Orbital ordering in ferromagnetic Lu2V2O7

We have observed the orbital ordering in the ferromagnetic Mott-insulator Lu2V2O7 by the polarized neutron diffraction technique. The orbital ordering pattern determined from the observed magnetic form factors can be explained in terms of a linear combination of wave functions vertical bar yz >, vertical bar zx > and vertical bar xy >; vertical bar 0 > = root 1/3 vertical bar xy > + root 1/3 vertical bar yz > +root 1/3 vertical bar zx > proportional to vertical bar(x + y + z)(2) - r(2)>, where each orbital is extended toward the center-of-mass of the V tetrahedron. We discuss the stability of the ferromagnetic Lu2V2O7, using a Hubbard Hamiltonian with these three orbitals.