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 |yz〉, |zx〉 and |xy〉; |0〉 = √1/3|xy〉 + √1/3|yz〉 + √1/3|zx〉 α |(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 Lu ₂V₂O₇, using a Hubbard Hamiltonian with these three orbitals.