Ordering on geometrically frustrating lattices: from fundamental physics to functionality ?

Geometrical frustration arises when geometrical constraints promote a locally degenerate ground state. A periodic system with this local geometry may “freeze” on cooling forming “ices” or remain liquid down to the lowest temperatures due to quantum effects. A third possibility is that of a structural phase transition that lowers the local symmetry and lifts the degeneracy. Two classic examples of geometrical frustration are the so-called pyrochlore lattice, which is also found in AB2X4 spinels, and the “J1-J2” model on a square lattice, which involves competing next- and next-near neighbour magnetic interactions. I will present recent results obtained by x-ray and neutron powder diffraction on orbital ordering in transition-metal spinels, leading to the concept of orbitally-driven Peierls state, and more recent data on MoOVO4, a realization of the J1-J2 model of interest in the so-called multi-ferroic materials has lead to revisit the role of geometrical frustration in coupling different degrees of freedom, “mimicking” a functional behavior. In this context, I will present our work on REMn2O5 by neutron single-crystal and powder diffraction.