Cooperative Dynamic Jahn-Teller Effect. II. Crystal Distortion in Perovskites

Abstract

A molecular-field-type theory is given for the second-order phase transitions occurring in perovskite crystals, in which a Jahn-Teller (JT) ion (${\mathrm{Mn}}^{3+}$, ${\mathrm{Cu}}^{2+}$, ${\mathrm{Cr}}^{2+}$) occupies an octahedral $B$ site. The dynamic character of the JT effect is taken into account and excited vibronic states are included. The ordered system consists of two sublattices, each having the same tetragonal, but opposite orthorhombic, mean distortion amplitudes. Near the transition temperature $T_t$, the two amplitudes behave as $T_t-T$ and ${(T_t-T)}^{\frac{1}{2}}$, respectively. Increasing the anisotropic JT coupling $\beta$ enhances the mean tetragonal distortion amplitude and diminishes the orthorhombic one. The transition temperature is studied as a function of the molecular field strength and of $\beta$, and characteristic regions of solutions are distinguished. The temperature dependence of the specific heat for some typical systems is presented.