Nanodomains and nanometer-scale disorder in multiferroic bismuth ferrite single crystals

We report on an investigation of state-of-the-art flux-grown multiferroic bismuth ferrite (BiFeO₃; BFO) single crystals by transmission electron microscopy and electron diffraction. The crystals were pre-characterized by piezoresponse force microscopy, electrical resistance and superconducting quantum interference device magnetization measurements. The structurally highly perfect crystals show a ferroelectric stripe domain structure characterized by a domain width of 55 nm. Inside these domains an additional contiguous nanodomain substructure occurs, consisting of 180° related domains, giving rise to satellite reflections at 121212-type positions along <110> directions in the electron diffraction pattern corresponding to a characteristic length in real space of 15.5 nm. Furthermore, we present the first atomic-resolution study on the short-range order by aberration-corrected transmission electron microscopy in which all atoms including oxygen are imaged directly. By measuring the -Fe-O-Fe- atom topology, bond angles and atomic distances we derive the electrical dipole moment as well as the magnitude of the magnetic moment on the unit-cell level. The results evidence substantial atomic- to nano-scale disorder. Both the nanodomain substructure as well as the disorder should affect the subtle magnetoelectric interactions in this material and thereby impede the formation of long-range cycloidal spin ordering which up to now was considered an intrinsic feature of the magnetic properties of BiFeO₃ single crystals. By Monte Carlo simulation on the basis of a state-of-the-art effective Hamiltonian we scrutinize certain aspects of the phase formation behavior in the BFO system forming the background of single-crystal growth. This study reveals a very sluggish phase evolution behavior, which should make it invariably difficult to obtain structurally fully equilibrated single crystals.