Liquid phase epitaxial garnet layers are grown on nonmagnetic garnet substrates by using a horizontal dipping technique. Figure 1(a) shows a typical vertical dipping apparatus with a furnace, electronics for control and a computer for analyzing and observing the interactions. The accessories of the equipment, including a 100-mm diameter platinum alloy crucible, 1-inch (1 inch = 2.54 cm) and 3-inch subtract platinum alloy holder, and a platinum alloy stirrer as shown in Fig. 1(b). The temperature distribution within the furnace is measured and controlled by thermocouples and a proportional integral derivative (PID) system, which is connected to a control and display computer. The growth part of the equipment consists of a vertical five-zone furnace, a scavenging duct to extract fumes, mechanisms to handle substrate crystals, six fixed thermocouples, and a crucible table in the furnace. The five-zone furnace is shown in Fig. 1(c), the upper motor is for rotating the substrate while growing; the crucible table is for lifting the crucible into the furnace and locating it at the uniform temperature zone; the thermocouples is for measuring the temperatures of the five-zone in the furnace and the temperature of the crucible. The five-zone crucible consists of five separated heater coils. Since the furnace is an unsealed chamber, the upper heater and the lower heater insulate the internal and the external environment temperature. The inner three heaters are for controlling and stabilizing the temperature at the crucible position. The fluxed melts are contained by the crucible at high temperature (800 °C–1100 °C). Usually, we melt the oxides at a temperature of 100 °C higher than the undercooling temperature and stir for 12 h to fully melt the flux. Nonmagnetic Gd₃Ga₅O₁₂ (GGG) and substituted GGG, e.g., Ca, Zr, Mg-doped GGG wafers are used as substrate crystals, and the diameter of a substrate is 75 mm. Single or multiple substrates are sustained by a jig made of platinum or platinum alloy. The GGG and substituted GGG wafers are prepared using the Czochralski method (crystal pulling) and sliced and polished. Liquid phase epitaxial garnet films grow on the substrates by dipping substrates into the slightly undercooled flux melts. By rotating substrates at a rotation speed of 50 rpm–100 rpm, garnet films of uniform thickness are obtained. After the growth of LPE films, substrates are withdrawn from the melt, and residual fluxed melts are removed by rotating the wafers at high speed. For Bi-substituted garnet films, however, the residual melt tends to adhere to the melt surface due to wetting, even after high-speed rotation. The surfaces of the Bi-substituted garnet films are stained with this residual fluxed melt. Since fluxed melt contains PbO and Bi₂O₃, with a relatively high vapour pressure at LPE temperature, fumes from these substances must be extracted through a scavenging duct, gathered and treated appropriately.

Fig. 1.

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	Fig. 1. (color online) (a) Photo of equipment, (b) platinum accessories, and (c) schematic diagram of the furnace.

To grow single garnet crystals or single crystalline films, the knowledge of phase equilibria between the crystals and environment phases is indispensable. The phase relationship between Fe₂O₃ and YFeO₃ has been reported by van Hook;^[4,5] Y₃Fe₅O₁₂ can be formed through a peritectic reaction between YFeO₃, which is a primary phase, and a melt, which contains more Fe₂O₃ than the Y₃Fe₅O₁₂ composition. Based on this phase diagram, highquality Y₃Fe₅O₁₂ single crystals were grown at temperatures between the peritectic (1555 °C) and eutectic (1469 °C) temperatures, either by a top-seeded solution growth or a travelling solvent-floating-zone method. Single crystal growth of Y₃Fe₅O₁₂ has been attempted for the first time from a PbO fluxed melt by Nielsen and Dearborn, i.e., a flux method. Through the flux growth of Y₃Fe₅O₁₂ single crystals, they prepared a phase diagram for the PbO·B₂O₃–Y₂O₃–Fe₂O₃ system. Later, Jonker reported precise phase diagrams for the pseudo-ternary PbO·B₂O₃–Y₂O₃–Fe₂O₃ system.^[6] The solubility of rare earth oxides can be enhanced by a factor of about ten if mixture of PbO–PbF₂ is used as solvent. The improvement in quality and size were obtained by adding a small amount of B₂O₃ into PbO and PbO–PbF₂. The PbF₂ has significant volatility and cannot be used in open crucible. Therefore, the current garnet films are grown by using solvent of PbO–B₂O₃–(Fe₂O₃) or PbO-Bi₂O₃–B₂O₃–(Fe₂O₃) for Bi-substituted magneto–optical garnets. For the LPE growth of Bi-substituted garnet cases, Bi ions acts both as solvent and as constituent.^[7]

The base to understand the growth kinetics of any crystal in solution is the knowledge of the liquidus curve. Liquidus curves are mostly defined for pseudo-binary systems, consisting of solvent, e.g., PbO–B₂O₃–(Fe₂O₃) and solute, e.g., Y₃Fe₅O₁₂. Therefore, the phase transition liquid(l)–solid(s) is described for a so-called single-molecule model as

Yttrium iron garnet (YIG) is one of the most extensively studied magnetic materials with the smallest known magnetic relaxation parameter. Decades ago, the motivation was to apply micron or even thicker films of YIG to microwave devices, such as microwave delay line, filter, circulator, oscillator, etc. In 1988, several review papers gave a conclusion of about 30-year studies on YIG. After that, only a few articles concentrated on fabricating YIG films via new technology. The spin pumping effect in YIG/Pt structure invokes intensive studies of magnonic information transport and procession devices using single crystal YIG films. Unlike the previous study, the demand for submicron or nanometer devices requires the thickness of YIG films to be at the same as or smaller than that of the film with low damping coefficient and allows magnons to propagate over distances exceeding several centimetres. In this case, submicron YIG films aroused lots of interest.^[8]

Due to the prolonged magnetic relaxation process in these materials, magneto-static surface and volume waves can propagate in the garnet film, allowing an analogue signal to be processed directly in the microwave range. Devices like filters, delay lines, oscillators and circulators have been designed by using such garnet films. These many devices need films with thickness more than few micrometres that cannot be obtained with pure YIG films grown on gadolinium gallium garnet (GGG) substrate without mechanical stresses and cracks induced by a lattice parameter mismatch of about 0.007 Å. In this case, we need to modify the lattice constant of YIG film without changing its magnetic properties. The garnet films with nominal composition Y_2.93La_0.07Fe₅O₁₂ were grown by the standard LPE method on a (111)-oriented GGG substrate from a supersaturated melt based on the PbO–B₂O₃ flux. The La:YIG thick films were thought to have the same magnetic properties as those of the YIG films. Using the found growth-strategy parameters, the La:YIG films with thickness up to 130 μm were successfully grown.^[9] Figure 2(a) gives the scanning electron microscopy (SEM) image of La:YIG/GGG cross-section with an excellent interface. Figure 2(b) shows the perfect soft magnetic properties of La: YIG films with thickness up to 40 μm. Figure 2(c) gives the ferromagnetic resonance (FMR) spectrum of thick La:YIG film via magnetic hole method, the main peak shows a linewidth of 0.72 Oe (1 Oe = 79.5775 A·m⁻¹). Figure 2(d) displays the x-ray diffraction (XRD) spectrum of 44.41-μm La:YIG film, the GGG peak and the La:YIG peak overlap, which means a perfect match between the substrate and the film.

Fig. 2.

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	Fig. 2. (color online) (a) scanning electron microscopy (SEM) image of La:YIG/GGG cross-section, (b) magnetic hysteresis loops of La:YIG films, (c) FMR spectrum of thick La:YIG film, and (d) XRD spectrum of 44.41-μm La:YIG film.

Fig. 3.

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	Fig. 3. (color online) microwave devices preparing YIG films for ((a) and (b)) tunable microwave filter,[12,21] (c) microwave phase shifter,[22] (d) microwave delay line.[13]

Based on thick YIG films, many devices have been reported. In 1987, Yoshikazu et al.^[10] used La:YIG (40 μm) to fabricate a tunable stripline band pass filter: when the bias field was between 1910 Oe and 3160 Oe, the centre frequency changed from 0.5 GHz to 4.0 GHz. To filter the low-frequency signal, the authors studied the response of YIG films with a crystal orientation of (111) and (100). The result showed that the frequency lower than 0.25 GHz cannot transmit in the (111) YIG film. In 2013, Yang et al. used local magnetisation technic to realize small tunable bias magnetic field YIG filter. The zero field centre frequency was about 6.17 GHz and 100 Oe bias field could tune about 320 MHz.^[11] Ustinov et al. used YIG thin film to design an HSEW phase shifter, and according to the operation of the electric field and magnetic field they achieved a 5-GHz phase shifter, providing a reference for the spin wave application.^[12] In 2015, Elena Bankowski et al. calculated and simulated the delay line with YIG films, and proposed the method to improve the delay of YIG.^[13] Other devices like microwave circulator,^[14–16] oscillator^[17–20] were also proposed.

The main techniques for growing YIG films are LPE for thick films (1 μm to 100 μm) and RF sputtering or PLD for thin films (< 100 nm). One is trying to reduce the thickness to the nanoscale by using LPE to obtain YIG thin films with lower damping than those fabricated by RF sputtering or PLD. With a few years’ development, YIG films thinner than 200 nm have been produced by LPE and have been used in some areas. However, LPE fabricated YIG films with thickness larger than 1 μm^[23] and smaller than 100 nm have quite different magnetic properties.^[2] To obtain nanoscale YIG thin films via LPE, several technological conditions should be carefully controlled. The first one is the Blank- Nielsen ratio, and a lower concentration can help reduce the growth rate. The second one is to control the growth temperature, making it as high as possible under the condition without significantly increasing the impurity (Pb²⁺, Pb⁴⁺, Pt⁴⁺) density in the film, and to control the rotation rate, transfer rate, etc.

The YIG (444) and GGG (444) peaks were mostly overlapped due to the tiny lattice mismatch. As the YIG film thickness increased, the right shoulders of the curves increased in intensity, which means a tensile-stressed YIG film. In contrast, the XRD peak in La: YIG film showed almost no shoulder on either side of the GGG peak and a smaller linewidth than that of GGG/YIG, indicated by the red curve in Fig. 4(a). The comparing HRXRD results give evidence of existence of tensile stress for pure YIG film epitaxially grown on GGG. The YIG film fabricated by RF sputtering or PLD on a GGG substrate showed a YIG diffraction peak with a lower Bragg angle than that on the GGG substrate, indicating considerable distortion of the YIG garnet cell.^[24–27] Figure 4(b) compares the magnetic hysteresis loops of YIG and La:YIG films with approximately equal thickness, revealing three phenomena that should be mentioned. First, at low film thickness (110 nm) the YIG film has a better magnetic hysteresis loop squareness ratio than the La:YIG film. Second, the magnetic hysteresis loops of the YIG film shows a thickness dependence, while those of the La:YIG films are stable across all studied thickness. Third, the 1000-nm-thick YIG film showeds relatively high H_c and H_s, while the La:YIG film still exhibits low H_c and H_s. The facts above show the essential difference between the GGG/YIG and GGG/La:YIG structures. Our La:YIG films were considered to be La_0.07Y_2.93Fe₅O₁₃. The La³⁺ replaced part of the Y³⁺ at the dodecahedron site, distorting the sublattices and further increasing the lattice parameter. This increase in lattice parameter leads to a perfect match with the GGG substrate as shown in the film prepared by HRXRD. In this case, the GGG/La:YIG interface has almost no stress, which is why the magnetic hysteresis loop is not thickness dependent. The lattice distortion affects both the tetrahedral site and the octahedral site, which is occupied by the antiparallel magnetic moment of Fe³⁺. The thickness of the easy magnetization area is can be estimated at about 423 nm, and the stress relaxation seems to start from this thickness.

Fig. 4.

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	Fig. 4. (color online) (a) HRXRD, ω-scan near the 444 Bragg reflection of the substrate/film; (b) magnetic hysteresis loops of YIG and La:YIG at various thickness; (c,) 4πMeff abstracted from FMR measurement as a function of film thickness; (d) frequency dependence of the FMR linewidth for YIG LPE films with various thickness. The unit 1 Gs = 10−4T.

The 4πM_eff values shown in Fig. 4(c) are fit from FMR results by using the Kittel formula

The cutting-edge research of YIG film is called YIG magnonics^[32] or magnon spintronics.^[33] Historically, bulk YIG crystals were used for studying magnonics on a micrometertomillimeter length scale needed for microwave devices. However, fabrication of integrated spintronic, magnonics or magneto–optical devices requires thin films with high structural and magnetic quality, instead. In particular, achieving very low damping in thin film YIG is a critical factor for fabricating the magnonics logic devices to transport, store, and process microwave and digital information for the post-CMOS (where CMOS stands for complementary metal–oxide–semiconductor) era. Applications include integrated multi-modal spin-wave devices, delay lines, filters, resonators, generators, multi-channel receivers, directional couplers, and Y-junctions. Also, low damping can be utilized for spin-based resonant sensing applications.^[34–36] Here we introduce four most studied devices or structures.

The seminal letter to Kajiwara et al. in 2010, showed that by depositing platinum strip (Pt, a normal metal) on the top of a 1.3-μm-thick yttrium iron garnet (a magnetic insulator), one could efficiently transfer spin angular momentum through the interface and generate voltage via inverse spin Hall effect in Pt as shown in Fig. 5(a). This finding was followed by comprehensive studies of this phenomenon: the dependence on the thickness of the non-magnetic metal and the YIG layer, as well as on the applied microwave power has been reported. The influence of the interface condition on the spin-pumping efficiency was revealed, and the contributions to the SP effect by different spin-wave modes were studied.^[37–42]

Fig. 5.

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	Fig. 5. (color online) Prototype devices of (a) electric-signal transmission via spin-wave spin currents by Kajiwara et al.,[37] (b) spin-torque nano-oscillator (STNO) by Collet et al.,[43] and (c) spin wave logic device or spin-wave majority gate by Fischer et al.[44]

Fig. 6.

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	Fig. 6. (color online) (a) XRD spectrum of 3-inch epitaxy Bi:TmIG thick film, (b) AFM image of epitaxy film, (c) NanoMOKE measurement of Bi:TmIG films with different growth rates, and (d) Faraday rotation as a function of growth rate.

To combine magnonic devices with electronic circuits, efficient means for magnon excitation by a charge current are required. Although magnons can be injected relatively easily by an a.c. electric current (for example, using antenna structures), it is a complicated problem if a d.c. current is used. One of the most promising solutions is to use the spin-transfer-torque (STT) effect. In 2016, Collet, et al. first reported the direct electrical detection of auto-oscillation in YIG/Pt structure and showed that the threshold current is increased by the presence of quasi-degenerate SW modes.^[43] This implies that the careful engineering of the spin-wave mode spectrum is required to optimize magnonic devices by making use of spin-orbit effect as shown in Fig. 5(b).

The scaling of conventional CMOS-based nanoelectronics is expected to become increasingly intrinsically limited in the next decade. Therefore, novel beyond-CMOS devices are being actively developed as a complement to expand functionally in future nanoelectronics technology nodes. In particular, the field of magnonics, which utilizes the fundamental excitations, i.e., spin waves and their quanta, of a magnetic system, magnons, as data carriers to provide the promising approaches to overcomeing crucial limitations of CMOS since they may provide ultralow power operation and nonvolatility. This report demonstrated the experimental realization of a majority gate based on the interference of spin waves as shown in Fig. 5(c). Here, the phase of the output signal is defined by the majority of the phases of the input signals. Recent progress of the miniaturization of YIG structures and techniques for a phase control by electric currents, by electric fields as described in the work by Ustinov et al., or by spin-polarized currents, and by a combination of domain wall-based waveguides and dot arrays, provides the promising drafts for the required advances towards applications.^[44]

Progress of integrated optics relies heavily on the development of single-crystal films which can serve both as optical waveguides and as active medium in electro- or magneto–optical devices. The single-crystal epitaxial garnet films on nonmagnetic garnet substrates can be used as optical waveguide at visible and infrared wavelengths. The use of garnet films as optical waveguides was first discussed. Films like these were developed for magnetic bubble devices, and some of them are found to have magnetic properties useful in integrated optics. In fact, Tien et al.^[45] have constructed a novel magneto–optical switch using a scandium-substituted yttrium iron garnet film, in which the light wave in one of the waveguide modes can be switched on and off by a small magnetizing circuit. The details of this magneto–optical switch and other magnetic film devices will be discussed elsewhere.^[46,47]

Bismuth substituted iron garnet films have been shown to be a prospective material for magneto–optic (MO) device applications such as Faraday isolators, MO modulators, visualizers, magneto-static wave devices, etc.

The garnet films of nominal composition Tm_2.28Bi_0.72Fe_4.3Ga_0.7O₁₂ were grown by standard LPE method on (111)-oriented GGG substrates each with a 3-inch diameter from a supersaturated melt based on the Bi₂O₃ flux. To calculate a charge composition the mole ratios (Blank–Nielsen coefficients) were used as follows:

After growth process the film surface is covered with flux residuals due to the high viscosity and adhesion of Bi₂O₃ based flux. To avoid the complicated high-speed rotation procedure to spin off the flux residuals, the film was kept after growth process above melt during some time till the full cleaning of film surface.^[48,49] The Bi:TmIG films of thickness 50 μm–60 μm were obtained using growth rates between 0.8 μm/min and 0.9 μm/min. The mismatch between the film and the GGG substrate is nearly completely mitigated. The FRA reached its maximum value of 0.54 μm/min, which is due to the slight increase in the number of Bi³⁺ ions in the film composition and leads to the splitting of excited energy levels. The combination of large size, excellent MO, and soft magnetic properties of these films leads to a wide scale adoption in MO and integrated magnetic devices.

Recently, integrated circuits with both MO and microwave devices have rapidly developed, and a new kind of garnet film combining good optical, MO effect and proper microwave properties are urgently needed. The (Bi:Lu)₃Fe₅O₁₂(LuBiIG) film is a kind of film that can meet these requirements, and it can be used in MO and microwave hybrid integrated systems. On the other hand, the fluxes used to grow garnet film by the LPE method are PbO–B₂O₃(–Bi₂O₃), BaO–BaF₂–B₂O₃, and MoO₃–Li₂O fluxes.^[50] Of them, PbO–B₂O₃(–Bi₂O₃)flux is most commonly used because it provides high growth rate and low growth temperature. However, the PbO flux is mordant and poisonous. Moreover, Pb ions would be incorporated into the garnet films in the epitaxy process, which has a seriously negative influence on the performances of microwave devices, both the optical and magneto–optical properties. Therefore, the growth of films from PbO-free flux is crucial to improving the quality and properties of YIG films. Non-magnetic Bi³⁺ ions and Lu³⁺ ions were incorporated into the garnet matrix to obtain large MO effect, and thus improving the lattice match between the film and the GGG substrate, respectively. In this paper, by optimizing the growth conditions, high-quality garnet films were successfully fabricated on GGG (111) substrates by the LPE method with Bi₂O₃ as the melting agent. The crystal structure, microwave characteristic and magnetic properties, as well as the optical and MO properties are investigated. An FMR linewidth of 2Δ = 2.8 Oe–5.1 Oe and a Faraday rotation of 1.64 deg/μm at 633 nm are obtained. Our film is a very attractive material for applications in microwave and MO as shown in Fig. 7.

Fig. 7.

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	Fig. 7. (color online) (a) The AFM image of the surface pattern of the LuBiIG thin film, (b) the XRD pattern of LuBiIG thin film on GGG substrate, (c) the FMR spectra versus ΔH of LuBiIG film on GGG substrate, and (d) specific Faraday rotation θF versus external magnetic field at 633 nm at room temperature.

We also investigate the absorption coefficients of LuBiIG thin film from microwave band to optical band. In microwave band, the absorption coefficient is represented by FMR linewidth and a very small value of 2ΔH = 2.8 Oe–5.1 Oe is obtained. In optical band, the absorption coefficient is as low as 600 cm⁻¹ in the visible range. In THz band, very low absorption coefficient is obtained to be less than 0.3 cm⁻¹ in a frequency range of 0.37 THz–0.95 THz and the minimum value 0.05 is observed at 2.24 THz. The combination of good optical, microwave, and THz properties of this garnet film indicates wide applications, such as in optical devices, magnetostatics wave devices, THz wave guide, and some integrated devices or systems.

Here, we list some of MO films which have not been motioned above. Due to the wide range of dopants available for garnet, lots of research work has been done to find the best MO materials, including Y₃Ga_1.1Sc_0.4Fe_3.5O₁₂ with 4πM_s of 600 Gs with an optical rotation of 0.0208 deg/μm,^[45] the Gd_3−xBi_xFe₅O₁₂ film with an optical rotation of 2.38 deg/μm,^[51] the LuSmIG film with an optical rotation of 2 deg/μm,^[52] the (LuNdBi)₃(FeA1)₅O₁₂ film,^[53] the Y_1.43Yb_0.82Bi_0.75Fe₅O₁₂ film,^[54] and (Bi, Lu)₃(Fe, Ga)₅O₁₂ film.^[55]

Magnetic garnets have a number of unusual properties which make them attractive for applications in devices. Due to the three magnetic sublattices which are ferrimagnetically coupled, magnetic garnets have a unique magneto–optical property: no any other magnetic material can rotate the polarization plane of light by the Faraday effect in a spectral region where the optical absorption is zero. The heat treatment and doping can considerably change the electrical properties of garnet film by as great as eight orders.^[56] A number of magneto–optical devices have been conceived and designed, and several working prototypes were built in the 1970 s. Figure 8 shows for the first time switching and modulation of light in a magneto–optic waveguide that is a single-crystal epitaxially grown iron-garnet film. These experiments involve the Faraday rotation of the magnetic film and the motion of magnetization in the plane of the film. We have modulated light from a 1.152-μm laser up to 80 MHz. We were also able to switch light between two waveguide modes by applying a magnetic field as small as 0.2 Oe. Figure 9 shows a waveguide optical isolator employing a nonreciprocal phase shift.^[53] The isolator has the advantage of needing neither phase-matching nor complicated magnetization control. It is shown that the degradation of characteristics due to deviations in the waveguide parameters can be retained within an acceptable limit by current technologies. Also, a rare earth iron garnet crystal suitable for constructing this isolator has been developed. Magnetostatic backward volume wave (MSBVW) efficiently enters into the film as expected from the measured small ferromagnetic resonance linewidth of 0.7 Oe, whereas magnetostatic surface wave and magnetostatic forward volume wave are subjected to the severe attenuation due to their coupling to spin-wave modes. The interaction between guided optical wave and MSBVW is investigated in a transverse configuration where the input optical wave passes almost orthogonally to MSBVW. The TM–TE optical-mode conversion induced by MSBVW is observed in a frequency range of 3.5 GHz–7.5 GHz. The experimental setup is shown in Fig. 10. Its efficiency, as high as 47%/0.8 W at 4 GHz, is obtained for the interaction length of 7 mm.^[57]

Fig. 8.

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	Fig. 8. Experimental arrangement of magneto–optical guided-wave modulator proposed by Tien et al.[45]

Fig. 9.

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	Fig. 9. (a) Structure of interferometric waveguide isolator employing nonreciprocal phase shift, and (b) branching device composed of tapered coupled waveguides by Mizumoto et al.[53]

Fig. 10.

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	Fig. 10. Experimental setup for TM–TE mode conversion induced by MSBVW by Tamada et al.[57]