The Jahn-Teller distortion that can remove electronic degeneracies in partially occupied states and results in systematic atomic displacements is a common underlying feature to many of the intriguing phenomena observed in $3d$ perovskites, encompassing magnetism, superconductivity, orbital ordering, and colossal magnetoresistance. Although the seminal Jahn and Teller theorem was postulated almost a century ago, the origins of this effect in perovskite materials are still debated, including propositions such as superexchange, spin-phonon coupling, sterically induced lattice distortions, and strong dynamical correlation effects. Although the end result of Jahn-Teller distortions often includes a mix of such various contributions, due to coupling of various lattice, spin, and electronic modes with the distortions (“fingerprints” or “consequences” of Jahn-Teller), it is not clear what the primary cause is, i.e., which cases are caused by a pure electronic instability associated with degeneracy removal, as implied in the Jahn-Teller theorem, and which cases originate from other causes, such as semiclassical size effects. We propose a way to distinguish the materials with an electronic instability associated with degeneracy removal being the primary cause of the Jahn-Teller distortions, from others with octahedral rotation or tilts from a steric effect playing the primary role in electron-lattice coupling. This work provides a unified and quantitative density functional theory explanation of the experimentally observed trends of octahedral deformations in $AB{X}_3$ perovskites, without recourse to the dynamically correlated vision of electron interactions codified by the Mott-Hubbard mechanism. We inquire about the origin and predictability of different types of octahedral deformation by using a Landau-esque approach, where the orbital occupation pattern of a symmetric structure is perturbed, finding whether it is prone to total energy lowering the electronic instability or not. This is done for a systematic series of $AB{X}_3$ perovskite compounds having $3d$-orbital degeneracies, using the density functional approach. We identify (i) systems prone to an electronic instability (a true Jahn-Teller effect), such as $\mathrm{KCr}{\mathrm{F}}_3, \mathrm{KCu}{\mathrm{F}}_3, \mathrm{LaV}{\mathrm{O}}_3, \mathrm{KFe}{\mathrm{F}}_3$, and $\mathrm{KCo}{\mathrm{F}}_3$, where the instability is independent of magnetic order, and forces a specific orbital arrangement that is accommodated by a $B{X}_6$ octahedral deformation with a specific symmetry. On the other hand, (ii) compounds such as $\mathrm{LaTi}{\mathrm{O}}_3$ and $\mathrm{LaMn}{\mathrm{O}}_3$ with delocalized $d$ states do not show any electronically driven instability. Here, the alternate orbital ordering, which is an energy-lowering event irrespective of the presence of electronic instabilities, simply results from the coupling of lattice modes induced by semiclassical size effects (sterically induced), such as $B{X}_6$ octahedra rotations. (iii) Although $R\mathrm{V}{\mathrm{O}}_3$ ($R=\mathrm{Lu}-\mathrm{La}$, Y) perovskites exhibit hybridizations similarly to $\mathrm{LaTi}{\mathrm{O}}_3$, their $t_{2g}^2$ electronic structure is highly unstable and preserves the Jahn-Teller effect. However, here coexisting steric deformations and Jahn-Teller distortions result in strongly entangled spin-orbital properties.

• Received 18 June 2019

DOI:https://doi.org/10.1103/PhysRevResearch.1.033131

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Published by the American Physical Society