The idea of the coordination polyhedron is essential to understanding chemical structure. Simple polyhedra in crystalline compounds are often deformed due to structural complexity or electronic instabilities so distortion analysis methods are useful. Here we demonstrate that analysis of the minimum bounding ellipsoid of a coordination polyhedron provides a general method for studying distortion, yielding parameters that are sensitive to various orders in metal oxide examples. Ellipsoidal analysis leads to discovery of a general switching of polyhedral distortions at symmetry-disallowed transitions in perovskites that may evidence underlying coordination bistability, and reveals a weak off-centre ‘d5 effect' for Fe3+ ions that could be exploited in multiferroics. Separating electronic distortions from intrinsic deformations within the low temperature superstructure of magnetite provides new insights into the charge and trimeron orders. Ellipsoidal analysis can be useful for exploring local structure in many materials such as coordination complexes and frameworks, organometallics and organic molecules.

The nature of the Verwey transition occurring at T V ≈ 125 K in magnetite (Fe 3 O 4 ) has been an outstanding problem over many decades. A complex low temperature electronic order was recently discovered and associated structural fluctuations persisting above T V are widely reported, but the origin of the underlying correlations and hence of the Verwey transition remains unclear. Here we show that local structural fluctuations in magnetite emerge below the Curie transition at T C ≈ 850 K, through X-ray pair distribution function analysis. Around 80% of the low temperature correlations emerge in proportion to magnetization below T C . This confirms that fluctuations in Fe-Fe bonding arising from magnetic order are the primary electronic instability and hence the origin of the Verwey transition. Such hidden instabilities may be important to other spin-polarised conductors and orbitally degenerate materials.

Incomplete transformations from ferromagnetic to charge ordered states in manganite perovskites lead to phase-separated microstructures showing colossal magnetoresistances. However, it is unclear whether electronic matter can show spontaneous separation into multiple phases distinct from the high temperature state. Here we show that paramagnetic CaFe3O5 undergoes separation into two phases with different electronic and spin orders below their joint magnetic transition at 302 K. One phase is charge, orbital and trimeron ordered similar to the ground state of magnetite, Fe3O4, while the other has Fe2+/Fe3+charge averaging. Lattice symmetry is unchanged but differing strains from the electronic orders probably drive the phase separation. Complex low symmetry materials like CaFe3O5 where charge can be redistributed between distinct cation sites offer possibilities for the generation and control of electronic phase separated nanostructures.

The semivalent oxyphosphate VOPO is found to have long-range V/V charge ordering up to 605 K where a monoclinic to tetragonal structural transition and a switch from positive to negative thermal expansion are observed. V-V bonding within orbital polymer chains is proposed as the key factor in the novel switch of thermal expansion behavior, as loss of V-V bonding enables transverse oxygen motions to dominate the thermal expansion at high temperatures. Ferrimagnetic order of V spin up and V spin down states is observed below a magnetic ordering transition at 164 K, and susceptibility measurements evidence local spin pairing correlations to higher temperatures.

The thermal evolution of electronic order in the complex Verwey ground state of magnetite (Fe 3 O 4 ) has been determined through 22 high-accuracy synchrotron x-ray structure refinements using three 10-40 μm grains of stoichiometric magnetite. A robust fitting function is introduced to extract values of order parameterlike quantities at zero temperature and at the upper limit of the Verwey phase T u = 123.4 K. The low-temperature structural distortion is found to be almost frozen below the Verwey transition but small changes in lattice and local mode amplitudes and Fe-Fe distances reveal an increase in electron localization on cooling. These distortions confirm that electron localization within trimerons is the driving force behind the Verwey transition. Electron localization is also revealed by anomalous decreases in the largest principal thermal displacement factors of Fe cations as electron-phonon decoupling occurs on cooling.