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 $\sim 100\mathrm{K}$, and the two nanoscale phases coexisted up to $\sim 140\mathrm{K}$. 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 $\sim 6$ to $\sim 11\mathrm{kOe}$. 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.

Figure 1

Newly developed HR Lorentz microscopy using aberration correction. (a) Schematic illustration of the optical system. (b) FFT pattern of the image observed around the focus for a AuPd cross grating. (c) Image observed around the focus for the ${\mathrm{K}}_2\mathrm{Ni}{\mathrm{F}}_4\text{−}\mathrm{type}$ layered manganite $\mathrm{N}{\mathrm{d}}_{0.2}\mathrm{S}{\mathrm{r}}_{1.8}\mathrm{Mn}{\mathrm{O}}_4$ in the [010] projection. The inset is the simulated image. The crystal structure of the manganite is shown below. (d) PCTF in the HR mode, where the defocus value is $-126\mathrm{nm}$, the Scherzer focus. $E_{\mathrm{s}}$ and $E_{\mathrm{c}}$ are envelope functions due to the convergence of the incident beam and the chromatic aberration, respectively.

Figure 2

Temperature dependence of Lorentz overfocused images for single-crystal Dy observed by HR Lorentz microscopy. The temperature is elevated from (a) 97 K to (e) 187 K. A schematic illustration of the areas of the corresponding FM, HAFM, and PM magnetic phases and magnetic solitons is shown below each image.

Figure 3

(a)–(d) Series of Lorentz images observed for the HAFM phase coexisting with magnetic solitons in Dy at 127 K at defocuses from $-12.8\mu \mathrm{m}$ (underfocus) to 12.8 μm (overfocus), FFT patterns, and PCTFs under the defocus condition. ${\mathrm{U}}_1$ and ${\mathrm{O}}_1$ indicate the first zero and ${\mathrm{U}}_2$ and ${\mathrm{O}}_2$ indicate the second zero. The solitons are selectively imaged at defocuses of $\pm 6.4$ and $\pm 12.8\mu \mathrm{m}$. (e) Schematic illustrations of Dy crystal structure, magnetic moments, and in-plane components of magnetic fields (upper) and intensity profiles on line A1-A2 in Lorentz images in (a)–(d), where each profile is shifted along the vertical axis (lower). A periodic variation in the sinusoidal profile with the defocus is clearly seen. (f) Phase image calculated from the Lorentz images for the square area indicated in (a)–(d) (left), the obtained in-plane components of the magnetic fields (middle), and illustration of the areas of a static magnetic soliton and the HAFM phase (right). In the left image, the phase of the electron wave increases with increasing brightness, where the monotone scale indicates the relative increase from the minimum phase. In the middle image, the colors indicate the direction and magnitude of the components, as shown by the color wheel.

Figure 4

(a),(b) Schematic illustrations of magnetic moments of (a) distorted HAFM phase and (b) fan phase. (c)–(f) Distributions of the in-plane magnetization obtained from Lorentz images of Dy in applied magnetic fields of up to 10.4 kOe at 142 K. The fields are normal to the $z$ axis. A schematic illustration of the areas of the corresponding HAFM, distorted HAFM, and fan magnetic phases is shown below each distribution. It can be seen that the boundaries between these phases are perpendicular to the $z$ axis.