## 1 Introduction  
Holographic memory has been attracting attention as a data-storage technology with high recording density and data transfer rates because two-dimensional (2D) page data can be recorded and read selectively from a single position [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11]. The Holographic Versatile Disk is an international standard for holographic memory and employs a collinear holographic system that can write and read data using a single optical axis with a spatial light modulator as the key device [12; 13; 14]. Most holographic memories use refractive-index-modulation-type photopolymers, whereas photopolymer-based hologram media can only be written once. In contrast, the magnetic hologram is a candidate for rewritable holograms and exhibits a high material stability, in which the interference patterns of light can be recorded as differences in the direction of magnetization; interference patterns have been recorded on thin films of MnBi and TbFe alloys as magneto-optical recording materials [15; 16; 17; 18]. A magnetic hologram is recorded using the thermomagnetic recording technique (Figure 1). When focused signal and reference beams were incident on a perpendicularly magnetized film, the light interference produces an intensity distribution in the order of the wavelength of light in the film. As a result, absorption of light produces a temperature distribution in the film corresponding to the interference pattern (Figure 1a,b). The magnetization of the heated region above the Curie temperature is reversed during cooling by stray and external magnetic fields (Figure 1c,d). By using this mechanism, the interference pattern of light can be recorded as differences in the direction of magnetization of the magnetic material in the magnetic hologram. To achieve a temperature distribution that corresponds to an interference fringe, the irradiation time of the laser beam must be sufficiently short to suppress thermal diffusion during irradiation [19]. A written hologram can be reconstructed by a magneto-optical effect such as the Faraday effect [15; 16; 17; 18; 19; 20; 21], and a large Faraday rotation angle results in a bright reconstruction image. We have conducted studies to realize magnetic hologram memory using polycrystalline magnetic garnet films such as bismuth-substituted rare-earth iron garnet (Bi:RIG), which has a sufficient transparency and long-term stability [21; 22; 23; 24; 25; 26; 27]. In the garnet films, volumetric magnetic holograms can be recorded with a high resolution because polycrystalline garnet films can have small magnetic domains originating from the crystal grains by the weak magnetic coupling between grains [28]. As a result, we have succeeded in recording 2D data and reconstructing them from the magnetic hologram without error [26; 27], whereas the diffraction efficiency of magnetic garnet films, an index for the brightness of an image, would not be sufficient for application to actual storage devices. The diffraction efficiency of magnetic holograms, \(\eta\), can be theoretically expressed as:  
\[\eta\propto T\sin^{2}(\theta_{\mathrm{F}}\times d/t)\cong T(\theta_{\mathrm{F} }\times d/t)^{2}, \tag{1}\]  
where \(T\) is the transmittance, \(\theta_{\mathrm{F}}\) is the Faraday rotation angle of the medium, \(d\) is the depth of the magnetic fringe, and \(t\) is the thickness of the medium [18]. Because the light intensity of the reconstruction image of the magnetic hologram depends on the diffraction efficiency, it is desirable to record a deep magnetic hologram in the recording material that has a large Faraday rotation angle and appropriate transmissivity according to Equation (1). To enhance the diffraction efficiency, one can use magnetophotonic microcavities or magnetophotonic crystals as recording media because of the higher Faraday rotation angle and depth of the formed magnetic fringes [22; 23; 24]. High diffraction efficiencies can also be achieved by forming deep fringes even for the same recording material.