Breakdown of the Small-Polaron Hopping Model in Higher-Order Spinels

The small-polaron hopping model has been used for six decades to rationalize electronic charge transport in oxides. The model was developed for binary oxides, and, despite its significance, its accuracy has not been rigorously tested for higher-order oxides. Here, the small-polaron transport model is tested by using a spinel system with mixed cation oxidation states (Mn_x Fe_{3- x} O₄ ). Using molecular-beam epitaxy (MBE), a series of single crystal Mn_x Fe_{3- x} O₄ thin films with controlled stoichiometry, 0 ≤ x ≤ 2.3, and lattice strain are grown, and the cation site-occupation is determined through X-ray emission spectroscopy (XES). Density functional theory + U analysis shows that charge transport occurs only between like-cations (Fe/Fe or Mn/Mn). The site-occupation data and percolation models show that there are limited stoichiometric ranges for transport along Fe and Mn pathways. Furthermore, due to asymmetric hopping barriers and formation energies, the $$ polaron is energetically preferred to the $$ polaron, resulting in an asymmetric contribution of Mn/Mn pathways. All of these findings are not contained in the conventional small-polaron hopping model, highlighting its inadequacy. To correct the model, new parameters in the nearest-neighbor hopping equation are introduced to account for percolation, cross-hopping, and polaron-distribution, and it is found that a near-perfect correlation can be made between experiment and theory for the electronic conductivity.