Pancakelike Ising domains and charge-ordered superlattice domains in ${\text{LuFe}}_2{\text{O}}_4$

We report magnetic and superlattice imaging of ferrimagnetic bilayered ${\text{LuFe}}_2{\text{O}}_4$ with strong uniaxial magnetic anisotropy. Magnetization reversal is imaged in magnetic fields up to 8 T at several temperatures below $T_N$ $\left(\sim 230\text{K}\right)$ and charge-ordered superlattice domains are imaged at 92 K. We observed random packing of irregular pancakelike magnetic domains $\left(\sim 100\text{nm}\times 30\text{nm}\right)$ and charge-ordered superlattice domains with similar shape $\left(\sim 30\text{nm}\times 6\text{nm}\right)$. The magnetic domain structure shows a strong memory effect in magnetization reversal. Our results are consistent with a spin-charge cross-coupling mechanism in ${\text{LuFe}}_2{\text{O}}_4$.

Figure 1

(Color online) (a) Side view of the stacking of basal planes ($ab$ planes) along the $c$ axis of ${\text{LuFe}}_2{\text{O}}_4$. (b) Top view of the basal planes. (c) Topographic and (d) MFM images (size: $\sim 6\times 6\mu {\text{m}}^2$) of one area of the cleaved surface of ${\text{LuFe}}_2{\text{O}}_4$ taken at 150 K with 8 T. The color scale is 35 nm (10 Hz) for topograph (MFM). (e) and (f) are the cross sections of the lines averaged over the boxes drawn in (c) and (d), respectively. The largest step height is about 10 nm, i.e., four times of the $c$-axis unit-cell size. (g) Schematic illustration. The MFM signal at a step edge of a uniform magnet is equivalent to that of a domain boundary of a thin film with uniaxial anisotropy.

Figure 2

(Color online) (a)–(j) MFM images taken on the same area as Fig. 1 at 150 K in magnetic fields marked in hysteresis loop in (k). The image size is $\sim 6\times 6\mu {\text{m}}^2$. The color contrast is 10 Hz for all images. (k) Hysteresis loop of normalized magnetization $M/M_s$ and the normalized peak-to-peak values $\Delta f/\Delta f\left(8\text{T}\right)$ of two atomic steps averaged over the rectangular box in (a).

Figure 3

High-resolution TEM dark-field image of ${\text{LuFe}}_2{\text{O}}_4$ taken at 92 K with a $\left(\frac{1}{3},\frac{1}{3},\frac{5}{2}\right)$ superlattice spot, which is circled in the inset. The CO domains (bright contrast) have size of $\sim 30\text{nm}$ within the $ab$ plane and $\sim 6\text{nm}$ along the $c$ axis. Inset: TEM diffraction pattern of ${\text{LuFe}}_2{\text{O}}_4$ with $\left(1\overline{1}0\right)$ incidence.