Real-space observation of nanoscale magnetic phase separation in dysprosium by aberration-corrected Lorentz microscopy

Magnetic phase separation in single-crystal dysprosium at 97-187 K was investigated using aberration-corrected Lorentz microscopy. The high-resolution Lorentz microscopy combined with the transport-of-intensity equation method successfully visualized the in-plane magnetization distribution of the coexisting magnetic phases. The onset of a phase transition from the ferromagnetic (FM) phase to helical antiferromagnetic (HAFM) phase was observed at similar to 100 K, and the two nanoscale phases coexisted up to similar to 140 K. The volume fraction of the FM phase decreased with increasing temperature, eventually resulting in the formation of static magnetic solitons, which are isolated single domains of the FM phase, at around 130 K. We also performed the in situ observation of the HAFM phase at 142 K by applying an external magnetic field normal to the helical axis. With increasing field, a distorted HAFM phase emerged and the nanoscale phase separation between the HAFM phase and the fan phase subsequently occurred from similar to 6 to similar to 11 kOe. It was proven that the boundaries between these nanoscale coexisting phases were perpendicular to the z axis, which is the rotation axis common to the modulated magnetic structures.