Unconventional crystal-field splitting in noncentrosymmetric BaTiO 3 thin films
Understanding the crystal-field splitting and orbital polarization in noncentrosymmetric systems such as ferroelectric materials is fundamentally important. In this work, taking BaTiO 3 as a representative material, we investigate titanium crystal-field splitting and orbital polarization in noncentrosymmetric TiO 6 octahedra with resonant x-ray linear dichroism at the Ti L 2,3 edge. The high-quality BaTiO 3 thin films were deposited on DyScO 3 (110) single crystal substrates in a layer-by-layer way by pulsed laser deposition. The reflection high-energy electron diffraction and element specific x-ray absorption spectroscopy were performed to characterize the structural and electronic properties of the films. In sharp contrast to conventional crystal-field splitting and orbital configuration (d xz /d yz < d xy < d 3z 2 -r 2 < d x 2 -y 2 or d xy < d xz /d yz < d x 2 -y 2 < d 3z 2 -r 2 ) expected from compressive or tensile epitaxial strain, respectively, it is revealed that d xz , d yz , and d xy orbitals are nearly degenerate, whereas d 3z 2 -r 2 and d x 2 -y 2 orbitals are split with an energy gap ~100 meV in the epitaxial BaTiO 3 films. We find that the unexpected degenerate orbitals d xz /d yz /d xy result from the competition between the orbital splitting induced by epitaxial strain and that induced by polar distortions of BaTiO 3 films. Our results provide a route to manipulate orbital degree of freedom by switching electric polarization in ferroelectric materials.