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1. Senn, Mark Stephen. Charge, orbital and magnetic ordering in transition metal oxides.

Degree: PhD, 2013, University of Edinburgh

Neutron and x-ray diffraction has been used to study charge, orbital and magnetic ordering in some transition metal oxides. The long standing controversy regarding the nature of the ground state (Verwey structure) of the canonical charge ordered material magnetite (Fe3O4) has been resolved by x-ray single crystal diffraction studies on an almost single domain sample at 90 K. The Verwey structure is confirmed to have Cc symmetry with 56 unique sites in the asymmetric unit. Charge ordering is shown to be a useful first approximation to describe the nature of the ground state, and the conjecture that Verwey made in 1939 has finally been confirmed. However, three-site distortions which couple to the orbital ordering of the Fe2+ ordered states (trimerons) are shown to provide a more complete description of the low temperature structure. Trimerons explain the rather continuous distribution of the valence states observed in magnetite below Tv, anomalous shortening of Fe-Fe distances and the off-centre distortions resulting in ferroelectricity. DFT+U electronic structure calculations on the experimental coordinates support the conclusion of this crystallographic study, with the highest electron densities calculated for those Fe-Fe distances predicated to participate in the trimeron bonds. The 6H-perovskites of the type Ba3ARu2O9 have been reinvestigated by high resolution neutron and x-ray power diffraction. The charge ordered state of Ba3NaRu2O9 has been characterised at 110 K (P2/c, a =5.84001(2) Å, b = 10.22197(4) Å, c = 14.48497(6) Å, β = 90.2627(3) °) and shown to consist of a structure with near integer charge ordering of Ru5+ 2O9 / Ru6+ 2O9 dimers. The ground state has been shown to be very sensitive to external perturbations, with a novel melting of charge ordering observed under x-ray irradiation below 40 K (C2/c, a =5.84470(2) Å, b = 10.17706(3) Å, c = 14.45866(5) Å, β = 90.2151(3)-° at 10 K). High pressure studies reveal that the Ru-Ru intra-dimer distance may dictate the response of the system to pressure. Empirical trends in the Ba3ARu2O9 series of compounds have shown that change in ‘chemical pressure’ in these systems may be rationalised in terms of Coulomb’s law. In A = La and Y the magnetic ordering is shown to be FM within the Ru2O9 dimers (1.4(2) μB and 0.5(1) μB, respectively per Ru), representing the first case of intra dimer FM coupling reported in a system containing face-sharing RuO6 octahedra . The overall AFM coupling of the dimers implies an as yet unobserved breaking of the parent symmetry. In A = Nd, a complex competition between the crystal field effect of Nd3+ and the magnetic ordering of the Ru2O9 FM moments has been observed, leading first vi to FM order of Nd at 25 K (1.56(7) μB) followed by ordering of Ru moments (0.5(1) μB) and a spin reorientation transition of Nd moments at 18 K. In A = Ca, the formation of a singlet ground state is observed in Ru2O9 rather than the expected AFM coupling and below 100 K Ba3CaRu2O9 is diamagnetic. All five systems indicate that the Ru2O9 dimer is the…

Subjects/Keywords: 661; transition metal oxides; Charge ordering; Verwey structure; orbital ordering; trimerons

…28 Section B: The Verwey structure of Magnetite… …41 Solution of the Verwey structure of magnetite by single crystal x-ray diffraction... 45… …59 3.3.3. Validation of the final model of the Verwey structure… …91 Electronic structure calculations on the Verwey ground state… …177 Appendix B : Details of the distortion mode analysis for the Verwey structure… 

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APA (6th Edition):

Senn, M. S. (2013). Charge, orbital and magnetic ordering in transition metal oxides. (Doctoral Dissertation). University of Edinburgh. Retrieved from

Chicago Manual of Style (16th Edition):

Senn, Mark Stephen. “Charge, orbital and magnetic ordering in transition metal oxides.” 2013. Doctoral Dissertation, University of Edinburgh. Accessed January 26, 2021.

MLA Handbook (7th Edition):

Senn, Mark Stephen. “Charge, orbital and magnetic ordering in transition metal oxides.” 2013. Web. 26 Jan 2021.


Senn MS. Charge, orbital and magnetic ordering in transition metal oxides. [Internet] [Doctoral dissertation]. University of Edinburgh; 2013. [cited 2021 Jan 26]. Available from:

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Senn MS. Charge, orbital and magnetic ordering in transition metal oxides. [Doctoral Dissertation]. University of Edinburgh; 2013. Available from: