Charge and Spin Ordering in the Mixed Valence Compound LuFe2O4

Landau theory and symmetry considerations lead us to propose an explanation for several seemingly paradoxical behaviors of charge ordering (CO) and spin ordering (SO) in the mixed valence compound LuFe2O4. Both SO and CO are highly frustrated. We analyze a lattice gas model of CO within mean field theory and determine the magnitude of several of the phenomenological interactions. We show that the assumption of a continuous phase transition at which CO or SO develops implies that both CO and SO are incommensurate. To explain how ferroelectric fluctuations in the charge disordered phase can be consistent with an antiferroelectric ordered phase, we invoke an electron-phonon interaction in which a low energy (20meV) zone-center transverse phonon plays a key role. The energies of all the zone-center phonons are calculated from first principles. We give a Landau analysis which explains SO and we discuss a model of interactions which stabilizes the SO state, if it is assumed commensurate. However, we suggest a high resolution experimental determination to see whether this phase is really commensurate, as believed up to now. The applicability of representation analysis is discussed. A tentative explanation for the sensitivity of the CO state to an applied magnetic field in field-cooled experiments is given.Comment: 36 pages, 17 figure

Spin Dynamics of Trimers on a Distorted Kagom\'e Lattice

We treat the ground state, elementary excitations, and neutron scattering cross section for a system of trimers consisting of three tightly bound spins 1/2 on a distorted Kagom\'e lattice, subject to isotropic nearest neighbor (usually antiferromagnetic) Heisenberg interactions. The interactions between trimers are assumed to be weak compared to the intra trimer interactions. We compare the spin-wave excitation spectrum of trimers with that obtained from standard spin-wave theory and attribute the differences at low energy to the fact that the trimer formulation includes exactly the effects of intra-trimer zero point motion. Application to existing systems is briefly discussed.Comment: 20 pages, 10 figure