# Nonlinear Optical Microscopy of Interface Layers of Epitaxial Gamet Films
## 3 Experimental Results  
Figure 1b shows the optical transmission image of the studied \((LuBi)_{3}Fe_{5}O_{12}\) film in the absence of the external magnetic field for the crossed polarizations of the incident and transmitted beams. Dark and light regions on the Figure correspond to stripe domains in the bulk of the garnet film with the period of the domain structure of about 4.4 \(\upmu\)m; the contrast in the image appears as the result of the opposite in sign Faraday rotation in the adjacent domains with residual magnetization oriented predominantly along the normal to the garnet layer. A magnetic force microscopy image of the (outer) \((LuBi)_{3}Fe_{5}O_{12}\)/air interface measured over the 20 \(\upmu\)m \(\times\) 20 \(\upmu\)m surface area is shown in Figure 1c. Besides the periodic magnetic structure associated with the aforementioned stripe domains, it reveals a zigzag-like pattern with the period of approximately 1.6 \(\upmu\)m associated with the block blind domains. It is worth noting that the high contrast of the MFM signal from the adjacent domains indicate the predominant perpendicular magnetic anisotropy of the film. Similar conclusions were made based on the studies of the second harmonic generation microscopy of the \((LuBi)_{3}Fe_{5}O_{12}\)/air interface, as the pump laser beam at the wavelength of 850 nm was incident on the sample from the substrate side (see Figure 2a). In that case, the SHG response at the wavelength of 425 nm is formed by the surface layer of 2-3 \(\upmu\)m in thickness (determined by the escape length of the radiation at the SHG wavelength), which allows the study of the surface domain structure of garnet film at this hidden interface. Figure 2b,d show the SHG intensity patterns for the parallel (panel \(b\)) and orthogonal (panel \(d\)) polarizations of the fundamental and SHG beams. In both cases the pump beam was polarized along the stripe domains oriented in the vertical direction on the Figure; the scanning was performed over the surface area of 7 \(\upmu\)m \(\times\) 7 \(\upmu\)m. One can see that in the first case, the SHG pattern reveals the stripe domains that appear as the bands with a strong difference in the SHG intensity, while for the crossed polarizations of the pump and SHG waves, a chessboard-like pattern of the SHG intensity is attained. Figure 2c shows the 3D distribution of the SHG intensity from the same surface region as in Figure 2d. It also demonstrates a strongly periodic modulation of the nonlinear optical response with the periods of about 4.2 \(\upmu\)m in the horizontal direction and corresponds to the stripe magnetic domains, while the period of 1.6 \(\upmu\)m appears along the vertical direction. These images confirm the existence of zigzag-shape closure domains with a predominant in-plane orientation of magnetization, which stems from the symmetry analysis discussed in [42]. Importantly, the stripe domains' alignment and relevant SHG patterns are independent on the crystallographic orientation of the film and follow the direction of the external magnetic field used for their magnetization, which was removed prior to the MFM or nonlinear optical studies. Similar SHG microscopy experiments were performed for the hidden \((LuBi)_{3}Fe_{5}O_{12}\) /GGG interface, which is inaccessible by the MFM technique (Figure 3). Really, in that case the MFM probe is separated from the garnet layer by a GGG substrate that is several hundreds of micrometers in thickness. In order to attend the \((LuBi)_{3}Fe_{5}O_{12}\)/GGG interface by the SHG microscopy probe, we reversed the experimental geometry so that the laser beam was incident on the sample from the film side, as shown schematically in Figure 3a. The effective thickness of the garnet layer participating in the SHG process was estimated by measuring the dependence of the SHG intensity on the coordinate along the normal to the film, z, which is shown in Figure 3b.