Magnetic state of ${\mathrm{La}}_{1.36}{\mathrm{Sr}}_{1.64}{\mathrm{Mn}}_2{\mathrm{O}}_7$ probed by magnetic force microscopy

We have investigated the ferromagnetic (FM) domain structure of a single-crystal bilayered manganite ${\mathrm{La}}_{2-2x}{\mathrm{Sr}}_{1+2x}{\mathrm{Mn}}_2{\mathrm{O}}_7$ $(x=0.32)$ by using low-temperature magnetic force microscopy. We observed that below $65\mathrm{K}$, the FM domains form stable treelike patterns with out-of-plane magnetization. With increasing temperature, the FM domain patterns gradually change in the form of domain wall motion. Above $80\mathrm{K}$, the FM domain patterns change more and more with each temperature step. The magnetization changes from the out-of-plane to an in-plane direction around $88\mathrm{K}$. The in-plane FM domains almost completely disappear near the Curie temperature of this sample $(T_C\approx 110\mathrm{K})$, where the resistivity exhibits a sharp increase. We also observed large changes in the magnetic structures upon thermal cycling. We concluded that the formation of FM domains at low temperatures $(T<80\mathrm{K})$ is determined by the energy associated with surface magnetic free poles and domain walls. At high temperatures $(80\mathrm{K}<T<T_C)$, the two-dimensional FM fluctuations in the basal plane may also play an important role in forming the domain structures. The evolution of the FM domain patterns with temperature coincides with the change in resistivity.

Figure 1

(Color online) Evolution of magnetic domain structures in ${\mathrm{La}}_{1.36}{\mathrm{Sr}}_{1.64}{\mathrm{Mn}}_2{\mathrm{O}}_7$ with temperature from $30\text{to}80\mathrm{K}$. (a)–(f) are MFM images taken at the area shown in (g) at various temperatures under zero field. Thermal drift of the tip with respect to the sample occurring during the measurement was compensated by the tube scanner offset. (g) is the topography with size $15\times 15\mu {\mathrm{m}}^2$. (h) is the resistivity data in the $ab$ plane (dotted) and the $c$ axis (solid) reported in Ref. 11 for the same samples. In MFM images, the magnetic force gradient generated by magnetic domains is expressed in terms of the resonant frequency shift of the cantilever, and is displayed in the color scale. A repulsive magnetic force results in a positive frequency shift, while an attractive magnetic force results in a negative frequency shift.

Figure 2

(Color online) Evolution of magnetic domain structures in ${\mathrm{La}}_{1.36}{\mathrm{Sr}}_{1.64}{\mathrm{Mn}}_2{\mathrm{O}}_7$ with temperature from $78\text{to}105\mathrm{K}$. The sample was zero-field cooled from room temperature down to $78\mathrm{K}$. The MFM images were taken in a warming up run. (a)–(e) are MFM images taken at the area shown in (f) under zero field. (f) is a topographic image with size $8\times 6\mu {\mathrm{m}}^2$. The step shown in the MFM images in (d) and (e) is due to the topographic effect, which occurs when the magnetic signal is weak.

Figure 3

(Color online) Thermal cycling behavior observed in the magnetic structures in ${\mathrm{La}}_{1.36}{\mathrm{Sr}}_{1.64}{\mathrm{Mn}}_2{\mathrm{O}}_7$ under zero field. The sample was zero-field cooled from room temperature down to $78\mathrm{K}$. (a) and (b) are MFM images taken at the area shown in (c) at initial $78\mathrm{K}$ and final $78\mathrm{K}$, respectively. (c) is topography with size ${\left(8.6\mu \mathrm{m}\right)}^2$. (d) is a histogram of the MFM images (a) (dotted curve) and (b) (solid curve).

Figure 4

(Color online) Evolution of the magnetic domain structures in ${\mathrm{La}}_{1.36}{\mathrm{Sr}}_{1.64}{\mathrm{Mn}}_2{\mathrm{O}}_7$ with magnetic field. (a) and (b) are MFM images taken at the area shown in (c) at $78\mathrm{K}$ under different external fields: (a) $0\mathrm{G}$ and (b) $185\mathrm{G}$. (c) is a topography with size $8.6\times 8.6\mu {\mathrm{m}}^2$. (d) and (e) are MFM images taken at the area shown in (f) at $88\mathrm{K}$ under different external fields: (d) $0\mathrm{G}$ and (e) $240\mathrm{G}$. (f) is a topography with size $7.3\times 6.9\mu {\mathrm{m}}^2$. See text for details.