Percolation features of cooperative Jahn-Teller systems: Ising EFT framework

Elastic exchange between two nearest Jahn-Teller (JT) centers in two or three dimensional dense crystals, can give an ordered macroscopic distortion known as cooperative JT effect (CJTE). A very diluted JT crystal does not show this effect. In the dynamic JT effect (DJTE), tunneling between different equivalent distorted wells has a pronounced influence on the CJTE. We investigate this phenomenon using a progressive increase in the concentration of these centers in the JT crystals, based on a bond percolation vector spin analogy technique within the framework of effective field theory (EFT). Mean field theory (MFT) was extensively used in previous studies of CJTE; however it neither includes correlation between JT centers in the lattice due to the complexity of the distortion field in the crystal nor the effect of tunneling between wells. We resort to an alternative procedure, by describing a JT center as a pseudo-spin vector \(\vec S\), induced to represent the degenerate JT-distorted states, where two nearest JT centers interact via an elastic exchange described by an Ising type spin interaction. The DJTE is considered to be similar to an elastic transverse field term in the Hamiltonian portraying the effect of tunneling between equivalent wells in the adiabatic potential energy surface (APES). We will be particularly discussing S = 1, S = 3/2 and S = 5/2 spin cases, where 2S + 1 wells in the APES are present and what JT systems they actually represent, with a percolative mechanism applied to the interactions between different JT centers. The different lattices are distinguished by their coordination numbers. Strong tunneling effects can suppress the CJTE and lead to a new state of criticality. Generalizations to higher spin systems will be obtained using a scaling technique. For the relevant distortions, we determine single site correlations, the macroscopic average distortion describing a structural phase transition and the elastic isothermal susceptibility as a function of temperature. The critical bond percolation threshold and the critical tunneling parameter are also obtained.