Jahn-Teller effect problems via ultrasonic experiments. Application to the impurity crystal CdSe:Cr

Based on the data analysis of ultrasonic experiments, a novel approach has been developed to explore Jahn-Teller effect (JTE) problems in non-cubic crystals with JT centers without involving additional experimental data beyond the information about the electronic term and crystal symmetry. Distinguished from cubic crystals, the axis of symmetry of the bulk non-cubic crystal do not necessarily coincide with those of the local impurity center, thus complicating the relation between the distortions produced by the ultrasound wave and the JTE active modes. We analysed the problem with corresponding calculations for the wurtzite-type hexagonal crystal CdSe:Cr²⁺, in which the chromium ion substitutes the cadmium one in the tetrahedral environment, resulting in its electronic ground state ⁵T₂(e₂t₂). Experimental investigation of this system by ultrasound at frequencies of 28-105 MHz in the temperature range of 4-180 K, yields a peak in the attenuation of the ultrasound below 40 K for the normal modes related to the c ₁₁, c ₄₄, c ₅₅, c ₅₅, and c ₆₆ elastic moduli. The peak has been interpreted as the manifestation of the JTE, similar to the one, observed in cubic crystals doped with 3d ions. However, no anomalies of attenuation have been detected for the mode related to the c ₃₃ elastic modulus, in contradiction to the theoretical predictions based on the previous method, worked out for cubic crystals. In the new method we obtained direct relations between the deformations, related to the crystal moduli, and the local JT modes, calculated the partition functions for each of the three possible JTE problems for systems with an electronic T term, T⊗e, T⊗t₂ and T⊗(e + t₂) revealed how these deformations alter the vibronic energy levels responsible for the relaxations in the JT centers. It emerged that in the wurtzite crystal under consideration, only in the T⊗e problem the deformation related to the elastic moduli c ₃₃ displaces all the vibronic energy level uniformly, without relaxation possibilities, thus supporting the new method and explaining the experimental observations.