Skewed electronic band structure induced by electric polarization in ferroelectric BaTiO₃

Skewed band structures have been empirically described in ferroelectric materials to explain the functioning of recently developed ferroelectric tunneling junction (FTJs). Nonvolatile ferroelectric random access memory (FeRAM) and the artificial neural network device based on the FTJ system are rapidly developing. However, because the actual ferroelectric band structure has not been elucidated, precise designing of devices has to be advanced through appropriate heuristics. Here, we perform angle-resolved hard X-ray photoemission spectroscopy of ferroelectric BaTiO₃ thin films for the direct observation of ferroelectric band skewing structure as the depth profiles of atomic orbitals. The depth-resolved electronic band structure consists of three depth regions: a potential slope along the electric polarization in the core, the surface and interface exhibiting slight changes. We also demonstrate that the direction of the energy shift is controlled by the polarization reversal. In the ferroelectric skewed band structure, we found that the difference in energy shifts of the atomic orbitals is correlated with the atomic configuration of the soft phonon mode reflecting the Born effective charges. These findings lead to a better understanding of the origin of electric polarization.