Ordering on geometrically frustrating lattices: The perspective of TOF neutron crystallography

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 nearest- and next-near-neighbor magnetic interactions. We present recent results obtained by time-of-flight (TOF) 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. A surge of interest in the so-called multiferroic materials has led to revisit the role of geometrical frustration in coupling different degrees of freedom. In this context, we present recent results on REMn2O5 obtained by neutron single-crystal and powder diffraction.