Doug at nanoscale views explains in his introduction post to a paper of his which is getting published in Nature materials:
It’s been known for nearly 70 years that the simple single-electron band theory of solids (so good at describing Si, for example) does a lousy job at describing magnetite. Fe3O4 is a classic example of a strongly correlated material, meaning that electron-electron interactions aren’t negligible. At room temperature it’s moderately conducting, with a resistivity of a few milli-Ohm-cm. That’s 1000 times worse than Cu, but still not too bad. When cooled, the resistivity goes weakly up with decreasing temperature (not a standard metal or semiconductor!), and at about 120 K the material goes through the Verwey transition, below which it becomes much more insulating. Verwey first noticed this in 1939, and suggested that conduction at high temperatures was through shifting valence of the B-site irons, while below the transition the B-site irons formed a charge ordered state. People have been arguing about this ever since, sometimes with amusing juxtapositions (hint: look at the titles and publication dates on those links).
This review encompasses the story of the Verwey transition in magnetite over a period of about 90 years, from its discovery up to the present. Despite this long period of thorough investigation, the intricate multi-particle system Fe3O4 with its various magneto-electronic interactions is not completely understood, as yet – although considerable progress has been achieved, especially during the last two decades. It therefore appeared appropriate to subdivide this retrospect into three eras: (I) from the detection of the effect to the Verwey model (1913-1947), being followed by a period of: (II) checking, questioning and modification of Verwey’s original concepts (1947-1979). Owing to prevailing under-estimation of the role of crystal preparation and qualitiy control, this period is also characterized by a series of uncertainties and erroneous statements concerning the reaction order (one or two) and type of the transition (multi-stage or single stage). These latter problems, beyond others, could definitely be solved within era (III) (1979 to the present) – in favour of a first-order, single-stage transition near 125 K – on the basis of experimental and theoretical standards established in the course of a most inspiring conference organized in 1979 by Sir Nevill Mott in Cambridge and solely devoted to the present topic. Regarding the experimental field of further research, the remarkable efficiency of magnetic after-effect (MAE) spectroscopy as a sensitive probe for quality control and investigation of low-temperature (4 K<T<Tv) charge transport mechanisms is pointed out. Under theoretical aspects two concepts, going back to Mott and Ihle-Lorenz, presently appear most promising. Mott’s view of the Verwey transition, as corresponding to the phase changing of a Wigner glass (T>Tv) into a Wigner crystal (T<Tv), describes most adequately the various low-temperature mechanisms in Fe3O4 in terms of tunnelling and variable range hopping of small polarons. On the other hand, the well-elaborated Ihle-Lorenz model, assuming a superposition of polaron-band and -hopping conductivity, is in better agreement with the high-temperature data (Tv<T<600 K).