Orbital Ordering Versus the Traditional Approach in the Cooperative Jahn–Teller Effect: A Comparative Study

Abstract

In Jahn–Teller crystals, at low temperatures, symmetry-breaking lattice distortion creates an ordering of otherwise degenerate atomic orbitals. In the theory of cooperative Jahn–Teller effect, the traditional approach includes solving the complex problem of coupled dynamics of the respective electron-vibrational system. During last two decades, an alternative way of treating the cooperative Jahn–Teller effect attracts increasing attention. It replaces ligand-mediated intercell coupling by an effective intersite orbital exchange of electron-degenerate atoms. Known as the orbital ordering approach, it explores stable ordered patterns due to the exchange coupling of orbital pseudo spins. The respective symmetry break of crystal lattice structure is treated as a secondary effect resulting from the orbital ordering. This paper examines some approximations implicitly included in the orbital ordering approach and compares it to the traditional theory of the Jahn–Teller effect. As the orbital ordering approach replaces ligand-mediated intersite coupling by an orbital exchange, the fundamental effect of dynamic strengthening chemical bonds with low-symmetry lattice distortions is lost. This may bring to a wrong conclusion about possible bond-ordered structures. On the other hand, a number of cases are outlined when both approaches yield close results. Based on these estimates, conclusions regarding applicability of the orbital ordering approach are derived and some general recommendations are given.