Abstract
The Verwey transition in Fe3O4 is the first metal-insulator transition caused by charge ordering. However, the physical mechanism and influence factors of Verwey transition are still debated. Herewith, the strain effects on the electronic structure of low-temperature phase (LTP) Fe3O4 with P2/c and Cc symmetries are investigated by first-principles calculations. LTP Fe3O4 with each space group has a critical strain. With P2/c, Fe3O4 is sensitive to the compressive strain, but it is sensitive to tensile strain for Cc. In the critical region, the band gap of LTP Fe3O4 with both two symmetries linearly increases with strain. When strain exceeds the critical value, DOS of spin-down t2g electron at Fe(B4) with P2/c and Fe(B42) with Cc changes between dx2-y2 and dxz + dyz. The trimerons appear in Cc can be affected by strain. With a compressive strain, the correlation of trimeron along x and y axes is strengthened, but broken along the face diagonal of FeB4O4, which is opposite at the tensile strains. The results suggest that the electronic structure of Fe3O4 is tunable by strain. The narrower or wider band gap implies a lower or higher transition temperature than its bulk without strains, which also gives a glimpse of the origin of charge-orbital ordering in Fe3O4.
Highlights
The Verwey transition in Fe3O4 is the first metal-insulator transition caused by charge ordering
The lattice structure of low-temperature phase (LTP) Fe3O4 was clarified by X-ray diffraction, Raman and infrared spectroscopy in recent thirty years[1,8,9,10,11]
TV, the lattice is a suppercell of 2 ac × 2 ac × 2ac with Cc symmetry
Summary
The electronic structures of the LTP Fe3O4 with structure (I) P2/c1 and structure (II) Cc19 are calculated by using the potential projector augmented wave method in Vienna Ab initio Simulation Package[27,28]. The lattice constants and atomic positions in the two structures are used as that in refs 1 and 19, respectively. The same parameters except for k-points of 3 × 3 × 3 are used to calculate the high-temperature phase (HTP) Fe3O4 with structure (III) Fd3m symmetry. Biaxial lattice strain is applied by fixing the in-plane lattice constants (a and b) and relaxing z direction throughout the calculations. In order to clarify the strain effects on the charge-orbital ordering, the structural optimization for structures (I) and (II) with lattice constants are carried out, where the atomic positions are fully relaxed. The structure optimization will stop until the total energy change is less than 10−5 eV and the Hellman–Feynman forces of optimized structure fall below 10−2 eV/Å
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