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Bloch lines are formed to reduce the magnetostatic energy generated by theBloch walls in uniaxial magnets. Recently, it is reported that Bloch lines playimportant roles in the emergence and helicity reversal of magnetic bubbles inSc-substitute M-type hexaferrites(BaFe$_{12-x-0.05}$Sc$_{x}$Mg$_{0.05}$O$_{19}$). Although Bloch lines have beendiscussed on the basis of micromagnetic simulations, the detailed structure wasnot observed directly. In this study, we investigated the microscopicstructures 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 misalignedin the Bloch lines of BaFe$_{10.35}$Sc$_{1.6}$Mg$_{0.05}$O$_{19}$. From themicromagnetic simulations based on the Monte-Carlo technique, we showed thatthe misaligned Bloch walls were caused by the dipole-dipole interactions in thehexaferrite. Our results will help to understand the microstructures of Blochlines at nanometer scale.

Microscopic magnetization distribution of Bloch lines in a uniaxial magnet