Magnetic inhomogeneity in a multiferroic EuTiO${}_3$ thin film

We report on variable temperature magnetic force microscopy studies of a strain-enabled multiferroic EuTiO${}_3$ film epitaxially grown on a (110)-oriented DyScO${}_3$ substrate. Our temperature- and magnetic-field-dependent studies clearly reveal an inhomogeneous magnetic state with the coexistence of ferromagnetic and nonferromagnetic states at low magnetic fields, which provides a microscopic origin of the anomalous missing moment in previous studies [Lee et al., Nature (London) 466, 954 (2010)]. The spins of the nonferromagnetic phase can be aligned by modest magnetic fields (>1.5 T). The observed magnetic inhomogeneity probably originates from the coexistence of nearly degenerate magnetic ground states.

Figure 1

(a) Topographic and (b)–(f) MFM images (size 6×6 μm${}^2$) were taken at the same location with zero magnetic field after ZFC. The color scale range is 50 nm (0.5 Hz) for the topography (MFM) image. (g) Temperature dependence of the rms values of MFM images. The blue line indicates the background of rms values (above $T_{\mathrm{C}}$).

Figure 2

(a)–(f) Magnetic-field-dependent MFM and (g) topographic images were taken at the same location at 3.2 K after ZFC. The cartoons above the MFM images represent the magnetic moments under various applied magnetic fields. (f) was measured at zero field after application of magnetic fields (5 T). (h) Magnetic field dependence of the rms value (blue) of the MFM images at 3.2 K and the cross-correlation coefficient (red) between the 0.3 T MFM image (c) and all the MFM images. The inset between (g) and (h) shows the crystallographic orientations of the sample relative to scan images.

Figure 3

(a) The topographic and (b)–(i) temperature-dependent MFM images taken under a 0.25 T out-of-plane external field. The scan size is 6×6 μm${}^2$, with a color scale 50 nm (1.5 Hz) for topography (MFM). Green boxes mark the same location in different images. (j) The temperature dependence of the magnetization of ETO/DSO at a 0.01 T in-plane field (black curve); the temperature dependences of the rms values were calculated from the whole MFM image (red) and green box area (green), respectively. (k) A representative line cut on the MFM image at 3.0 K along the blue line (upper panel) and a schematic illustration of the magnetization (lower panel) along the line profile. The blue (green) color represents the FM (non-FM) phase in the film.