Structure of Fe₃O₄ at low temperatures

Abstract

Based on all the experimental results hitherto obtained, the structure of Fe₃O₄ at low temperatures is analysed in detail. Experimental results by N.M.R. and Mössbauer-effect experiments are regarded as most important and, carefully extending Mizoguchi's analysis (Mizoguchi 1978), the idealized superstructure at 0 K, has been uniquely derived. The space group is C_2h ⁵ P2₁/c with two glide planes and eight centres of symmetry in the unit cell and it seems that nature likes pairing and equivalence. It was concluded that a pseudo-metallic unit, composed of four Fe²⁺-II ions surrounding one Fe³⁺ ion, couples with the Δ₅ ⁽¹⁾ phonon mode and creates the first-order phase transition at about 125 K. The actual structure at finite temperatures, however, is disturbed by the presence of anti-phases and this disturbance is intrinsic because of the strong long-range correlation between the electron ordering (ring diffusion is involved) and the thermal phonon excitations. The intrinsic presence of the microscopic anti-phases explains the diffraction experiments in which the apparent symmetry is base-centred monoclinic with Δ₅ ⁽¹⁾ modulation. Two mechanisms are proposed for the appearance of ferroelectricity and magnetoelectric effects. Fe²⁺ ions on A sites may displace along the a direction cooperatively when squeezed by the unit formation. This modifies the space group into C_s ² Pc, i.e. still monoclinic with glide planes but without centres of symmetry, and explains the principal term of the magnetoelectric effects. Further, the antiphase boundaries tend to become asymmetrically unidirectional and take out from the crystal any kind of symmetries (the translational symmetry as well).