Orthorhombic distortion drives orbital ordering in the antiferromagnetic 3$d$ 1 Mott insulator PrTiO 3
The orbital, which represents the shape of the electron cloud, very often strongly influences the manifestation of various exotic phenomena, e.g., magnetism, metal-insulator transition, colossal magnetoresistance, unconventional superconductivity, etc. in solid-state systems. The observation of the antiferromagnetism in $RE$TiO 3 ($RE$ = rare-earth) series has been puzzling since the celebrated Kugel-Khomskii model of spin-orbital superexchange predicts ferromagnetism in an orbitally degenerate $d$ 1 system. Further, the existence of the orbitally ordered vs. orbital liquid phase in both antiferromagnetic and paramagnetic phase have been unsettled issues thus far. To address these longstanding questions, we investigate single crystalline film of PrTiO 3 . Our synchrotron x-ray diffraction measurements confirm the retention of bulklike orthorhombic ($D_{2h}$) symmetry in the thin film geometry. We observe similar x-ray linear dichroism signal in both paramagnetic and antiferromagnetic phase, which can be accounted by ferro-orbital ordering (FOO). While the presence of $D_{2h}$ crystal field does not guarantee lifting of orbital degeneracy always, we find it to be strong enough in these rare-earth titanates, leading to the FOO state. Thus, our work demonstrates the orthorhombic distortion is the driving force for the orbital ordering of antiferromagnetic $RE$TiO 3 .