Origin of Electrical Conduction in Domain Walls of BiFeO${_3}$ Thin Films*

BiFeO${_3}$ thin films grown on DyScO${_3}$ substrates unexpectedly exhibit metallic electrical conduction at ferroelectric (FE) domain walls (DWs). Resonant x-ray scattering near Fe L and O K absorption edges was used to probe the electronic structure of these films. In-plane wavevectors of resonant Fe edge magnetic scattering, and non-resonant Cu K $\alpha $ diffraction peaks near the (0, 0, 1) BiFeO${_3}$ Bragg peak, match the domain period observed by PFM. Fe edge scattering intensifies as the beam energy is tuned to Fe 2p $\to$ ligand-3d transitions. No O K charge scattering is observed. These results suggest that metallic conduction does not arise from charge build- up at the DWs from FE polarization discontinuities, but from the bandgap closing near DWs as the crystal symmetry changes from rhombohedral-like in the domain bulk to higher-symmetries.