Fig. 3.
Thermal variations of parameters from magnetite pair distribution function (PDF) fits. a Isotropic temperature factors Uisos for tetrahedral FeA, octahedral FeB, and oxygen sites and the cubic cell parameter from fits to the First Unit Cell PDF range. b Verwey shifts fV fitted to First, Second and Third Unit Cell PDF ranges. fV represents the magnitude of structural distortions due to electronic fluctuations in the cubic phase of magnetite above TV. The First Unit Cell values show that substantial local structural distortions persist up to TC and closely match the variation of bulk magnetisation data taken from ref. 18. This demonstrates that the structural and electronic fluctuations responsible for the Verwey transition are a direct result of the long-range magnetic order. c Comparison of the atomic displacements due to electronic fluctuations dV, calculated from atomic coordinates for the First Unit Cell fV values, and those due to thermal motion taken as dT = √Uiso from values shown in a. Error bars are estimated standard deviations from the refinements