Magnetocrystalline anisotropy in iron garnets originates from the interplay between lattice symmetry, cation site preference, and spin-orbit coupling mediated by oxygen. We develop a dual order parameter framework that quantitatively connects site-selective occupation of inequivalent dodecahedral (24c) sublattices to the magnetic anisotropy energy in Bi substituted yttrium iron garnet (Bi:YIG). We introduce a site-order parameter eta(so)(sublattice imbalance between alpha and beta within 24c) and a composition parameter eta(co) (total Bi fraction on 24c) and use density-functional theory across 13 representative (eta(so),eta(co)) states. K(eta(so),eta(co)) obeys a compact Landau-type expansion dominated by a large odd-in-eta(so) linear term and a weaker even-in-eta(so) curvature. The fitted map yields an analytic switching boundary K=0 in the (eta(so),eta(co)) plane and order-resolved three-dimensional surfaces and weight maps that make the hierarchy (linear >> quadratic >> cubic) explicit. This unified framework rationalizes growth-induced anisotropy trends in Bi:YIG and suggests actionable routes for engineering uniaxial anisotropy via controlled A-sublattice ordering.

To study the effect of large area uniform garnet film on the consistency of image quality of a magneto-optical imaging system, the effect of lattice mismatch on a large area uniform domain structure of magneto-optical materials was studied. In this paper, (BiTm)(3)(GaFe)(5)O-12 thin garnet films with different stress were prepared on the surface of gadolinium gallium garnet by liquid phase epitaxy. The results show that the magnetic hysteresis mechanism exists in the (BiTm)(3)(GaFe)(5)O-12 thin films with tensile stress, and the domains can preferentially respond to magnetic signals in very small regions. This is mainly the phenomenon of magnetic domain partitioning caused by cracks. In addition, the non-uniform distribution of coercive force in a large range is the main cause of hysteresis. The thin films with weak compressive stress (BiTm)(3)(GaFe)(5)O-12 are uniformly distributed over a large area.

Magneto-optical garnet shows great potential in integrated optical isolators due to its highly efficient non-reciprocity. In this work, we prepared magneto-optical lithium-modified terbium bismuth iron garnet films using the liquid phase epitaxy method and systemically investigated the effect of lithium modification on magnetic properties. We found a trace amount of lithium modification induced in-plane magnetization and a minimum in-plane driving field around 2 Oe. Meanwhile, high remanence over 70% was obtained in tensile-strain samples. Most importantly, in comparison to unmodified samples, the calculation of anisotropy demonstrated the giant reduction of growth-induced anisotropy in the Li: TbBiIG up to 105erg/cm3. It reveals a new rule of ions’ preferred occupation in dodecahedral sublattices indirectly. This permits Furthermore, enhanced Faraday rotation in the near-infrared band was confirmed in the samples about 1 micrometer, up to 48% higher than unmodified samples. Our work shows Li:TbBiIGs enable a prime candidate material with substantial potential for integrated optical isolation applications.

In-plane easily magnetized scandium substituted thulium iron garnet films(Tm3Fe5-xScxO12) with soft magnetic properties have recently attracted attention for fluxgate magnetometer applications. In this paper, thin Tm3Fe5-xScxO12 films were prepared on gadolinium gallium garnet substrates by liquid phase epitaxial(LPE) method. Microstructural properties, composition, magnetic properties and the in-plane anisotropy of the films were discussed. We found that the films turned from tensile stress to compressive stress as the Sc3+ substitution decreased, and the in-plane anisotropy was mainly caused by stress reducing as Sc3+ declined. By analyzing the in-plane magnetic hysteresis loops, the magnetic performance was the best when x = 0.75. Tm3Fe4.25Sc0.75O12 film had the lowest in-plane coercive field(0.006 Oe) and the highest initial magnetic permeability(3 7 8), which was more beneficial to realize fluxgate magnetometers.

The laser damage properties of magneto-optical (MO) materials are the most important constraint for their application in high-power laser systems in the near-infrared (NIR) band. Rare-earth ion doped garnet (RIG) materials are widely used in optical communication systems and compact laser systems due to their superior MO properties -- small size and low driving magnetic field. In this study, high-quality (TbBiCa)3Fe5O12 films with hundreds of microns thickness were fabricated by liquid phase epitaxy (LPE) method. These films have lower optical absorption than conventional (TbBi)3Fe5O12 films after annealing in reducing atmosphere while possessing outstanding magneto-optical properties and their optical and MO properties are investigated in detail, which has a high specific faraday rotation angle of 1413 deg/cm at 1310 nm and 2647 deg/cm at 1064 nm, and transmittance is 51.2 % at 1064 nm and 71.6 % at 1310 nm. After that, ion beam polishing (IBP) treated the samples at different depths, and atomic force microscopy (AFM) was used to observe their surface morphology. Finally, the laser-induced damage threshold (LIDT) of samples was tested by a multi-frequency laser in different frequencies using the R-on-1 method. The LIDT of (TbBiCa)3Fe5O12 irradiated by a multi-frequency at 50 kHz is 10.92 J/cm2. Scanning electron microscopy (SEM) and optical microscopy were used to observe the surface morphology of the sample after the damage.

Yttrium iron garnet (YIG) is a promising material for various terahertz applications due to its special optical properties. At present, a high-quality YIG wafer is the desire of terahertz communities and it is still challenging to prepare substrate-free YIG single crystal films. In this work, we prepared wafer-level substrate-free La:YIG single crystal films, for the first time, to our knowledge. Terahertz optical and magneto-optical properties of La:YIG films were characterized by terahertz time domain spectroscopy (THz-TDS). Results show that the as-prepared La:YIG film has an insertion loss of less than 3 dB and a low absorption coefficient of less than 10 cm −1 below 1.6 THz. Benefitting from the thickness of the substrate-free YIG films and low insertion loss, their terahertz properties could be further manipulated by simply using a wafer-stacking technique. When four La:YIG films were stacked, there was an insertion loss of less than 10 dB in the range of 0.1−1.2 THz . The Faraday rotation angle of the four-layer-stacked La:YIG films reached 19°, and the isolation could reach 17 dB. By further increasing the stacking number to eight pieces, a remarkable Faraday rotation angle of 45° was achieved with an isolation of 23 dB, which is important for practical application in the THz band. This material may provide a milestone opportunity to make various non-reciprocal devices, such as isolators and phase shifters.

In this work, BaFe12O19 thin films with perpendicular magnetic anisotropy have been deposited on GGG (111) substrates by pulsed laser deposition in an oxygen atmosphere using a KrF excimer laser. The effects of annealing temperature on the microstructural, magnetic, and microwave properties of BaFe12O19 thin films were investi-gated. It is found that the properties of BaFe12O19 films are very sensitive to the annealing temperature, and excellent films are obtained when the annealing temperature is above 900 & DEG;C. X-ray diffraction diagrams show that films annealed at higher temperatures (>950 & DEG;C) have better crystallization and higher perpendicular orientation. Atomic force images show the surface morphology of annealed films above 900 & DEG;C to be very smooth, with a minimum roughness of 0.754 nm. Hysteresis loops reveal that the saturation magnetization of the films annealed above 1000 & DEG;C is similar to that of bulk barium ferrite, and the maximum value of 4676 Gs is obtained at 1100 celcius. The anisotropy field increases with the increase in annealing temperature, reaching a maximum of 18.0 kOe at 1050 & DEG;C. The remanence ratio and saturation magnetization also show an upward trend as the annealing temperature rises. The film annealed at 1100 & DEG;C shows a very narrow ferromagnetic resonance linewidth with a width of about 256 Oe at 39 GHz. And the ferromagnetic resonance linewidth of the films decreases as the temperature rises, which means that films annealed at higher temperatures have less microwave loss.

Ultra-thin rare earth iron garnet (RIG) films with a narrow ferromagnetic resonance (FMR) line width and a low damping factor have attracted a great deal of attention for microwave and spintronic applications. In this work, 200 nm Y3(GaAlFe)5O12 garnet (GaAl-YIG) films were prepared on gadolinium gallium garnet (GGG) substrates by liquid-phase epitaxy (LPE) with low saturation magnetization. The microstructural properties, chemical composition, and magnetostatic and dynamic magnetization characteristics of the films are discussed in detail. According to the structural analysis, these films exhibit a low surface roughness of less than 0.5 nm. The GaAl-YIG films show an obvious temperature dependence of lattice parameter and strain state, and the film's parameter is perfectly matched with that of the GGG substrate at 810°C. There is a clear variation in the Pb level, which brings about a gradual enhancement of the coercivity and a diminution of the squareness ratio of magnetic hysteresis loops as the growth temperature is reduced. Slight changes in surface roughness, strain condition and content of Pb induce the FMR line width and damping factor to vary on a small scale. The line width is less than 10.17 Oe at 12 GHz and the damping factor is of the order of 10-4. All these properties demonstrate that these ultra-thin GaAl-YIG films are of benefit for the development of devices operated at lower frequencies and in lower fields.

M-type barium hexaferrites thin films with molecular formula Ba1-xLaxFe12O19 were prepared using the liquid phase epitaxial (LPE) method, in which Ba2+ was substituted by La3+. The influence of La3+ substitution on the structure and magnetic properties of Ba1-xLaxFe12O19 has been investigated by XRD, VSM, XPS, Ramam, and the Mössbauer spectrum. X-ray diffraction shows all the samples are single-crystal M-type hexaferrites, and with the increase of La3+ substitution amount x, the lattice constant c decreases gradually. It has been found that substitution of La3+ may significantly increase saturation magnetization 4πMs. With the increase of La3+ substitution amount, 4πMs shows a trend of increasing first and then decreasing and reaching a maximum value of 4425 Gs at x=0.20. The coercivity Hc decreases compared to when x=0. The shift of the Raman spectrum confirmed that the substitution of La3+ caused the appearance of some vacancies. Mössbauer spectroscopy of 57Fe and XPS spectra have shown that there is no Fe2+ present in the material, so the substitution of Ba2+ by La3+ does not cause a valence change of Fe3+ to Fe2+. The chemical valence equilibrium of the entire system is achieved through Fe3+ or O2- vacancies.

•BaFe12O19 thin films with perpendicular magnetic anisotropy have been deposited on GGG (111) substrates by pulsed laser deposition in an oxygen atmosphere using a KrF excimer laser.•The effects of annealing temperature on the microstructural, magnetic, and microwave properties of BaFe12O19 thin films were investigated.•The films annealed at 1050 ℃ have the best magnetic properties, with the highest Mr/Ms, a high Hc and 4πMs.•The film annealed at 1100 °C shows a very narrow ferromagnetic resonance linewidth with a width of about 256 Oe at 39 GHz.

With the development of miniaturization of high-energy laser systems, a new Faraday rotator material must be studied to realize the miniaturization and integration of optical isolators. In this paper, high-quality (TbBi)3Fe5O12 (TbBiIG) and Ca-doped (TbBi)3Fe5O12 (Ca: TbBiIG) single crystal films with hundreds of microns thickness were grown by liquid phase epitaxy method on (111) oriented garnet substrate. The crystal structure, magneto-optical (MO), optical and laser induced damage properties were investigated in detail. We found that the (TbBi)3Fe5O12 film has outstanding magneto-optical and laser-induced damage properties. Optical and MO properties indicate that TbBiIG films have a high specific faraday rotation angle of 1452 deg/cm at 1310 nm, and 2812 deg/cm at 1064 nm, absorption coefficient (α) is 5.63 cm-1 and 15.7 cm-1 at 1310 nm and 1064 nm, respectively. The laser-induced damage threshold (LIDT) of TbBiIG irradiated by a multi-frequency laser is 8.91 J/cm2. The light absorption has a significant impact on LIDT value. Rare-earth ion doped iron garnet (RIG) material is a very potential MO material, which can greatly reduce the size and weight of optical isolators in the 1064 nm band.

The terahertz optical and magneto-optical response of Bi-substituted rare-earth iron garnet film were studied from 0.2 to 1.2 THz. The thickness of film is 406 μm. The maximum transmittance is over 55% near the frequency point of 0.35 THz. When the external magnetic field change from -100 mT to +100 mT, the Faraday rotation angle is between -5° and +7°. Large Verdet constants approaching 270 °/T/mm are found. The overall change of ellipticity is relatively small.

As an important component in magneto-optical devices, bismuth-substituted rare-earth iron garnet films play a significant role in guarantying a unidirectional light propagation in optical communication system. In this study, (GdYbBi)3(FeGe)5O12 film with a thickness of 120 μm was successfully grown by liquid phase epitaxy (LPE) technology. Lattice mismatch and internal stress between the epitaxial film and substrates were discussed in detail. Tested results shown that (GdYbBi)3(FeGe)5O12 films exhibit high crystal quality and large specific faraday rotation angle, which indicate that the prepared (GdYbBi)3(FeGe)5O12 films have a great potential to be used in optical communication system.

Liquid-phase epitaxy (LPE) is one of the best techniques for the preparation of single crystal garnet films. However, the specific Faraday rotation angle of Yttrium iron garnet (YIG) is small, and its easy magnetization axis is parallel to the film surface. The YIG requires a large external saturation field, which cannot meet the development needs of magneto-optical devices. It is found that Bi-substituted YIG(Bi:YIG) film has a larger specific Faraday angle. By adjusting the easy magnetization axis of Bi: YIG perpendicular to the film surface, the saturation magnetization of Bi: YIG can be reduced, so that it can work under a small external magnetic field. This meets the development needs of miniaturization and energy saving of magneto-optical device. The saturation magnetization of garnet film can be effectively reduced by substituting Ga3+ for YIG crystal, mainly for Fe3+ at the 24d position of its tetrahedron. And the lattice constants of Gd3Ga5O12 (GGG) and YIG are 1.2383 nm and 1.2376 nm, respectively. However, the radius of Bi3+ (10.8 nm) is larger than that of Y3+ (9.0 nm), the lattice mismatch of garnet film increases with the incorporation of Bi3+. In order to neutralize the lattice expansion caused by Bi3+, Tm3+ (8.69 nm) with a radius smaller than that of Y3+ (9.0 nm) is selected. Based on the theoretical analysis of the magnetocrystalline anisotropy of garnet film, (BiTm)3(GaFe)5O12 mono-crystalline films with different growth temperatures and different thickness values are grown by LPE on GGG (111) substrates. The experimental results show that when the thickness of epitaxial film is greater than 1 μm, the influence of shape anisotropy on magnetocrystalline anisotropy can be ignored. With the increase of growth temperature, the substitution number of Bi3+ ions decreases gradually, the lattice constant of epitaxial film decreases gradually, and the lattice mismatch first decreases and then increases. Then, the state of compressive stress gradually changes into that of tensile stress. Compared with growth-induced anisotropy, the stress-induced anisotropy is dominant in the change of magnetocrystalline anisotropy. The Verdet constant of (BiTm)3(GaFe)5O12 film is 11.8 × 104 rad/Tm@1064 nm. The results show that the prepared (BiTm)3(GaFe)5O12 mono-crystalline films have great development potential in magneto-optical devices.

We report the magneto-optical Faraday response of bismuth-gadolinium-substituted rare-earth iron garnet at terahertz frequencies ranging from 100 GHz to 1.2 THz. The maximum transmittance of ±45° component is about 60% near the frequency point of 0.63 THz. When the external magnetic field change from -100 mT to +100 mT, the Faraday rotation angle is between -6° and +7.5°. The overall change of ellipticity is relatively small. The maximum value of the Verdet constant is about 260 °/mm/T at 0.1 THz and then gradually decreases to 80 °/mm/T at 1.2 THz. Within the considered frequency range, the thick film exhibits magnetically tunable, non-reciprocal characters and a strong magneto-optical effect within a small external magnetic field at room temperature, which will be widely used for the terahertz isolators, circulators, nonreciprocal phase shifters, and magneto-optical modulators.

Rare-earth iron garnet thin films with perpendicular magnetic anisotropy (PMA) have recently attracted a great deal of attention for spintronics applications. Bismuth substituted iron garnets are particularly popular among these various films because Bi3+ with a larger ion radius can adjust the lattice constant, strain state, and PMA of the films. In this paper, Tm2BiFe5O12 (TmBiIG) and Y2BiFe5O12 (YBiIG) garnet films with a series of thicknesses are prepared by radio frequency magnetron sputtering, and these films exhibit robust PMA. The microstructural properties, magnetic properties, and the anomalous Hall effect of these two kinds of films are discussed in detail. Due to their larger magnetostriction coefficient and proper tensile strain, TmBiIG films exhibit better PMA than YBiIG films, which have lower damping. As the thickness of TmBiIG and YBiIG films increases, the PMA becomes weaker, and the 40 nm YBiIG turns back to in-plane easy magnetization, but PMA is still obvious for the 64 nm TmBiIG. The ferromagnetic resonance linewidth of the 32 nm TmBiIG film is 249.08 Oe @ 13 GHz, and the damping factor is 1.49 × 10−2, which is close to that of Tm3Fe5O12. YBiIG films have better damping characteristics than TmBiIG films; however, the value is larger than that of yttrium iron garnet because of surface roughness and defects caused by larger lattice mismatch. In addition, on account of fewer defects and smaller surface roughness, the Hall voltage and Hall resistivity in TmBiIG/Pt heterostructures are larger than in YBiIG/Pt.

(NdGdBi)(3)Fe5O12 mono-crystalline films with high magneto-optical figure of merit (FOM) and high laser-induced damage thresholds (LIDTs) at a wavelength of around 1 mu m have been grown in this study. Crystal structure, phase composition, magneto-optical (MO) properties and LIDTs of the grown (NdGdBi)(3)Fe5O12 films were discussed in detail. Tested results show that (NdGdBi)(3)Fe5O12 films exhibit a low insertion loss of 0.5 dB, a high FOM of 78.7 deg/dB and a high LIDTs of 9.12 J/cm(2) at 1.06 mu m wavelength. Lattice constant and dopants are two key factors to determine FOM and LIDTs of Bi-doped iron garnet films grown by liquid-phase epitaxial method. The excellent MO properties and LIDTs indicate that (NdGdBi)(3)Fe5O12 films grown in this study have a great potential to be used in 1-1.1 mu m high-power lasers.

Rare-earth iron garnet thin films with perpendicular magnetic anisotropy (PMA) have recently attracted a great deal of attention for spintronic applications. In this study, magnetic anisotropy of epitaxial garnet films was analyzed theoretically, and (YBiLuCa)(3)(FeGe)(5)O-12 mono-crystalline films with PMA have been successfully grown with liquid phase epitaxial (LPE) method on Gd3Ga5O12 (GGG) substrates. Microstructural properties, chemical composition and magnetic properties of the epitaxial films were discussed in detail. We found that growth temperatures played a significant role in the uniaxial anisotropy of the epitaxial (YBiLuCa)(3)(FeGe)(5)O-12 mono-crystalline films. Ferromagnetic resonance linewidth of (YBiLuCa)(3)(FeGe)(5)O-12 films with thickness of 170 nm was 8.06 Oe@12 GHz, which indicated that the epitaxial (YBiLuCa)(3)(FeGe)(5)O-12 mono-crystalline films had a great potential application in spintronic devices.

Rare-earth iron garnet (RIG) thin films with perpendicular magnetic anisotropy (PMA) property have recently attracted a great deal of attention for spintronic applications. In this paper, thin (YBiLuCa)3(FeGe)5O12 garnet films were prepared on gadolinium gallium garnet (GGG) substrate by liquid phase epitaxial (LPE) method showing large PMA property. Microstructural properties, chemical composition, magnetic and anomalous Hall effect (AHE) properties of the films were discussed in detail. And we found that the PMA property of this kind of films was mainly controlled by stress-induced anisotropy and growth-induced anisotropy, which were mainly affected by growth temperature. As the growth temperature decreased, the films turned from tensile stress to compressive stress, however, the growth-induced anisotropy increased and would further dominant PMA. By analyzing AHE curves, the thinner films were easier to realize magnetization reversal due to the influence of domains width and interface reflection.