Numerical adiabatic potentials of orthorhombic Jahn-Teller effects retrieved from ultrasound attenuation experiments. Application to the SrF₂:Cr crystal

A methodology is worked out to retrieve the numerical values of all the main parameters of the sixdimensional adiabatic potential energy surface (APES) of a polyatomic system with a quadratic T-term Jahn-Teller effect (JTE) from the ultrasound experiments. The method is based on a verified assumption that ultrasound attenuation and speed encounter anomalies when the direction of propagation and polarization of its wave of strain coincides with the characteristic directions of symmetry breaking in the JTE. For the SrF₂:Cr crystal, employed as a basic example, we observed anomaly peaks in the temperature dependence of attenuation of ultrasound at frequencies of 50-160 MHz in the temperature interval of 40-60 K for the wave propagating along the [110] direction, for both the longitudinal and the shear modes, the latter with two polarizations along the [001] and [11-0] axes, respectively. We show that these anomalies are due to the ultrasound Relaxation by the system of non-interacting Cr²⁺ JT centers with orthorhombic local distortions. The interpretation of the experimental findings is based on the T2g - (eg+t2g) JTE problem including the linear and the quadratic terms of vibronic interactions in the Hamiltonian and the same-symmetry modes reduced to one interaction mode. Combining the experimental results with a theoretical analysis, we show that on the complicated six-dimensional APES of this system with three tetragonal, four trigonal, and six orthorhombic extrema points, the latter are global minima, while the former are saddle points, and we estimate numerically all the main parameters of this surface, including the linear and quadratic vibronic coupling constants, the primary force constants, the coordinates of all the extrema points and their energies, the energy barrier between the orthorhombic minima, and the tunneling splitting of the ground vibrational states. To our knowledge, such a based-on-experimental-data numerical reconstruction of the APES of a JTE problem in the five-dimensional space of all active tetragonal and trigonal displacements has not been reported before.