Disappearance of peculiarly large atomic displacement in the high-temperature phase of magnetite with substitution of Fe ²⁺ by Ni ²⁺ and Mn ²⁺

Single crystal specimens of Fe_2.992O₄ (magnetite), Fe_3-x-yMn_x□_yO₄ (x ≤ 0.980) and Fe_3-x-yNi_x□_yO₄ (x ≤ 0.513, □ denotes point defects) are prepared using a floating-zone technique, and changes in their structural parameter values with x are examined at room temperature. Preferences of Mn, Ni and point defects at A, B and B sites, respectively, are confirmed by single-crystal X-ray diffraction experiments, while preference of Mn at the A site is not perfectly accomplished in Fe_2.010Mn_0.980O₄. Mean-square displacements of atoms along the 3 axis in [111] are peculiarly large at the B site in Fe_2.992O₄ and the displacement decreased smoothly in both series, to nearly half in Fe_2.00Mn_0.980O₄, with increasing amount of heteroatom. On the other hand, displacements normal to the direction show only slight convexity with x due to coexistence of the heteroatom. As a result anisotropy in displacements (dominant in [111] at x = 0) is inverted at x = 0.3 in FeMn series and would expectedly be inverted at x ≃ 0.55 in FeNi series. In spite of different locations of heteroatoms and slightly different inversion points on anisotropy, changes in mean-square displacements at the B site in [111] in these series are found on similar lines with changing amounts of heteroatom. In other words, the amount of this displacement is a function of the amount of Fe²⁺, or remnant electron from the itinerant-electron point-of-view, on the B-site substructure in these compounds. This characteristic lattice mode on the B-site substructure could be interpreted as an average of local distortion of the substructure due to `trimeron' [Senn et al. (2012). Nature, 481, 173-176] and some other modes such as distortion in 〈001〉 [Siratori & Kino (1980). J. Magn. Magn. Mat. 20, 87-90], which moves in the high-temperature structure.