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Abstract
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.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) waves bridge the gap between the microwave and infrared band, which has been widely used in material spectroscopy, wireless communication, and imaging [1,2]. The development of THz technology has led to higher demands on efficient devices for manipulating the amplitude, phase, and polarization of waves. Among various THz devices, magneto-optical (MO) devices are of great significance in applications of the modulator, isolator, rotator, or other non-reciprocal devices [3]. However, in the THz region, the lack of efficient MO materials limits the fabrication and practical application of these devices [4].
Garnets have a complex body-centered cubic structure that contains a variety of transition metals and rare earth elements. The general chemical formula of garnet is A3B2C3O12, with A-, B-, and C-sites can be occupied by divalent, trivalent, and tetravalent cations. With substituting or doping different ions into the A, B and C sites, the garnets, such as GGG [5], TGG [6], TIG [7], YAG [8], BIG [9], YIG [10], have different functional properties for various emerging applications [11]. The rare earth iron garnets (RIG), with the highest MO Verdet constants at communication wavelengths, are the most common materials for optical rotators and isolators [12]. The basic and most investigated RIG material is yttrium iron garnet (YIG), which is widely used in spintronics, electromagnetism, optics, etc. This material is one of the most promising materials for terahertz wide-band MO devices due to its characteristics in both microwave and optical applications.
The liquid-phase epitaxy (LPE) provides monocrystalline films of the highest quality in terms of both magnetic and optical properties [13]. The films with thickness >300 µm are required as commercial isolators in optical or infrared systems, and even thicker in the terahertz system. According to our previous studies, the large radius La3+ substituted YIG (La:YIG) were much better lattice-matched with the GGG substrate benefitting for the preparation of large size thick films [14]. The La:YIG film with the thickness of 105 µm could realize the Faraday rotation of about 1.5° with a 150 mT external magnetic field in the terahertz band. To realize a 45° rotation, the film thickness requires at least 3.15 mm. The small rotation angle is far from being used in a terahertz isolator. Even thicker film and much stronger magneto-optic response are needed for practical applications in the terahertz band.
Fortunately, the epitaxial iron garnet films of bismuth (Bi) and gadolinium (Gd) co-substituted garnets ((BiGd)3Fe5O12) have been demonstrated to have merits in the application of MO devices at visible and near-infrared frequencies [15,16]. Firstly, Bi ions could enhance Faraday and Kerr MO effects. Secondly, a large atom radius of Bi could increase the lattice constant. By reasonably controlling the proportion of Bi, Gd, and Yb, wafer-scale ultra-thick films can be obtained on SGGG substrates. Thirdly, Gd ions reduce the net magnetization, thus decreasing the saturating magnetic field compared to La:YIG. If these could work at terahertz frequencies as well, that would be meaningful for the practical application of THz MO devices. Further, the substituted RIG materials with unique properties have been studied extensively from microwave to optical band, which can potentially be applied to broadband MO devices covering the whole terahertz-to-visible range [5–14].
In this paper, we report on the successful synthesis of bismuth-gadolinium-substituted rear-earth iron garnet (Bi:RIG) thick-film through the LPE method, especially discussed the magneto-optical Faraday response in terahertz regime by using the terahertz time-domain spectroscopy (THz-TDS) system and orthogonal polarization detection. The measured Faraday rotation angle, polarization ellipticity, and Verdet constant spectra are presented. The results show that the film has a strong Faraday magneto-optical effect within a small external magnetic field at room temperature, and the Faraday rotation angle could be controlled by the magnitude and direction of the external magnetic field. The terahertz properties of Bi:RIG systematically characterized in this work will provide important information which is critical for the future development of broadband terahertz magneto-optical devices.
2. Methods
The nominal composition of Bi:RIG sample is (GdYbBi)3Fe5O12. The sample was prepared by a horizontal dipping liquid phase epitaxial (LPE) method on a quarter of 3-inch (1 1 1) oriented SGGG substrate. The optimized growth parameters of Bi:RIG film are shown in Table 1. By adjusting epitaxial temperature and growth time, (GdYbBi)3Fe5O12 films with good lattice matching and desired thickness were obtained. To remove the solution remnants of the sample surface, the obtained sample was stored in a diluted hot acidic-acid solution after room temperature cooling. After chemical-mechanical polishing, the samples were cut into appropriate chips by a standard mechanical cutter (HP 603) for testing. The crystal structure was examined by high-resolution X-ray diffraction (HRXRD, D1 Evolution, JVS, Germany). Vibrating sample magnetometry (VSM, RIKEN DESNSHI Japan) was used to obtain the magnetic hysteresis loops. The thickness of the sample was estimated by scanning electron microscope (SEM, Akashi DS-130C).
Table 1. Optimized growth parameters for Bi:RIG film.
The optical and magneto-optical properties of Bi:RIG sample in the THz regime were measured with a THz-TDS system as depicted in Fig. 1(a). The femtosecond laser beam with 50 fs duration of 1000 Hz repetition rate is generated by a mode-locked Ti: sapphire laser (λ=800 nm). The laser was divided into a pump beam to produce THz pulses and a probe beam to detect THz signals. Two ZnTe crystals were used in the system, one for radiating THz waves via optical rectification and another one for detecting THz signals via linear electro-optic effect. The magnetically tunable THz Faraday rotation effect in perpendicular magnetized Bi:RIG film were experimentally investigated, which were measured with the different external magnetic field (EMF) and orthogonal polarization detection. A set of permanent magnets is used to apply an EMF to the sample, which can be mechanically adjusted from –100 mT to +100 mT. Positive and negative represent opposite directions of the EMF. The magnitude of EMF was measured by a tesla-meter (Lakeshore 425). As shown in Fig. 1(b), the sample is placed in the middle of two magnets as Faraday configuration and the direction of EMF is parallel with the THz wave vector (along with z-axis). Two terahertz wire-grid polarizers (WGP) were placed relatively parallel in the system. Along the z-direction, the first WGP is used to ensure that all incident waves are linearly polarized (LP) strictly (electrical vector along with y-axis), the second WGP is applied to characterize the different polarization components of the THz signal. By rotating the second WGP, the transmitted time-domain spectra of 0° and ±45° polarization directions were measured. The spot size of the THz beam is about 3 mm. All experiments were performed at room temperature with the humidity of about 10% and use air as reference. To calculate the state of an output signal, the formulas are employed as follows [17]:
Fig. 1. Schematic diagram: (a) the THz-TDS system, (b) the THz Faraday configuration and orthogonal polarization detection.
3. Results and discussion
The normalized hysteresis loops of the sample with the external magnetic field direction parallel or perpendicular to the film plane (film surface) are shown in Fig. 2(a). The saturation magnetic field in the perpendicular direction is ∼86 mT, and in the parallel direction is ∼100 mT. Thanks to these we can conduct magneto-optic experiments at relatively small EMF. This is of great significance for reducing the external size of the magnets in practical application. The sample is easier to be magnetized by the perpendicular magnetic field. And the sample showed nonlinear distortion when were magnetized by the parallel magnetic field, shown in the lower right inset of Fig. 2(a). That is typical of films prepared by the LPE method, which is caused by the existence of film/substrate interface buffer and hard magnetization magnetic moments [18,19]. The upper-left inset of Fig. 2(a) is a cross-sectional SEM image of the sample. The thickness of SGGG substrate is 220 μm and Bi:RIG film is 406 μm, so the total thickness of sample is 626 μm. The lower left inset of Fig. 2(a) is the XRD pattern of film. The film had only one diffraction peak and the peak center is located at 50.6°, which means that the prepared sample possesses a pure single crystal garnet phase.
Fig. 2. (a) Hysteresis curve of film/substrate obtained from VSM measurements, the left insets are cross-sectional SEM image and XRD pattern of Bi:RIG film. (b) Experimentally measured 0°, +45° and –45° linearly polarized time-domain THz pulses of the sample and reference.
The LP time-domain pulse signals of the sample and the air as reference were measured by the THz-TDS system when the second WGP is rotated to 0° and ±45°. The transmitted time-domain spectra are plotted together as shown in Fig. 2(b). Compared to the reference, the transmitted pulse delay of the sample is about 7.2 ps. According to the definition of refractive index (with 7.2 ps time delay and 626 μm thickness), a high refractive index of sample about 4 could be calculated. A relatively high real part of permittivity about 16 could get. Considering the relatively high refractive index and polished surface of film, many pulses will be reflected away, which will reduce the transmission of incident THz pulses, which increase the insertion loss of a device and is not good for the MO Faraday application. Fortunately, there are ways to reduce the reflection and increase the transmittance, such as surface treatment [20,21]. Without any EMF, the ±45° signals of reference are nearly overlapped, and of the sample have only a small variation, which is probably caused by the hard magnetization magnetic moments. The inset of Fig. 2(b) is a whole terahertz pulse passing through the sample.
When different EMF is applied, the measured time-domain signals of +45° component are showing in Fig. 3(a). The amplitudes become different and no phase delay is found. To show the difference more intuitively, the corresponding transmission spectra of +45° component are demonstrated in Fig. 3(b) by using Eq. (1). The sample has a stable magnetic modulation effect from 0.2 to 1.2 THz. The maximum transmittance (over 60%) is near the frequency point of 0.63 THz. The transmission spectra of –45° component are shown in Fig. 3(c). The transmittance of –45° component is declined and +45° component is enhanced when the EMF is +100 mT, however, when reversing the EMF (–100 mT), the result is opposite. These are caused by non-reciprocal optical rotation (Faraday effect). By the comparison of ±45° component, the amplitude change modulated by EMF is less than +45° component. The different rates of change in ±45° component can be considered as the difference in absorption of the left circularly polarized light (LCP) and right circularly polarized light (RCP). When the EMF is 0, the difference in absorption is related to the natural property of materials, that crystal lattice structure features distribute electric charge in a spatial array. In contrast, when the EMF is applied, the difference in absorption is due to electromagnetic interaction of the external field with electronic charge within the sample [22]. First-principle calculation and material modeling are needed for elucidating the detailed microscopic mechanism that gives rise to the difference in absorption. Further, the Faraday rotation angle spectra under different EMF were calculated from Eqs. (2) from 0.2-1.2 THz, as shown in Fig. 3(d). When the EMF change from –100 mT to +100 mT, the Faraday rotation angle is approximately between –6° and +7.5°. The differential absorption between LCP and RCP is the main cause of optical rotation. Meanwhile, the sample has a partial intrinsic rotation angle (about 1° at 0.7 THz) when the EMF is 0, due to remanence after magnetization which could be confirmed in Fig. 2(a). By now, we have experimentally verified that the sample can lead to non-reciprocal transmission and magnetically tunable rotation of LP THz wave from 0.2 to 1.2 THz.
Fig. 3. (a) Experimentally measured THz time domain signals of +45° component with different external magnetic fields. The transmission spectra of +45° component (b), –45° component (c), by using Fourier transform and the air signal without sample as reference. (d) Experimentally measured Faraday rotation angle spectra of sample.
Further, the ellipticity $\chi $ spectra under different EMF were calculated by Eq. (3), as shown in Fig. 4(a). The overall change of ellipticity is relatively small from 0.2 to 1.2 THz, which can be considered as the sample does not change the polarization state of the input LP light. When the EMF is applied (±100 mT), the ellipticity of the sample is close to 0 in low-frequency region, and decreases slightly with the increase of frequency, which shows a very weak magnetic circular dichroism. The slight changes of ellipticity are probably caused by the magnetostriction of material. More specifically, the magnetic domains are migrated by the influence of the EMF. The shape and width of magnetic domains can be thought of as gratings, which could affect the transmission of THz waves in different wavelengths. However, when reversing the direction of EMF, the difference between the red and blue lines is not obvious. The specific interaction mechanism between terahertz wave and magnetic domain needs to be analyzed by combining dynamic Magnetic Force Microscopy in the future.
Fig. 4. (a) The polarization ellipticity spectra of sample under different external magnetic field. (b) The Verdet constant spectrum of sample derived from the polarization rotation angle at an external magnetic field of +100 mT.
The Verdet constant spectrum was derived from Eq. (4) by using the Faraday rotation spectrum under +100 mT, as shown in Fig. 4(b). The maximum value is about 260 °/mm/T at 0.1 THz and then gradually decrease to 80 °/mm/T at 1.2 THz. In the low frequency region, it shows a strong dependence of frequency, and in the high frequency region, it tends to be stable gradually. It is inversely proportion to the frequency and dependent on the wavelength of light, which is basically consistent with the classical magneto-optical theory at room temperature [23]. The Verdet constant is much larger than before (100 °/mm/T) in low frequencies region [14], which means that the magneto-optical response in low frequencies is better and more promising for using in commercial terahertz imaging and communication systems from 100 to 300 GHz.
In the terahertz band, some materials, such as HgTe, InSb, (Cd, Mn)Te, carbon nanotubes, and graphene [24–27], are electrically conductive materials, which exhibit gyrotropic response under magnetic bias. They exhibit a strong magneto-optical response. However, they often need to work at low temperatures or strong magnetic field conditions. Some metasurface structures or metamaterials can also achieve optical rotation, but they are often accompanied by a narrow band, strong dispersion (change in polarization state), or high resonance absorption to achieve large rotation angles or optical rotation enhancement. Meanwhile, most of them are reciprocal in the absence of a magnetic field. These materials are not in the same category as ours.
In contrast, several magneto-optical materials similar to ours are compared in Table 2. Most of them are garnet structures, and there is also a magnetoplumbite structure. These materials (except GGG\SGGG) could operate at room temperature (∼300 K) and relatively low external magnetic field conditions over a wide frequency band. The GGG\SGGG are usually used as substrate materials for liquid phase epitaxy. The terahertz magneto-optical response can only be measured under low-temperature conditions and the Verdet constant is about 17 °/T/mm. The Verdet constant of Tb3Sc2Al3O12 is the smallest in Table 2. SrFe12O19 was used in the fabrication of the first terahertz isolator, while the insertion loss of the material was really large due to the polycrystalline structure. Besides, the Verdet constant (∼90 °/T/mm) is smaller than La:YIG. If a single crystal SrFe12O19 film is prepared, the performance should be the best in Table 2. Compared to the previous three, the La:YIG could operate in a smaller external magnetic field and has the largest Verdet constant (∼100 °/T/mm). The only regret is that the rotation angle of a single piece is small (∼3°). Now, more progress has been made in Bi:RIG. The external magnetic field can be further reduced to 0.1 T, and the rotation angle of one piece is also increased, up to 7.5°. At 0.2 THz, the Verdet constant is nearly twice than La:YIG. Therefore, compared with our previous La:YIG film, the thickness of Bi:RIG film is twice the previous, the rotation angle is increased to 7.5° (about 2.5 times), and the required external magnetic field is reduced by one third.
Table 2. Optimized growth parameters for Bi:RIG film.
4. Conclusion
On summary, the Bi:RIG films with the thickness of 406 microns were successfully prepared by LPE method on SGGG substrate. The SGGG substrate does not show terahertz magneto-optical response in small external magnetic field condition at room temperature, so the magneto-optical response of the sample is mainly provided by the thick Bi:RIG film. The terahertz optical and magneto-optical properties were studied 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°. Large Verdet constants approaching 260 °/mm/T are found. The overall change of ellipticity is relatively small and negligible. It is experimentally verified that the substitution of Gd and Bi is feasible to reduce the saturated external magnetic field. While reducing the magnetic field, a thicker single crystal film and a larger rotation angle is obtained. In brief, the thick film exhibits high refractive index, magnetically tunable, non-reciprocal characters and strong magneto-optical effect within small external magnetic field at room temperature, which will be widely used for the terahertz isolators, circulators, nonreciprocal phase shifters and magneto-optical modulators.
Funding
National Natural Science Foundation of China (61831012); Science Challenge Project (TZ2018003); International Science and Technology Cooperation Programme (2015DFR50870); Sichuan Province Science and Technology Support Program (2021JDTD0026).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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