Orthorhombic distortion drives orbital ordering in antiferromagnetic 3d¹ Mott insulator

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 strongly correlated transition metal oxides. The observation of the antiferromagnetism in RETiO₃ (RE = rare-earth) series has been puzzling since no Jahn-Teller distortion was observed and therefore, the celebrated Kugel-Khomskii model of spin-orbital superexchange predicts ferromagnetism in an orbitally degenerate d¹ system. Further, the existence of the orbitally ordered vs. orbital liquid phase in both antiferromagnetic (AFM) and paramagnetic phases remains highly debated. To address these longstanding questions, we investigate single crystalline film of PrTiO₃, a prototypical AFM Mott insulator (3d¹). 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 signals in both paramagnetic and antiferromagnetic phases that originate due to robust ferro-orbital ordering (FOO). While the presence of D_2h crystal field does not always guarantee the lifting of orbital degeneracy, we find it strong enough in these rare-earth titanates, leading to the FOO state. Thus, our work demonstrates that orthorhombic distortion is the driving force for the orbital ordering of antiferromagnetic RETiO₃.