Individual domain characteristics determined by second-harmonic generation diffractometer for multi-domain multiferroics

We investigated the multi-domain states of a multiferroic La-doped BiFeO₃ (BLFO) thin film by examining diffraction patterns in optical second-harmonic generation (SHG) measurement. By directing a laser onto the domain wall within the domain-patterned sample, we observed clear diffraction signatures of SHG waves generated from two ferroelectric domains. We explained the experimental results of the diffraction patterns, including the intensity distribution and the polarization characteristics, using Fresnel propagation of SHG waves. From this, we could determine the amplitude and phase of the SHG waves generated from each domain, and figure out not only the polarization direction of each ferroelectric domain but also the phase related to the complex-valued second-order susceptibility tensor. Consequently, we could present SHG diffractometry as an effective measurement method to reveal the phase details of electric polarization of the multi-domain states of ferroic materials.