Revisiting Jahn--Teller Transitions in Correlated Oxides with Monte Carlo Modeling

TL;DR

This paper uses Monte Carlo simulations to investigate Jahn--Teller transitions in correlated oxides, suggesting displacive transitions are more common than previously thought, with lattice geometry significantly influencing the transition type.

Contribution

It introduces a modified Hamiltonian and simulation approach to distinguish between order-disorder and displacive Jahn--Teller transitions in oxides.

Findings

Displacive-like Jahn--Teller transitions are more prevalent than previously believed.

Differences in transition behavior are linked to lattice geometry and configurational entropy.

Simulations align with experimental observations for perovskites and layered nickelates.

Abstract

Jahn--Teller (JT) distortions are a key driver of physical properties in many correlated oxide materials. Cooperative JT distortions, in which long-range orbital order reduces the symmetry of the average structure macroscopically, are common in JT-distorted materials at low temperatures. This long-range order will often melt on heating, \textit{via} a transition to a high-temperature state without long-range orbital order. The nature of this transition has been observed to vary with different materials depending on crystal structure; in LaMnO$_3$ the transition has generally been interpreted as order-disorder, whereas in layered nickelates $A$NiO$_2$ ($A$=Li,Na) there is a displacive transition. Alternatively, recent theoretical work has suggested that previous attributions of order-disorder may in fact be a consequence of phonon anharmonicity, rather than persistence of JT distortions, which would suggest that the displacive transition may be more common than currently believed. In this work, we run Monte Carlo simulations with a simple Hamiltonian which is modified to include terms dependent on the JT amplitude $\rho$, which is allowed to vary within the simulation \textit{via} the Metropolis algorithm. Our simulations yield distributions of JT amplitudes consistent with displacive rather than order-disorder behaviour for both perovskites and layered nickelates, suggesting that displacive-like JT transitions may be more common than previously assumed in both perovskites and layered nickelates. We also find significant differences between the transition observed for perovskites compared with layered nickelates, which we attribute to differing extensivity of configurational entropy on the two lattices, showing the crucial role of lattice geometry in determining behaviour.