Determining the parameters of the Jahn–Teller effect in impurity centers from ultrasonic experiments: application to the ZnSe : Ni$^{2+}$ crystal

The earlier developed methodology of ultrasonic investigation for determining the parameters of the Jahn–Teller effect (JTE) in impurity centers in crystals is further developed in application to Ni$^{2+}$ impurities in ZnSe : Ni$^{2+}$. For all normal modes propagating along the [110] axis, the temperature dependences of the attenuation of ultrasound are measured in the frequency range 25–165 MHz. At a temperature of about 13 K, for all these modes, attenuation peaks are observed, which indicate the presence of local distortions of both trigonal and tetragonal types. Following the previously developed method, it is shown that these anomalies of attenuation are caused by the relaxation transitions between equivalent local distortions induced by the JTE at the Ni$^{2+}$ centers. In the tetrahedral environment of selenium, this ion is in the threefold degenerate ground electron state $^{3}T_{1}$, in which three types of the JTE can be realized. The data of ultrasonic experiments indicate the realization of the $T\otimes(e+t_{2})$ problem, in which the potential energy surface has four equivalent minima of the trigonal type, slightly deformed toward tetragonal saddle points. The trigonal vibronic constants, the stabilization energies of the trigonal minima, and the activation energy of the barriers between them are ev-aluated.