Local structure and orbital ordering in YTiO$_3$

YTiO$_3$, with the strongest GdFeO$_3$-typed distortion in RTiO$_3$, is a ferromagnet below $T_C$ of 30 K and many theoretical and experimental studies suggest it is of antiferro-orbital ordering due to magnetic superexchange. Here, the local atomic structure of YTiO$_3$ has been investigated by using elastic (inelastic) neutron scattering and the (dynamic) pair density function analysis from 5 to 350 K. Deviations are observed of the local from the average crystal symmetry and these are attributed to distortions involving the Y and O atoms. In the case of Y, the in-plane $x-y$ displacements result in an antiferrodistortive motion exerting influence on Y-O1 (apical sites of octahedral) bonds seen in the temperature dependence. At the same time, the O ion site in the basal plane of the octahedron is split to two (O2 and O3), giving rise to two unequivalent Ti-O bonds, which results consequently in different tilting of basal plane of octahedra (0.5$^\circ$ larger in O3), A-O covalency and about 2$^\circ$ larger Ti-O-Ti bond angle in O3 sites. These facts may be regarded as the structural evidences on antiferro-orbital ordering in YTiO$_3$ and suggest electron-lattice interaction may play an important role in the orbital ordering, in addition to magnetic superexchange interation.