Ferroelectric domain states of a tetragonal BiFeO₃ thin film investigated by second harmonic generation microscopy

We investigate the ferroelectric state of a tetragonal BiFeO₃ thin film grown on a LaAlO₃ (001) substrate using an optical second harmonic generation (SHG) microscope. Whereas the ferroelectric state of this material hosts nanometer-sized domains which again form micrometer-sized domains of four different configurations, we could figure out the characteristic features of each domain from the SHG mapping with various sizes of the probe beam, i.e., from 0.7 to 3.9 μm in its diameter. In particular, we demonstrate that a single micrometer-sized domain contributes to the SHG as a coherent summation of the constituent nanometer-sized domains, and multi-micrometer-sized domains contribute to the SHG as an incoherent summation of each micro-domain.