Simulating Charge, Spin, and Orbital Ordering: Application to Jahn–Teller Distortions in Layered Transition-Metal Oxides

The degrees of freedom associated with orbital, spin, and charge ordering can strongly affect the properties of many crystalline solids, including battery materials, high-temperature superconductors, and naturally occurring minerals. This work reports on the development of a computational framework to systematically explore the ordering of electronic degrees of freedom and presents results on orbital ordering associated with Jahn–Teller distortions in four layered oxides relevant for Li- and Na-ion batteries: LiNiO2, NaNiO2, LiMnO2, and NaMnO2. Our calculations reveal a criterion for the stability of orbital orderings in these layered materials: each oxygen atom must participate in two short and one long transition-metal/oxygen bond. The only orderings that satisfy this stability criterion are row orderings, such as the "zigzag" ordering. The near degeneracy of such row-orderings in LiNiO2 suggests that boundaries between domains with distinct but symmetrically equivalent Jahn–Teller distortions will be relatively low in energy. Based on this result, we speculate that a microstructure consisting of nanoscale Jahn–Teller domains could be responsible for the apparent absence of a collective distortion in experiments on LiNiO2.