## 3 Results and Discussion  
### Garnet Film Morphology and Magnetic Fringe Shape  
A typical cross-sectional view of the garnet film used in the experiments is shown in Figure 3[21]. The polycrystalline garnet film consists of grains measuring 20-55 nm and is enough small to record the interference pattern of the collinear hologram with a sufficient resolution. Figure 4 shows the experimentally and numerically obtained maximum diffraction efficiencies normalized to that of 500 line-pairs/mm against the spatial frequency of the fringes written in the 3-\(\upmu\)m-thick Bi:RIG single-layer medium. The diffraction efficiency decreases with spatial frequency to approximately 20% at 1500 line-pairs/mm in both the experiment and simulation [19]. The simulation results are in good agreement with the experimental results, with the former being slightly larger than the latter. Figure 3: Cross sectional view of a typical garnet film that consists of grains with size 20–55 nm. Because the grain size is approximately 50 nm or less, interference fringes with 1500 line-pairs/mm (667 nm periods) are recorded with 13 or more grains. Adapted with permission from Reference [21]. Figure 2: Experimental setup for two-beam and collinear interference systems [27]. In the collinear system, both reference and signal parts shown on the digital micromirror device are irradiated on the recording medium for recording, and only the reference parts are irradiated for reconstructing the hologram. In the two-beam interference system, a laser beam is divided into two by a half mirror and incident on the medium for recording, and one of the beams is stopped by a shutter for reconstruction. This decrease in diffraction efficiency with spatial frequency could be because of the decrease in fringe depth [19]. In contrast, to investigate why the experimental diffraction efficiencies are lower than those of the simulation, direct observation of magnetic fringes was performed using X-ray radiation at SPring-8. Figure 5a shows an XMCD observation result of a 500 line-pairs/mm sample in which an interference fringe interval of approximately 2 \(\upmu\)m was observed. As shown in the figure, contrast changes are observed at 2-\(\upmu\)m intervals; this means that interference fringes could be observed with XMCD mapping. In contrast, in the case of the 1500 line-pairs/mm sample in which an interference fringe interval of 0.7 \(\upmu\)m was observed, the interference fringes are not very clear, as shown in Figure 5b. To determine the reason for these results, the Fe K\(\upalpha\) fluorescent X-ray intensity distribution simultaneously evaluated in the same location as that in Figure 5a is shown in Figure 5c. From this figure, the contrast, which indicates the concentration of Fe, is found to be nonuniform in the film, and the magnetic fringes observed in the XMCD image tend to be disturbed in the inhomogeneous part of the Fe composition. This suggests that composition fluctuations at a 1-\(\upmu\)m scale or less may exist in the Bi:RIG film, and the compositional heterogeneity of this film is a factor influencing the heterogeneity observed in the XMCD image. In addition, by comparing the XMCD intensity of the uniformly magnetized region in the opposite direction to the intensity of the interference fringes, it was found that the magnetization of the magnetic fringes may not be completely reversed by thermomagnetic writing. These observation results indicate that compositional inhomogeneity exists in the Bi:RIG film and disturbs the precise recording of magnetic fringes. Therefore, the improving compositional homogeneity is needed for improving the shape of magnetic fringes, and magnetic assist recording is effective for increasing the magnetic fringe reversal. Figure 4: Diffraction efficiency of the magnetic hologram normalized to that at 500 line-pairs/mm: Comparison between simulation and experimental results at various spatial frequencies.