Orthorhombic distortion drives orbital ordering in an antiferromagnetic 3$d^1$ Mott insulator

Abstract: 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 super exchange predicts ferromagnetism in an orbitally degenerate $d^1$ systems. 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 long-standing questions, we investigate single crystalline film of PrTiO$_3$. Our synchrotron X-ray diffraction measurements confirm the retention of bulk-like 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$_3$.