Manifestation of the Jahn–Teller effect subject to quadratic T⊗e+t2 problem in ultrasonic attenuation. Case study of CaF₂:Cr crystal with isovalent and aliovalent substitution

Abstract

A new approach is introduced to obtain information about the adiabatic potential energy surface of the Jahn-Teller complexes subject to the T ⊗ (e + t2) problem in doped crystals. It employs simulation of the contribution of the Jahn-Teller 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 CaF2 crystal doped with chromium. The experiment has been carried out at the frequencies of (13 – 158) MHz 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 Jahn-Teller effect manifestation by the sub-system of Cr2+F8 complexes. Symmetry properties of the global minima and saddle points have been identified, the Jahn-Teller 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 Cr3+F8 sub-system.

Ultrasonic investigation of the Jahn-Teller effect in BaF2:Cu crystal

“…The parameters of the summands to the relaxation rate initiated by thermal activation, tunneling, and two-phonon mechanisms were obtained from the data on temperature dependence of the imaginary part of the trigonal elastic modulus c 44 . The parameters which characterize relaxation time of the JT subsystem in BaF 2 :Cu crystal occupy an intermedium position between ones obtained in CaF 2 :Cr [4] and CaF 2 :Cu [6].…”

“…Ultrasonic technique makes it possible (i) to reveal the mechanisms of relaxation, (ii) to define the symmetry properties of the global minima of the adiabatic potential energy surface (APES), (iii) to estimate the vibronic coupling constants, (iv) to determine the energies of the JT stabilization and (v) the positions of the extrema points of APES in the coordinate system of symmetrized displacements. Implication of this technique to the fluorite-structure crystals comprising 3d ions with triply degenerate orbital states, such as SrF 2 :Cr 2+ [2], CaF 2 :Cr 2+ [3,4], CaF 2 :Ni 2+ [5,3], CaF 2 :Cu 2+ [6] indicated the orthorhombic symmetry of the gobal minima that can be only due to account of the quadratic terms in vibronic Hamiltonian [7,8]. However, the quantitative information about the APES can be obtained only if concentration of the JT ions is known.…”

Quantum dynamics of the Jahn-Teller complexes investigated by ultrasonic technique

“…In Figure 7, we demonstrate the results of employing such an approach to the species of fluorite crystals doped with different 3d ions, which have triply orbital-degenerate ground ground states and whose cubal JT complexes possess the orthorhombic global minima of APES. The used parameters B, B/Θ 2 , τ 0 , and V 0 which characterize relaxation mechanisms were determined earlier (Cu 2+ F − 8 [12], Cr 2+ F − 8 [15], and Ni 2+ F − 8 [16]).…”