A-type antiferro-orbital ordering with I4(1)/a symmetry and geometrical frustration in the spinel vanadate MgV2O4.

: We conduct a detailed structural analysis of the S=1 pyrochlore antiferromagnet MgV2O4, which exhibits an antiferromagnetic ordering marginally at TN=40  K, triggered by a structural transition from cubic to tetragonal symmetry at TS=62  K, using high resolution synchrotron x-ray diffraction and convergent beam electron diffraction. We reveal that the tetragonal phase below TS has the symmetry of I4(1)/a and that the distortion pattern of VO6 octahedra is consistent with A-type antiferro-orbital ordering with alternating stacking of layers with yz/xy orbital chains and zx/xy orbital chains along the tetragonal c axis. This implies that an anisotropic coupling of V moments produced by the orbital ordering below TS primarily brings about the antiferromagnetic ordering.