Microscopic magnetization distribution of Bloch lines in a uniaxial magnet

Bloch lines are formed to reduce the magnetostatic energy generated by the Bloch walls in uniaxial magnets. Recently, it is reported that Bloch lines play important roles in the emergence and helicity reversal of magnetic bubbles in Sc-substitute M-type hexaferrites (BaFe${}_{12-x-0.05}$Sc${}_x$Mg${}_{0.05}$O${}_{19}$). Although Bloch lines have been discussed on the basis of micromagnetic simulations, the detailed structure was not observed directly. In this study, we investigated the microscopic structures of Bloch lines in BaFe${}_{10.35}$Sc${}_{1.6}$Mg${}_{0.05}$O${}_{19}$ uniaxial magnets. Differential-phase contrast scanning transmission microscopy (DPC-STEM) directly revealed that the edges of the Bloch walls were misaligned in the Bloch lines of BaFe${}_{10.35}$Sc${}_{1.6}$Mg${}_{0.05}$O${}_{19}$. From the micromagnetic simulations based on the Monte-Carlo technique, we showed that the misaligned Bloch walls were caused by the dipole-dipole interactions in the hexaferrite. Our results will help to understand the microstructures of Bloch lines at nanometer scale.