A Potts model for the distortion transition in LaMnO$_3$

TL;DR

This paper models the Jahn-Teller transition in LaMnO₃ using a modified 3-state Potts model, successfully predicting transition order, entropy, and orbital ordering consistent with experimental observations.

Contribution

It introduces a specific Potts model with orbit-dependent interactions that accurately describes the transition in LaMnO₃, including its first-order nature and entropy.

Findings

Predicts a first-order transition consistent with experiments

Accurately models the temperature dependence of orbital order

Shows the transition is near a disordered phase in the Potts model

Abstract

The Jahn-Teller distortive transition of \lmo is described by a modified 3-state Potts model. The interactions between the three possible orbits depends both on the orbits and their relative orientation on the lattice. Values of the two exchange parameters which are chosen to give the correct low temperature phase and the correct value for the transition temperature are shown to be consistent with microscopy theory. The model predicts a first order transitions and also a value for the entropy above the transition in good agreement with experiment. The theory with the same parameters also predicts the temperature dependence of the order parameter of orbital ordering agreeing well with published experimental results. Finally, the type of the transition is shown to be close to one of the most disordered phases of the generalised Potts model. The short range order found experimentally above the transition is investigated by this model.