Observation of magnetic domain and bubble structures in magnetoelectric $\mathrm{S}{\mathrm{r}}_3\mathrm{C}{\mathrm{o}}_2\mathrm{F}{\mathrm{e}}_{24}{\mathrm{O}}_{41}$

The magnetic domain and bubble structures in the Z-type hexaferrite $\mathrm{S}{\mathrm{r}}_3\mathrm{C}{\mathrm{o}}_2\mathrm{F}{\mathrm{e}}_{24}{\mathrm{O}}_{41}$ were investigated using Lorentz microscopy. This hexaferrite exhibits a room-temperature magnetoelectric effect that is attributed to its transverse conical spin structure (TC phase). Upon heating, the TC phase transforms into a ferrimagnetic phase with magnetic moments in the hexagonal $ab$ plane between 410 and 480 K (FM2 phase) and into another ferrimagnetic phase with moments parallel to the $c$ axis between 490 and 680 K (FM1 phase). Accordingly, in this study, the magnetic domain structures in $\mathrm{S}{\mathrm{r}}_3\mathrm{C}{\mathrm{o}}_2\mathrm{F}{\mathrm{e}}_{24}{\mathrm{O}}_{41}$ were observed to change dramatically with temperature. In the TC phase, irregular fine magnetic domains were observed after cooling the specimen from the FM2 to TC phase. In the FM1 phase, striped magnetic domain walls with pairs of bright and dark contrast were formed parallel to the $c$ axis. Upon applying an external magnetic field, the striped magnetic domain walls transformed into magnetic bubbles. The topology of the magnetic bubbles was dependent on the angle between the external magnetic field $\left(H\right)$ direction and the easy $c$ axis. Namely, magnetic bubbles with the topological number $N=1$ (type I) were created for $H\parallel c$, whereas magnetic bubbles with $N=0$ (type II) were created when the magnetic field was tilted from the $c$ axis by $5^{\circ }$. We attribute the high magnetocrystalline anisotropy of $\mathrm{S}{\mathrm{r}}_3\mathrm{C}{\mathrm{o}}_2\mathrm{F}{\mathrm{e}}_{24}{\mathrm{O}}_{41}$ to the emergence of magnetic bubbles in the FM1 phase.

Figure 1

Schematic of imaging in the Fresnel method. The red marks represent the magnetization directions in the respective domains. The green arrowheads mark the positions of the domain walls.

Figure 2

(a) HAADF STEM image of SCFO. Atomic-resolution EDS chemical maps showing the (b) Fe $K$, (c) Co $K$, and (d) Sr $K$ edges. (e) Merged image of (b)–(d). The incident electron beam is along the $a$ axis, and the white arrow in panel (c) shows the direction of the $c$ axis. (f) Schematic of the crystal structure of SCFO along the $a$ axis. The blue, red, and yellow spheres represent Fe, Sr, and O atoms, respectively. The metal sites, $Me4\left(12k\right)$, are marked in green.

Figure 3

(a) Temperature dependence of the magnetization parallel and perpendicular to the $c$ axis of SCFO. The inset shows the derivative of the magnetization $(\mathrm{d}M/\mathrm{d}T)$ at approximately 400 K. Schematics of the magnetization directions are indicated by red arrows. PM, FM, and TC represent the paramagnetic, ferrimagnetic, and transverse conical phases, respectively. (b) Magnetic-field dependence of the magnetization parallel and perpendicular to the $c$ axis at various temperatures. The arrowheads mark the anisotropy field $H_k$.

Figure 4

Magnetic domain structures in the TC [(a) and (d)], FM2 [(b) and (e)], and FM1 [(c) and (f)] phases observed using the Fresnel method. The widest faces of the thin samples used for these experiments were parallel [(a)–(c)] and perpendicular [(d)–(f)] to the $c$ axis. The white and black lines in (a) and (b) represent bright and dark contrast, respectively. The defocus value was $-5\mu \mathrm{m}$. (g)–(i) Schematics of the magnetic domains in panels (a), (b), and (f), respectively. The arrowheads mark the domain walls in the FM1 and FM2 phases. The red arrows represent the magnetization directions in the respective domains and domain walls.

Figure 5

(a) Fresnel image of clockwise and counterclockwise type-I magnetic bubbles at 95 mT and 520 K (FM1 phase). The plane is perpendicular to the $c$ axis, and the magnetic field was applied parallel to the $c$ axis. The defocus value was $-2\mu \mathrm{m}$. (b) and (c) Formation process of type-II magnetic bubbles at 520 K (FM1 phase). The specimen (the $c$ axis) was tilted by $5^{\circ }$ from the magnetic-field direction. The defocus value was $-5\mu \mathrm{m}$. The inset of (c) presents a magnified image of the magnetic bubble marked by a red dashed rectangle. Schematics of magnetic bubbles of (d) type I and (e) type II and their corresponding Fresnel images in an underfocused condition. The blue arrowheads mark the positions of Bloch lines, where the chirality of a domain wall is reversed.