Magneto–Optical Properties and Applications of Magnetic Garnet

Abstract

The interaction between light and the magnetization of a material is called the magneto–optical effect. It was used in magneto–optical recording such as MO disks and has been applied to optical isolators etc. with the development of optical communications. The magneto–optical properties of magnetic garnets and their applications are briefly reviewed in this article. In the first half, after a brief overview of the phenomenology of the magneto–optical effect, the effects of element substitution on properties such as Faraday rotation and optical absorbance of magnetic garnets are shown. In the second half, some interesting applications such as imaging technologies and other novel applications using the magneto–optical effect of magnetic garnets are also introduced.

1. Introduction

The interaction between light and the magnetization of a material is called the magneto–optical effect, and examples of this include the Faraday effect and the magnetic Kerr effect [1]. The magneto–optical effect has been applied to magneto–optical recording and optical isolators, and in recent years, attempts have been made to apply it to optical deep neural networks. To utilize the magneto–optical effect, a transparent magnetic material is desirable. For such transparent magnetic materials, nano-crystalline iron oxides such as magnetite (Fe₃O₄) [2] and hematite (Fe₂O₃) [3,4] were proposed, and nanogranular thin films in which magnetic nanometal particles are dispersed in a transparent matrix are recently reported to show a large Faraday effect and attracting attention [5,6,7,8,9,10]. Their properties can be controlled by the materials and volume fraction of the nanomagnetic particles and basically show isotropic properties, but it has also been reported that anisotropic properties can be exhibited by controlling the shape and dispersion of the magnetic particles, and research aimed at actual applications is also carrying out. On the other hand, rare-earth iron garnets (RE₃Fe₅O₁₂; REIG, RE is a rare-earth element), represented by yttrium iron garnet (YIG), are known as magnetic oxide materials with sufficient transparency and a large magneto–optical effect and are also known for their high magnetic permeability, strong magnetic anisotropy, low magnetic loss, and high-frequency properties. These properties make them a potential candidate in the latest technological fields, including optical applications, microwave applications using ferromagnetic resonance [11,12], spintronics applications [13], and spin-wave logic devices [14,15,16]. The magnetic properties of REIG depend on their composition and the arrangement of magnetic ions, i.e., by substituting various elements into the rare-earth and iron sites; the properties of REIG including their magnetic anisotropy can be tuned for the applications by controlling their composition. Due to these properties, much research has been reported on magnetic garnets to date.

In this article, we focus on their magneto–optical properties, particularly the Faraday effect, and review the properties of magnetic garnets (see

Table 1. The parameters and focused properties of garnets considered in this review.

Parameters		Properties
Composition	Substitution sites Substitution elements Substitution amounts	Faraday rotation Transmittance or absorption
Wavelength Temperature

) and recent research on magneto–optical applications using the Faraday effect. The outline is as follows: the background is shown in Section 1, Section 2 shows the phenomenology of the Faraday effect, Section 3 describes the properties of rare-earth iron garnets and the effects of substitution on their properties, Section 4 describes the applications, and Section 5 summarizes this review.

2. Magneto–Optical (Faraday) Effects

The interaction between light and the magnetization of a material is called the magneto–optical effect, and the Faraday effect and the magnetic Kerr effect are typical examples. The Faraday effect is a phenomenon in which the polarization plane of light rotates when linearly polarized light passes through a material as schematically shown in Figure 1. This rotation angle is called the Faraday rotation angle θ_F, and in ferromagnetic materials, it is expressed as follows:

$${\theta }_{\mathrm{F}}=F{\displaystyle \frac{M}{M_{\mathrm{s}}}}l$$

(1)

where, F is the Faraday rotation angle per unit length specific to the material, M_s is the saturation magnetization, M is the magnitude of magnetization, and l is the length of the magnetic material.

First, we present the formula that phenomenologically describes Faraday rotation. This rotation of the polarization plane arises from the different response of the material to right-handed and left-handed circularly polarized light [1]. When the magnetization M is along the z direction, the dielectric constant tensor, $\tilde{\epsilon }$, of an isotropic material is written as Equation (2):

$$\tilde{\epsilon }=\left(\begin{array}{ccc}{\epsilon }_{xx}& {\epsilon }_{xy}& 0\\ {-\epsilon }_{xy}& {\epsilon }_{xx}& 0\\ 0& 0& {\epsilon }_{zz}\end{array}\right)$$

(2)

The off-diagonal components contribute to the magneto–optical effect. Considering a plane wave traveling in the z direction, let N₊ and N_– of this material be the complex refractive indices for right- and left-handed circularly polarized light, respectively. Then, these indices are written as Equation (3).

$${N_{\pm }}^2={\epsilon }_{xx}\pm \mathrm{i}{\epsilon }_{xy}$$

(3)

where, $N_{+}=n_{+}+\mathrm{i}{\kappa }_{+}$ and $N_{-}=n_{-}+\mathrm{i}{\kappa }_{-}$. n₊, n_–, κ₊, and κ_– are the refractive index and extinction coefficient for right- and left-handed circularly polarized light, respectively, and i is the imaginary unit. Since the difference between N₊ and N_– is generally not large, if we write $\Delta n=n_{+}-n_{-}$, $\Delta \kappa ={\kappa }_{+}-{\kappa }_{-}$, $n=\left(n_{+}+n_{-}\right)/2$, and $\kappa =\left({\kappa }_{+}+{\kappa }_{-}\right)/2$, and express each component of the dielectric constant tensor as ${\epsilon }_{xx}={\epsilon \prime }_{xx}+\mathrm{i}{\epsilon ″}_{xx}$, ${\epsilon }_{xy}={\epsilon \prime }_{xy}+\mathrm{i}{\epsilon ″}_{xy}$, then we can express Δn and Δκ as,

$$\Delta n={\displaystyle \frac{{\kappa \epsilon \prime }_{xy}-n{\epsilon ″}_{xy}}{n^2+{\kappa }^2}}$$

(4)

$$\Delta \kappa ={\displaystyle \frac{{n\epsilon \prime }_{xy}+\kappa {\epsilon ″}_{xy}}{n^2+{\kappa }^2}}$$

(5)

Using these, the rotation angle and ellipticity η_F due to the Faraday effect are written as follows,

$${\theta }_{\mathrm{F}}=-{\displaystyle \frac{\omega l}{c}}\Delta n=-{\displaystyle \frac{\omega l}{c}}·{\displaystyle \frac{{\kappa \epsilon \prime }_{xy}-n{\epsilon ″}_{xy}}{n^2+{\kappa }^2}}$$

(6)

$${\eta }_{\mathrm{F}}=-{\displaystyle \frac{\omega l}{c}}\Delta \kappa =-{\displaystyle \frac{\omega l}{c}}·{\displaystyle \frac{{n\epsilon \prime }_{xy}+\kappa {\epsilon ″}_{xy}}{n^2+{\kappa }^2}}$$

(7)

where ω is the angular frequency of light.

3. Rare-Earth Iron Garnets

Yttrium iron garnet (Y₃Fe₅O₁₂: YIG) is a ferrimagnetic material with a garnet structure belonging to the cubic crystal system. Its crystal structure is shown in Figure 2 [1,17,18,19,20]. In the garnet structure, there are three cation positions: tetrahedral positions, octahedral positions, and dodecahedral positions. Three Fe³⁺ ions occupy the tetrahedral positions and two Fe³⁺ ions occupy the octahedral positions per molecule, where these Fe³⁺ ions of two sites are antiferromagnetically bonded by superexchange interactions, and Y³⁺ ions occupy the dodecahedral positions. Rare-earth iron garnets in which the yttrium positions are replaced by other rare-earth elements also show magneto–optical properties similar to YIG [21,22,23,24,25,26,27,28,29,30], and the Faraday rotation angle has been reported to increase especially when Bi³⁺ is replaced [21,31,32,33,34,35,36,37,38,39,40,41,42]. In addition, the magnetic and magneto–optical properties are greatly affected by replacing the Fe sites with other elements [43,44,45,46,47,48,49,50,51,52,53,54,55,56].

Figure 3 shows the wavelength dependence of the Faraday rotation angle for various rare-earth iron garnets (REIG) [21,25,26,27]. As shown in the figure, The REIGs show a peak rotation angle at a wavelength of around 520 nm, and the rotation angle tends to decrease as the wavelength becomes longer. Although there are some differences in the Faraday rotation angle when the type of rare-earth element is different, the shape of the rotation angle spectrum itself looks similar. This is attributed to the similar environments around the Fe³⁺ ions in the garnet crystal, and the corresponding crystal fields and charge transfer transitions are similar.

Figure 4 shows the temperature dependence of the Faraday rotation of YIG, TbIG, and GdIG at a wavelength of 1.15 µm reported by Crossley et al. [23]. They analyzed the temperature dependence of this rotation angle and evaluated the influence of the two Fe³⁺ sites and the rare-earth sites on this rotation. As a result, they reported that the tetrahedral and octahedral Fe³⁺ ions give opposite signs, with the octahedral ions contributing twice as much as the tetrahedral ones.

3.1. Effect of Rare-Earth Site Substitution

3.1.1. Bi and RE Substitution

As mentioned before, the substitution of Bi into rare-earth sites is known to increase the Faraday rotation in various REIGs [21,31,32,33,34,35,36,37,38,39,40,41,42,57,58,59,60,61,62,63,64,65,66,67,68,69]. Figure 5 shows the dependence of the Faraday rotations of Bi-substituted YIG (Bi:YIG) and GdIG (Bi:GdIG) on the amount of Bi substitution [59,64]. As shown in the figure, the Faraday rotation increases almost in proportion to the increase in the amount of Bi substitution, reaching approximately 8 deg/µm. Figure 6 shows the wavelength dependence of the Faraday rotation of Bi:YIG and Bi:GdIG [32,35]. The sign of the Faraday rotation changes from positive to negative due to Bi substitution, and its absolute value increases as the amount of Bi substitution increases. The increase is larger in Bi:GdIG than in Bi:YIG, reaching more than 10 deg/µm at a wavelength of 0.52 µm with a substitution amount of x = 1.4. Figure 7 shows the wavelength dependence of the optical absorption of Bi:YIG and Bi:GdIG [32,33]. As the amount of Bi substitution increases, the absorption increases. In addition, without Bi substitution, YIG and GdIG show similar absorption spectra, but as the amount of Bi substitution increases, the absorption increases over the entire wavelength range, and in particular, the absorption increases significantly around 0.55 to 0.57 µm, and the drop in this region disappears.

Figure 8 shows the wavelength dependence of the Faraday rotation of REIGs highly substituted with Bi reported by Urakawa et al. [69]. Although the value of the Faraday rotation differs depending on the rare-earth element, the shape of the Faraday rotation spectra looks similar, with a large negative rotation peak at around 520 nm. This is also shown in YIG shown in Figure 6, which means that the fundamental mechanism of Faraday rotation in REIG is similar. Figure 9 shows the optical transmittance spectra of the same films. For each film, the transmittance is almost zero in the wavelength range shorter than 500 nm, increases rapidly above 500 nm, and shows a tendency to gradually increase above 600 nm. A similar tendency is also seen in samples with a high Bi substitution in NdIG [36,70].

3.1.2. Effect of Ce Substitution

As shown in the previous section, rare-earth iron garnet shows a large Faraday rotation angle around 520 nm by Bi substitution, but the transmittance is also reduced. On the other hand, in the near-infrared wavelengths used in optical communications, the optical absorption is small, but the rotation angle is not large enough. Gomi et al. [71] reported that the rotation angle can be increased by substituting Ce into YIG, and since a large rotation angle and small light absorption can be achieved at the same time, especially in the near-infrared region, much research has been carried out on this field [70,71,72,73,74,75,76,77,78,79,80]. Figure 10 and Figure 11a show the wavelength dependence of the Faraday rotation [71,72,78]. As shown in Figure 10, by substituting Ce with x = 1 or more, a large Faraday rotation of more than 1 deg/µm is shown at wavelengths of 400–800 nm and around 1000 nm. As shown in Figure 11b, the samples with Ce substituted with x = 1 or more show relatively large optical absorption in the wavelength region shorter than 800 nm, but the optical absorption becomes small in the wavelength longer than 1000 nm; that is, a large Faraday rotation and small optical absorption can be achieved in that region. Figure 12 shows the dependence of the Faraday rotation angle on the amount of substitution, and the Ce substituted sample shows a larger Faraday rotation angle than the Bi-substituted sample at a wavelength of 1150 nm. Due to these properties, CeRIG is tried to be used in applications such as isolators for optical communication. The properties of samples with Ce substituted with BiIG or TbIG instead of Y have also been evaluated, and Bi_0.8Ce_2.2Fe₅O₁₂ is reported to show a large Faraday rotation of 0.55 deg/µm [74] and Ce_0.36TbIG is reported to show a Faraday rotation of 0.45 deg/µm [79] at 1550 nm.

3.2. Effect of Fe Site Substitution

It has been reported that the substitution of non-magnetic elements such as Al [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48], Cu [49], Zn [50], Ga [51,52,53,54,55,56], and Sc [47] into the Fe site tends to decrease the saturation magnetization and affects the magnetic properties, as a result, which affects the magneto–optical effect. Figure 13 shows the wavelength dependence of the Faraday rotation and optical absorption of Y₃Ga_yFe_5–yO₁₂ [49]. In wavelengths of 500–1000 nm, the optical absorption decreases as the amount of Ga substitution increases.

Figure 14 shows the Faraday rotation and optical absorption dependence of Y₃Ga_yFe_5-yO₁₂ at a wavelength of 633 nm as a function of the amount of Ga substitution [51]. As shown in this figure, the optical absorption decreases linearly as the amount of Ga substitution increases, while the Faraday rotation shows a peak at a Ga substitution amount around x = 0.5–1.0 and then decreases. The effect of Ga substitution affects the Faraday rotation through the magneto–optical coefficient and the magnetization of the sublattice. In the case of Y₃Fe₅O₁₂ with λ = 633 nm, the Faraday rotation is reported to increase due to the decrease in the tetrahedral contribution caused by Ga substitution, when the amount of substitution increases further and the Fe³⁺ ions in the tetrahedral sublattice are completely replaced by Ga³⁺ ions, the Faraday rotation decreases due to the decrease in exchange interaction and approaches zero. Figure 15 shows the wavelength dependence of the Faraday rotation of Bi_1.5Y_1.5Ga_yFe_5-yO₁₂ [52]. The Bi-substituted sample has a large negative peak at a wavelength of around 500 nm, and as the amount of Ga substitution increases, the position of the peak moves toward shorter wavelengths.

Figure 16 and Figure 17 show the dependence of Faraday rotation at λ = 633 nm on the amount of Al and Bi substitution for the Fe site of (Bi,Dy)₃(Fe,Al)₅O₁₂ and (Bi,Y)₃(Fe,Al)₅O₁₂ [43]. As shown in Figure 16, the rotation angles of (Bi,Dy)₃(Fe,Al)₅O₁₂ and (Bi,Y)₃(Fe,Al)₅O₁₂ tend to decrease with increasing the amount of Al substitution although the change in Faraday rotation due to Al substitution is different. As shown in Figure 17, even in the Al-substituted sample, the Faraday rotation increases linearly with increasing the amount of Bi substitution, and the rate of change with respect to the amount of Bi substitution is larger in (Bi,Dy)₃AlFe₄O₁₂ than in (Bi,Y)₃AlFe₄O₁₂ [43].

4. Applications

4.1. Isolator

With the development of optical communication using optical fiber cables and laser processing machines for precision machining, optical isolators that can cut backlight and stabilize the laser source become important. Many studies have been carried out on optical isolators that utilize the magneto–optical effect of magnetic garnets [81,82,83,84,85,86,87,88,89,90,91,92]. The basic principle of operation is shown in Figure 18. Forward incident light is linearly polarized by Polarizer P1, and the polarization plane is rotated by 45° by passing through Faraday rotator F. This transmitted light passes through a second analyzer P2 tilted at 45° and is guided to the optical system. Conversely, only the polarized component tilted by 45° is transmitted by P2 for the reverse light returning from the optical system and is rotated another 45° by Faraday rotator F. So the polarization plane differ 90° from the transmission direction of polarizer P1, and no light returns to the laser source.

The properties required for materials of the Faraday rotator include low forward loss, sufficiently high reverse loss, and a low temperature coefficient of Faraday rotation, β, less than 0.04 deg/°C at −20 to +60 °C. As a method to reduce this temperature coefficient. Minemoto et al. [81] proposed a method to use a two-layer epitaxial film using (Bi,Gd)₃(Fe,Ga)₅O₁₂ with negative temperature coefficient β, and (Bi,Lu,Gd)₃Fe₅O₁₂ with positive β, thinking of the temperature coefficient as a parameter. The temperature coefficient of the obtained sample was β = 0.00 deg/°C, and the absorption loss was 0.9 dB at a wavelength of 1.3 µm and 0.5 dB at a wavelength of 1.55 µm. Wei et al. [85] also reported that the change in the Faraday rotation angle at 1.55 µm for Dy₂Ce₁Fe₅O₁₂ was suppressed to less than 5% at temperatures between 25 and 70 °C. Jiang et al. [82] reported that the YIG ceramic-based isolator exhibited an extinction ratio of 25.26 dB and an insertion loss of 1.01 dB at 2.1 µm wavelength, and there showed noticeable damages on the surfaces of YIG ceramic at a power density of 10.2 W/cm². This suggests that the YIG ceramic will provide a high-performance and cost-effective solution for high-power mid-infrared isolators. Using magnetic garnets as optical isolators in optical waveguides such as silicon photonics, direct deposition, or bonding technologies to silicon is important. A bonding technique using surface activation technology to bond magnetic garnets such as Ce:YIG directly onto silicon or compound semiconductor waveguides has been developed, which allows the magnetic garnet to be used as an upper cladding layer obtaining effective MO interactions with the propagating light. Mach-Zehnder interferometers (MZIs) or ring resonators with this MO cladding layer enable nonreciprocal optical propagation, and MZI-based isolators have been realized [83,84]. Magnetic garnets have also been directly deposited monolithically on silicon or SiN waveguides and have been reported to show optical isolation of up to 30 dB and low insertion loss of 5 dB, making them the best-performing broadband optical isolators on silicon [86].

4.2. Imaging

Magneto–optical imaging has been used to observe the magnetization dynamics of superconductors [93]. Recently magneto–optical imaging technology has been developed to display the change in the spatial distribution of the magnetic field [35,94,95,96,97,98,99,100]. Bi-substituted rare-earth iron garnets with a large rotation angle are used as the materials for MO imaging films. Ishibashi et al. reported that a highly Bi-substituted (Bi,Nd)₃(Fe,Ga)₅O₁₂ (Bi:NdIGG) film prepared by the MOD method has a large rotation angle [95,96] and reported the formation of a uniform Bi:NdIGG film on a ϕ6 inch glass substrate for imaging [98]. Nagakubo et al. [97] also developed an 11 × 15 cm MO imaging plate consisting of an electroluminescence (EL) sheet, a polarizing film, and a Bi_2.5Nd_0.5Fe₅O₁₂ film fabricated on a ϕ150 mm glass substrate, and used this backlight MO imaging plate to measure the magnetic field distribution using a 45° polarizer method. The results show that quantitative MO imaging using the EL sheet emitting white light is promising for large-scale magnetic imaging. Furthermore, an MO color imaging technique that can quantitatively observe the magnetic field distribution in real time was proposed, and the magnetic field was displayed in color using a light-emitting diode (LED) as a light source, and MO color imaging of a spherical magnet was demonstrated [99].

Based on such imaging techniques, many studies are also carried out to detect defects [101,102,103,104,105]. A schematic of a defect detection system using MO imaging is shown in Figure 19. An MO imaging film is placed on the surface of the sample, and laser light is irradiated to it. The magnetization change in the MO imaging film due to the leakage magnetic field from the sample causes a rotation of the polarization plane, which is detected by an analyzer, and defects in the sample are evaluated using a 2D image. Hashimoto et al. reported that they could evaluate semi-quantitatively the defect depth from the obtained 2D image by using a magneto–photonic crystal made by sandwiching a Bi:REIG film between dielectric mirrors to increase the rotation angle of the MO imaging film [101]. Similarly, using a magnetic flux leakage detection system based on the magneto–optical effect, the effect of defect size on the leakage magnetic field distribution was experimentally verified using a cracked rail test piece, and the defects up to 0.4 mm wide and 0.5 mm deep were reported to be detected [103]. A magneto–optical non-destructive testing system for robot-based non-destructive testing has also been investigated using deep learning to classify defect shapes from MO images [105].

Recently, the imaging technique can be used to obtain a two-dimensional rotation angle distribution image directly using a polarization camera without using an analyzer and is reported to calculate the three-dimensional magnetic field distribution from the image [106]. This technique is attracting attention as a method for obtaining three-dimensional magnetic field distribution from simple magnetic imaging results.

4.3. Magnetic Holography

The magneto–optical effect was used in magneto–optical recording on such as MO disks in the past, but such media are no longer used due to the development of high-capacity hard disks and semiconductor memories. On the other hand, a magnetic holographic memory using magnetic garnet as a recording media is proposed [107,108,109,110,111,112,113,114,115,116]. For recording in magnetic holographic memory, a thermomagnetic recording method using the light absorption of magnetic materials similar to those used in MO disks is used, and interference fringes are recorded as magnetization patterns. For reconstruction, a reconstruction image is obtained by using the interference between the rotated components of the polarization plane due to the Faraday effect. For recording materials for such magnetic holograms, materials with good squareness in the magnetic hysteresis loop, large Faraday rotation, large coercive force, moderate light absorption, and a Curie temperature of 200 °C or less are desirable. To obtain a bright reconstruction image, it is necessary to form a deep magnetic hologram. However, even if high energy is used to record a deep hologram, the magnetic fringes near the surface are merged by thermal diffusion after laser irradiation, and the interference fringe information is lost. So, the use of multilayer media with transparent heat dissipation layers (HDLs) inserted in magnetic layers is proposed. In fact, even when recording on such multilayer HDL recording media using the collinear interference method, an error-free reconstructed image was reported to be obtained as shown in Figure 20 [114,115,116].

4.4. MO Neural Network

In recent years, research on diffractive deep neural networks (D2NN) using light diffraction has been progressing as a neural network that is the basis of artificial intelligence [116,117]. Recently, Ishibashi et al. proposed magneto–optical diffractive deep neural network (MO-D2NN) using the magneto–optical effect [118,119].

As shown in Figure 21, MO-D2NN uses magnetic garnet films with magnetization patterns of 1 µm order as the intermediate layers and utilizes the diffraction and interference of light due to the magnetization patterns. Specifically, a hidden layer structure with five layers of 100 × 100 magnetic domains with a width of 1 µm and 0.7 mm intervals was used as hidden layers. Simulations showed that the classification accuracy for the MNIST handwritten digit dataset was 90% when the light intensity was used as the classification scale, and 80% classification accuracy was obtained even for small Faraday rotation angle of π/100 rad in each hidden layer when the rotation angle of the polarization plane was used as the classification scale. In fact, they fabricated a two-layer MO-D2NN containing 100 × 100 magnetic domains with a domain size of 1 µm, and experimentally evaluated. As a result, the classification accuracy was reported to be several percent lower than the simulation results [118]. This reduction from simulation was thought to be due to the recording accuracy of the actual magnetization pattern, and this suggests that the MO-D2NN is expected to be feasible to implement.

4.5. Other Applications

New applications using the magneto–optical effect of magnetic garnets have been proposed such as magneto–optical Q-switch and random number generator. Both applications use the magnetic domains of single-crystal garnet films. In the magneto–optical Q-switch [120,121,122], a magnetic garnet film is used as an attenuator. The state in which the laser light is scattered by the magnetic domains appearing in a zero magnetic field is set as a high attenuation state (OFF state), and the state in which the magnetic domain is uniform under a magnetic field is set as the ON state, allowing the Q-switch to operate. Morimoto et al. constructed a MO-Q-switch laser with a cavity length of 10 mm using a 190 µm REIG film, achieving a maximum peak power of 255 W and a FWHM of 5 ns [121].

On the other hand, Kawashima et al. reported that random numbers can be generated from the magnetic domain pattern of magnetic garnets prepared by the LPE method. The chaotic magnetic domain images that appeared in the garnet film were photographed using a polarizing microscope, and random numbers were generated from these magnetic domain images by post-processing such as binarization and exclusive OR. The generated random numbers passed NIST SP-800-22 statistical tests, suggesting the possibility of realizing a relatively simple and fast random number generator using MO materials [123].

Finally, the important properties required for the garnets used in the applications shown here are summarized in

Table 2. The important properties of garnets needed for the applications shown in this review.

Applications	Important Properties
Isolator	Large Faraday rotation (45 deg) High transmittance
Imaging	Perpendicular or in-plane magnetization Small coercivity (soft magnetic garnets)
Magnetic hologram memory	Perpendicular magnetization Large residual Faraday rotation High coercivity
MO neural network	Perpendicular magnetization
MO Q-switch	Fine magnetic domain
Random number generator	Fine magnetic domain

. A large Faraday rotation per unit thickness is important for all applications, so it is not shown in this table.

5. Conclusions

In this report, we reviewed the magneto–optical effect (especially the Faraday effect) exhibited by magnetic garnets and its applications. There are many reports on the magnetic properties and magneto–optical effect of magnetic garnets and their applications, and it is impossible to cover them all here, so we introduced some useful for considering recent applications. We also cited some reviews as references, so please refer to them as well. The magneto–optical effect, which is the interaction between magnetism and light, is a very interesting phenomenon, and its applications are considered in various fields, and tuning of material properties according to the application is also necessary. New application fields such as the MO neural network, Q-switched laser, and random number generation introduced at the end are expected to develop in the future.

From the material’s point of view, research on high-entropy rare-earth iron garnets containing five rare-earth elements has been carried out recently, and their magnetic properties have been reported [124,125,126,127,128]. Although there have been no reports on magneto–optical effects yet, further progress is expected. On the other hand, as mentioned previously, we focus on the properties of magnetic garnets and their applications using the Faraday effect while the magneto–optical Kerr effect (MOKE) is also an important magneto–optical property, and the following papers may be useful regarding their properties and applications [129,130,131,132,133,134]. We hope that this paper will help you become interested in such fields.