  We study noncentrosymmetric effects on resonant x-ray scattering (RXS) in
magnetite. The noncentrosymmetry at A sites in spinel structure makes the 4p
states strongly hybridize with the 3d states through neighboring oxygen 2p
states, giving rise to the non-vanishing contribution of the dipole-quadrupole
(E1-E2) process in the RXS spectra. We substantiate this observation by
introducing a microscopic model of a FeO_4 cluster with multiplets and the 4p
band. We show that the hybridization changes its sign between two kinds of A
sites and accordingly the local amplitude from the E1-E2 process changes its
sign, resulting in non-vanishing RXS intensities at forbidden spots (002) and
(006) in the pre-edge region in agreement with the experiment. A large
dependence of the pre-edge intensity on the direction of the applied magnetic
field is predicted as a consequence of breaking both centrosymmetry and
time-reversal symmetry. Furthermore we analyze the intensity difference between
two opposite directions of the applied magnetic field at the allowed spot (222)
in connection with the experiment. We obtain the intensity difference of a
"dispersion" form, which resembles the observed spectra at the Mn pre-K-edge in
MnCr_2O_4 but is quite different from the observed one in magnetite. Although
the observed spectra are claimed to arise from "magnetoelectric" amplitude, we
argue that this claim has no ground.
