Manifestation of the Jahn-Teller effect subject to quadraticT⊗e+t2problem in ultrasonic attenuation. Case study of CaF 2 :Cr crystal with isovalent and aliovalent substitution.

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.
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