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

TL;DR

The paper addresses whether Jahn–Teller transitions in correlated oxides are best described as order-disorder or displacive. It extends a simple Monte Carlo model to include a variable JT amplitude rho, with a single-ion term and a geometry term, and applies it to both perovskites and layered nickelates. The simulations reveal that high-temperature JT distortions persist but do not exhibit a sharp order-disorder peak, instead signaling displacive-like dynamics as the system explores the JT phase space. Lattice geometry and entropy govern the quantitative differences between the two families, suggesting displacive JT transitions may be more common than previously thought and highlighting avenues for applying the approach to other JT-distorted materials and integrating with more advanced vibrational models.

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 $ρ$, 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.

Figures (30)

• Figure 1: The room-temperature crystal structures and JT-ordering of (a) many JT-ordered perovskites such as KCuF$_3$ and LaMnO$_3$Khomskii2021OrbitalOpportunities and (b) layered nickelates such as NaNiO$_2$ and stoichiometric LiNiO$_2$Dyer1954AlkaliMNiO2Phillips2025Collinearsub2/sub. Pink metal-oxygen bond lengths indicate JT-elongated bonds. Only octahedra associated with JT-active sites are displayed. In the perovskites, purple sites are the JT-distorted site (i.e. Mn, Cu, Cr) and green sites are the A-site (i.e. La, K). In the nickelates, grey sites are Ni$^{3+}$ and yellow sites are the alkali metal.
• Figure 2: Diagram showing the JT configurations associated with zero and non-zero geometric energies as used in Equations \ref{['Potts_model_modified_perovskite']} and \ref{['geometry_term_nickelate']}. (a) The case for perovskites, which is a reproduction of the Potts model of Ahmed and Gehring Ahmed2005TheModelAhmed2006PottsLaMnO3Ahmed2009VolumeModel. (b) The case for intra-layer nearest-neighbour NiO$_6$ octahedra within layered nickelates. Blue solid circles indicate JT-active sites, red solid circles (for the layered nickelate case) indicate O atoms, and solid lines indicate JT elongations.
• Figure 3: The results of a Monte Carlo refinement with dynamic $\rho$ ($p_\mathrm{switch}=1/2$), reproducing Phase 5 (C-type) of the Ahmed and Gehring Ahmed2005TheModel phase diagram for the anisotropic Potts model in a $8\times8\times8$ perovskite supercell. (a) Example configuration in the $bc$-plane in a randomly-selected cross-section. (b) Example configuration in the $ac$-plane in a randomly-selected cross-section. Energy parameters $\alpha=-1$,$\beta=1/2$ from equation \ref{['hamiltonian_equation']}. Simulated annealing was used before settling on a final $T=0.001$. This run lasted for $10^7$ iterations. Plots of energy and $\langle \rho\rangle$ with iteration can be seen in Figure \ref{['figure_dynamic-rho_phase5']}.
• Figure 4: The mean energy terms $E_\mathrm{total}$, $E_\mathrm{Geometric}$ (Eq \ref{['Potts_model_modified_perovskite']}), and $E_\mathrm{single-ion}$ (Eq \ref{['E_single-ion_term']}), heat capacity $C$, and mean $\langle\rho\rangle$, averaged over the final 10% of iterations in Monte Carlo simulations, as a function of temperature for the collinear and C-type orbital orderings in a $8\times8\times8$ perovskite lattice. The Monte Carlo simulations ran for $10^7$ iterations in total at each temperature. This figure is reproduced on a non-logarithmic temperature scale in SI Figure \ref{['perovskite_VT_simulation_nonlog']}.
• Figure 5: Histograms of $\rho$ for (a) $8\times8\times8$ perovskite collinear ordered supercell and (b) the final $10\times30$ nickelate layer with $K_\mathrm{oxy}=10^{10}$ after $10^7$ iterations, with simulated annealing. For other configurations see Figures \ref{['nickelate_Koxy1_rho_histogram.pdf']} to \ref{['phase5_rho_histogram.pdf']}.