Tunneling relaxation mechanisms of the Jahn–Teller complexes in a CaF$_2$:Cr$^{2+}$ crystal

The temperature dependences of attenuation and the velocity of ultrasonic waves at frequencies of $26$–$158$ MHz in a $\mathrm{CaF}_2$ fluorite crystal at the substitution of Jahn–Teller $\mathrm{Cr}^{2+}$ centers for calcium ions have been studied. An abnormally high relaxation rate, which is two orders of magnitude higher than the relaxation rate in other previously studied $\mathrm{CaF}_2:\mathrm{Ni}^{2+}$ and $\mathrm{SrF}_2:\mathrm{Cr}^{2+}$ fluorites, has been found in the system of Jahn–Teller complexes in the low-temperature region. It has been shown that the global minima of the adiabatic potential energy surface of the $\mathrm{Cr}^{2+}\mathrm{F}_8^-$ complexes in the $\mathrm{CaF}_2:\mathrm{Cr}^{2+}$ crystal also have orthorhombic symmetry but are separated by significantly lower potential energy barriers than in $\mathrm{CaF}_2:\mathrm{Ni}^{2+}$ and $\mathrm{SrF}_2:\mathrm{Cr}^{2+}$ crystals. It has been found that tunneling relaxation mechanisms (direct and two-phonon transitions) are dominant, rather than thermal activation, in $\mathrm{CaF}_2:\mathrm{Cr}^{2+}$ in the temperature range where the Jahn–Teller effect is manifested in an ultrasonic experiment. The parameters characterizing these relaxation mechanisms have been determined.