Magnetic order and ice rules in the multiferroic spinel FeV ₂O ₄

We present a neutron-diffraction study of FeV ₂O ₄, which is rare in exhibiting spin and orbital degrees of freedom on both cation sublattices of the spinel structure. Our data confirm the existence of three structural phase transitions previously identified with x-ray powder diffraction and reveal that the lower two transitions are associated with sequential collinear and canted ferrimagnetic transitions involving both cation sites. Through consideration of local crystal and spin symmetry, we further conclude that Fe2 ⁺ cations are ferro-orbitally ordered below 135 K and V3 ⁺ orbitals order at 60 K, in accordance with predictions for vanadium spinels with large trigonal distortions and strong spin-orbit coupling. Intriguingly, the direction of ordered vanadium spins at low temperature obey "ice rules" more commonly associated with the frustrated rare-earth pyrochlore systems.