  Inelastic neutron scattering results on magnetite (Fe3O4) show a large
splitting in the acoustic spin wave branch, producing a 7 meV gap midway to the
Brillouin zone boundary at q = (0,0,1/2) and E = 43 meV. The splitting occurs
below the Verwey transition temperature, where a metal-insulator transition
occurs simultaneously with a structural transformation, supposedly caused by
the charge ordering on the iron sublattice. The wavevector (0,0,1/2)
corresponds to the superlattice peak in the low symmetry structure. The
dependence of the magnetic superexchange on changes in the crystal structure
and ionic configurations that occur below the Verwey transition affect the spin
wave dispersion. To better understand the origin of the observed splitting, we
have constructed a series of Heisenberg models intended to reproduce the
pairwise variation of the magnetic superexchange arising from both small
crystalline distortions and charge ordering. We find that none of the models
studied predicts the observed splitting, whose origin may arise from
charge-density wave formation or magnetoelastic coupling.
