On the basis of the pure ionic model the charge ordering in magnetite is studied with due account of the wa vevector-dependen t polarization -screening effect. The Verwey ordering (Tf,) is found to be unstable for the electronic polarizability of oxygens larger than [ac] c =0.91A', where the stablest charge-ordering pattern must be of X, symmetry. It is also shown that one fourth of the total modes of the charge fluctuation are nearly degenerate at the critical polarizability [ae] 0 • §I.

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... uction Recent experiments on magnetite (electron microscope observation, v electron diffraction, 2 ) neutron diffraction, 3 J Mossbauer effecel and magnetic resonance')) have proved the inyalidity of the Venvey ordering, 6 > which has been believed to occur below the transition temperature Tv= 123K. 7 ) The actual ordering in the octahedral (B) sites inyolves doubling of the unit cell along a cube edge with a slight monoclinic distortion. 8 > The monoclinic symmetry is also in contradistinctio n with the previous result. 9 J By the critical neutron scattering, Shirane et al. 10 > observed the condensation of the phonon mode with wave vector k = (0, 0, 1/2) in units of 2TC/a with a the edge length of the cubic unit cell. Yamadaw showed that the condensed phonon mode has .:15 symmetry and suggested that the charge ordering with the same symmetry might be realized below Tv. However the latest neutron experiment does not exclude the possibility of the other structure of x4 symmetry. 12 ) Theoretically the charge ordering in magnetite is one of very difficult subjects, even if one left its complex structure aside. The ordering seems to occur as a resultant of the two competing effects; the short-range interactions which make electrons delocalize and the long-range ones which make the charge ordering. The mentioned competition is manifested in a dramatic lowering of the transition temperature under high pressures, 13 J as a result of increasing hopping effect. Now in the present paper we shall reexamine the previous result on the basis of the long-range interactions which are of the electrostatic character. In the pure ionic picture the Verwey pattern gives the minimum electrostatic energy,w assuming the bare charge-charge interactions. The ordering energy (9.966 X 10 3 K