(-5) dyn revealed from attenuation measurements, while a slightly different value |F(E)| = 5.57 × 10(-5) dyn emerges from phase velocity measurements. Contributions of other active vibronic modes to the elastic modulus C(l) = (C(11) + C(12) + 2C(44))/2 are analyzed and it is shown that the influence of the totally symmetric mode is negligible. Using additional information about this system obtained from independent sources, we also estimated the primary force constant in the E direction (K(E)≈(1.4-4.2) × 10(4) dyn cm(-1)) and orthorhombic and trigonal saddle points of the APES in the five-dimensional space of the tetragonal and trigonal coordinates, their stabilization energies being E(JT)(O)≈81-450 cm(-1) and E(JT)(T)≈48-417 cm(-1), respectively (the variations of the K(E), E(JT)(O) and E(JT)(T) values are due to different literature data for E(JT)(E)). With these data the APES of the JT linear [Formula: see text] problem for the Cr(2+) ion in the ZnSe:Cr(2+) system is revealed.

Theory of ultrasonic absorption and dispersion, based on the Zener equation, was used for constructing the equations, those made it possible to restore the temperature dependences of relaxation time, adiabatic and isothermal elastic moduli on the basis of experimental data on the temperature dependences of ultrasound absorption and phase velocity. This method was used for processing the experimental results obtained in single crystals of ZnSe:Ni and ZnSe:Cr.

Ultrasonic investigations have been carried out in geometry of the experiment corresponding to acoustic analogy of the Faraday effect with the use of a super pure crystal like indium. Lowering the temperature from 4.2 K to 1.28 K has revealed new peculiarities of in the magnetic field dependences of absorption and phase velocity of circularly polarized ultrasonic waves. The peculiarities have been interpreted as manifestation of multiple doppleron-phonon and Doppler-shifted cyclotron resonances. The discovery of these resonances has changed interpretation of some anomalies observed in the previous experiments.

The dispersion equation for doppleron-phonon modes was constructed and solved analytically in the strong coupling regime. The Fermi surface model proposed previously for calculating the doppleron spectrum in an indium crystal was used. It was shown that in the vicinity of doppleron-phonon resonance, the dispersion curves of coupled modes form a gap qualitatively different from the one observed under helicon-phonon resonance: there is a frequency interval forbidden for existence of waves of definite circular polarization depending upon direction of the external DC magnetic field. The physical reason for it is interaction of the waves which have oppositely directed group velocities.