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Landau theory and symmetry considerations lead us to propose an explanationfor several seemingly paradoxical behaviors of charge ordering (CO) and spinordering (SO) in the mixed valence compound LuFe2O4. Both SO and CO are highlyfrustrated. We analyze a lattice gas model of CO within mean field theory anddetermine the magnitude of several of the phenomenological interactions. Weshow that the assumption of a continuous phase transition at which CO or SOdevelops implies that both CO and SO are incommensurate. To explain howferroelectric fluctuations in the charge disordered phase can be consistentwith an antiferroelectric ordered phase, we invoke an electron-phononinteraction in which a low energy (20meV) zone-center transverse phonon plays akey role. The energies of all the zone-center phonons are calculated from firstprinciples. We give a Landau analysis which explains SO and we discuss a modelof interactions which stabilizes the SO state, if it is assumed commensurate.However, we suggest a high resolution experimental determination to see whetherthis phase is really commensurate, as believed up to now. The applicability ofrepresentation analysis is discussed. A tentative explanation for thesensitivity of the CO state to an applied magnetic field in field-cooledexperiments is given.

Charge and Spin Ordering in the Mixed Valence Compound LuFe2O4