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PRINCIPAL PUBLICATION AND AUTHORS

Temperature-Driven Self-Doping in Magnetite, H. Elnaggar (a,b), S. Graas (a), S. Lafuerza (c), B. Detlefs (c) W. Tabiś (d,e), M. Gala (d), A. Ismail (a), A. van der Eerden (a), M. Sikora (f), J. Honig (g), P. Glatzel (c), F. de Groot (a), Phys. Rev. Lett. 127, 186402 (2021); https:/doi.org/10.1103/PhysRevLett.127.186402 (a) Debye Institute for Nanomaterials Science, Utrecht (The Netherlands) (b) Sorbonne Université, CNRS UMR 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimi, Paris (France) (c) ESRF (d) Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow (Poland) (e) Institute of Solid State Physics, TU Wien, Vienna (Austria) (f) Academic Centre for Materials and Nanotechnology, AGH University of Science and Technology, Krakow (Poland) (g) Department of Chemistry, Purdue University, West Lafayette, Indiana (USA)

REFERENCES

[1] E.J.W. Verwey, Nature 144, 327 (1939). [2] M.S. Senn et al., Nature 481, 173 (2012). [3] G. Perversi et al., Nat. Commun. 10, 2857 (2019).

dependence of key physical properties such as electrical conductivity and magnetism.

Figure 95 shows the temperature-induced hole-doping described by two parameters, α and β, according to the formula: α Fe2+Oh + β Fe3+Td + (8 - α) Fe2+Td + (16 - β) Fe3+Oh. The first regime is identified by α = β = 8, meaning that no charge transfer effect takes place (highlighted in blue in Figure 95). Here, short-range Fe3+-Fe2+-Fe3+ trimerons exist. The second regime is identified by α = β < 8, where the extra electron at the octahedral site is transferred to the tetrahedral sites (highlighted in brown in Figure 95). In this regime, the self-doping modifies the trimerons and leads to their gradual destruction. The onset of the third regime is identified by α ≠ β (highlighted in red in Figure 95). This implies that cations (and not only charge) are exchanged between the two sublattices where the occupation of the interstitial B sites increases. The trimerons do not exist in this regime.

These results shed light on the role of trimerons: short- range trimerons act as descriptors of correlations (i.e., they describe the evolution of electrical and magnetic properties) in magnetite, and collapse due to the temperature-driven hole self-doping. The results provide an elegant analogy between the effect of chemical doping (where the ratio of

Fe2+/Fe3+ ions is chemically modified by adding impurity atoms of different valency) and temperature-driven self- doping in magnetite, and inspires the question: can this analogy be generalised to other systems exhibiting the metal-insulator transition? Future research will include studying magnetite under high pressure and high temperature.

Fig. 94: Occupation of Fe3+ and Fe2+ ions in octahedral (Oh, plotted in purple and blue) and in tetrahedral (Td, plotted in green and orange) sites per unit cell of Fe3O4 shown for the temperatures between 300 - 1200 K, where charge

redistribution is observed. The vertical bars are shown to guide the eye. Note that the total Fe charge remains constant.

Fig. 95: Temperature evolution of the redistribution parameters α (red) and β (brown) in Fe3O4. Linear and exponential fits are plotted in grey and black dashed lines. A cartoon of the ion transfer in a unit cell of Fe3O4 is shown in the inset.