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Abstract
The wafer-scale La:YIG single crystal thick films were fabricated on a three-inch gadolinium gallium garnet (GGG) substrate by liquid phase epitaxy method. The terahertz (THz) optical and magneto-optical properties of La:YIG film were demonstrated by THz time domain spectroscopy (THz-TDS). The results show that a high refractive index of approximately 4.09 and a low absorption coefficient of 10–50 cm−1 from 0.1 to 1.6 THz for this La:YIG film. Moreover, the THz Faraday rotation effect of La:YIG film was measured by the orthogonal polarization detection method in THz-TDS system, which can be actively manipulated by a weak longitudinal magnetic field of up to 0.155 T. With 5 samples stacked together, the Faraday rotation angle varies linearly from −15° to 15°, and the Verdet constant of La:YIG is about 100 °/mm/T within the saturation magnetization. This magneto-optical single crystal thick film with large area shows low loss, high permittivity and strong magneto-optical effect in the THz regime, which will be widely used in magneto-optical polarization conversion, nonreciprocal phase shifter and isolator for THz waves.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) wave whose frequency lies from 0.1 THz to 10 THz bridges the gap between the microwave and infrared band. It has the characteristics of both electronics and optics, thus make it has important and special merits in scientific and applied researches [1]. In the past decade, great progress has been made in THz sources [2], detectors [3], and applications [4]. That pushed a high demand for efficient devices within a broad band for guiding, modulating, and manipulating THz wave in its amplitude, phase, and polarization [5]. Based on electricity, magnetism, light, etc., various modulation methods are widely used by researchers. The unique non-reciprocal and magnetic tunability of magneto-optical (MO) effect play an irreplaceable role in a high-performance isolator, polarization controller, MO modulator, and magnetic field sensor [6–8]. It is meaningful to fill the THz gap by not only electrical but also magnetic-optical methods. In 1901, Rayleigh described a one-way transmission system based on the mechanism of Faraday rotation firstly [9]. The Faraday effect (external magnetic field direction is parallel to the direction of light propagation) can lead to non-reciprocal rotation of the linearly polarized light in MO materials, which could be used in Faraday rotator and isolator. The Faraday rotation angle (θF) provided by MO materials determines the performance of MO devices directly. At THz frequencies, only some special MO materials have a small specific θF under a particular condition. Narrow-gap compound semiconductors such as InSb, InAs, and HgTe are known to show giant free-carrier Faraday rotation in THz frequency [10,11]. However, serious carrier absorption, low working temperature and large magnetic field limit their application. In 2013, M. Shalaby et al. found a kind of ferrite SrFe12O19 has giant MO Faraday effect, and they presented the first THz Faraday isolator at room temperature, but the performance of isolator was limited by the large insertion loss [12]. In 2018, Ding et al. measured the MO properties of Tb3Sc2Al3O12. The absorption and loss are small, but unfortunately the MO effect is too weak in the THz band [13]. Due to the lack of high-performance THz MO materials, the improvement of THz MO devices is still in challenge.
Yttrium iron garnet (YIG) is one of the most important gyromagnetic materials for constructing MO Faraday devices, which has been widely used in microwave and optical frequency band [14–16]. The YIG films, especially single crystals films, have a relatively small absorption and could be used in low-loss tunable devices, including resonators, isolators, and phase shifters operating in THz band [17,18]. LuBiIG single crystal film was been demonstrated has a very small absorbance value in the THz band. It has the possibility of application in THz integrated device [19]. However, those YIG films with thickness from 100 nm to a few micrometers are too thin to application for THz waves, since the wavelength of THz waves are sub millimeter. Therefore, the fabrication of large area, ultra-thick single crystal YIG films is in high demand, while it is very difficult to obtain pure thick YIG films on the gadolinium gallium garnet (GGG) substrates without mechanical stresses and cracks induced by a lattice parameter mismatch of about 0.007 Å [20]. Liquid-phase epitaxy (LPE) to date is the best techniques to obtain large size (>3 inch) thick film with high-quality and atomic substitution could change the lattice parameter of YIG in order to get thick films [21]. La3+ substituted YIG films were much better lattice-matched with the GGG substrate [22]. With La3+ ions substitution, the stress between the two layers is less, and the ultra-thick (>100 um) epitaxial film could be obtained for long THz path length which could realize a large Faraday rotation angle. However, this substitution distorted the sublattice, which further affect the electromagnetic characteristics. The action mechanism of La:YIG interacting with THz wave needs further study. Nevertheless, this provides the conditions for preparing large-size wafers using in integrated THz devices and systems. The ions-substituted single crystal YIG films with different properties from pure YIG have a promising future using in THz integrated MO devices such as modulator, phase shifters, Faraday isolators or switches. Meanwhile, its THz optical and MO performance should be demonstrated and compared with traditional YIG films.
In this paper, we fabricated the wafer-scale La:YIG single crystal thick films on three-inch GGG substrates grown by LPE method. The high refractive index and low absorption coefficient of this MO film were measured in the THz regime. A magnetically tunable THz Faraday rotation effect in longitudinally magnetized La:YIG were experimentally investigated, which were measured with different external magnetic field (EMF) by the THz time domain spectroscopy (THz-TDS) system and orthogonal polarization detection. The results show that this is a large area, high-quality, single crystal thick film with low loss, high permittivity and strong MO effect in the THz regime.
2. Methods
2.1 Sample preparation
The single-crystalline lanthanum-doped YIG films were prepared by standard LPE method on a three-inch (111)-orientated GGG substrate. The nominal composition was determined by the x value in Y3-xLaxFe5O12. When x=0.07, the lattice constant of Y2.93La0.07Fe5O12 is calculated to be 12.384 Å, which is very close to the lattice constant of the GGG substrate (12.383 ± 0.001 Å) [23]. The growth parameters of the film were carefully optimized to obtain the best quality, as listed in Table 1. With these growth parameters the 3 inches La:YIG single crystal films were successfully fabricated on GGG substrates, and the thickness of the film could be altered by controlling the growth time. The thickness of the films was estimated by Scanning electron microscope (SEM, Akashi DS-130C). The crystal phase and crystallinity was examined by X-ray diffraction (XRD, Jordan Vallay D1 Evolution), high-resolution transmission electron microscope (HR-TEM), and the surface morphology of the La:YIG films on GGG substrate was observed with Atomic force microscopy (AFM, SEIKO SPA-300HV), and composition of the La:YIG film is determined by Electron probe micro analyzer (EPMA, Shimadzu EPMA-1720H). Vibrating sample magnetometry (VSM, RIKEN DESNSHI Japan) was used to obtain the magnetic hysteresis loops of La:YIG/GGG.
Table 1. Optimized growth parameters for La:YIG films.
2.2 THz experiment system
The optical and MO properties of the La:YIG films in the THz regime were measured with a THz-TDS system as depicted in Fig. 1(a). The femtosecond laser beam with 75 fs duration of 80 MHz repetition rate is generated by a mode-locked Ti: sapphire laser (λ=800 nm). A low temperature grown GaAs photoconductive antenna (PCA) was used to generated the THz pulses. It is a dipole radiation antenna composed of two parallel metal wires. Therefore, the polarization direction of the electromagnetic wave radiated from it will be strictly perpendicular to the metallic wire (i.e. y- direction), in our experiment, all incident waves are y-linearly polarized. A set of permanent magnets is used to apply an EMF to the sample, which can be mechanically adjusted from 0 to 0.155 T. The configuration of THz wave and EMF for sample testing is shown in Fig. 1(b). The samples are placed between the magnets as the Faraday configuration, i.e. the direction of EMF is coincidence with THz wave vector. THz wave vector along z-axis with a LP electrical vector along y-axis, is incident perpendicular to the surface of the La:YIG sample. The spot size of THz beam is about 4 mm. The sample is flat and thin enough, and spot size is smaller than the sample, which could maintain a good homogeneous magnetic field on the sample. A wire-grid polarizer (WGP) is placed behind the sample, so that the transmitted wave intensity of different LP directions can be obtained by rotating the polarizer. The y-axis direction is defined as 0°, the clockwise rotation is positive, and the counter clockwise is negative. The transmitted time domain spectra of the 0° and ±45° polarization directions were measured in our experiments. All experiments were performed at room temperature with the humidity of about 10%.
Fig. 1. (a) Schematic diagram of THz-TDS system, (b) Faraday configuration of longitudinal magnetized La:YIG sample.
3. Results and discussion
3.1 Composition and quality analysis of La:YIG film
The composition of the as-grown La:YIG single crystal film was determined by EPMA chemical analysis. Three random positions on the surface of the film were examined, and the results are summarized in Table 2. It shows that chemical formula of the La-substituted YIG can be written as Y2.93La0.04Fe4.8O11.08 approximately, which is quite close to Y2.93La0.07Fe5O12. The obtained values were normalized using Y=2.93. Y and La were measured to a precision of two decimal places. The Gd and Ga content is small (less than 0.03 mol%), and Pb and B (PbO-B2O3 flux) were not detected in our sample within the detection limit of EPMA. Nevertheless, we can conclude that our Y2.93La0.04Fe4.8O11.08 single crystal films are Pb free. If optimizing the composition ratio and the growth process further, the ideal composition of Y2.93La0.07Fe5O12 may be achieved, and this could guarantee an even thicker film.
Table 2. Y, La, Fe, O mole fractions obtained by EPMA from the surface of La:YIG sample.
Illustration of Fig. 2(a) is the photograph of three-inch (wafer-scale) La:YIG sample, it shows a smooth mirror-like surface which could also be confirmed in Fig. 2(b). Figure 2(b), AFM image of sample reveals a uniform surface morphology without microcracks and residual flux droplets. Average surface roughness (RA) is 0.293 nm and the root-mean-square (RMS) roughness is 0.44 nm. This epitaxial film has lower surface roughness compared with the films prepared by other methods such as RF sputtering, pulsed laser deposition (PLD) [23]. For a piece of La:YIG sample, the total thickness of it is 748 µm and the La:YIG films are d1 = 210 µm (105 µm of one side), so the thickness of the substrate GGG is d2 = 538 µm. These could be confirmed from the SEM image of Fig. 2(c). There is a sharp interface between film and substrate showing from Fig. 2(c). Figure 2(d), the cross-sectional HR-TEM images shows that the epitaxial La:YIG film is of good quality and that only a tiny lattice mismatch exists between the La:YIG film and GGG substrate. The lattice constants of the film and the substrate are very close, and the lattice matching is quite good. Furthermore, as indicated by the inset of Fig. 2(d), the corresponding diffraction pattern of epitaxial La:YIG film reveals an excellent crystallization quality and the defect-free feature, which is very important to reduce the transmission loss of THz wave.
Fig. 2. (a) Photograph of three-inch La:YIG sample. (b) AFM images of the surface pattern of La:YIG film. The cross-section image of La:YIG film on GGG substrate: (c) SEM image, (d) High resolution TEM image of La:YIG/GGG interface. (e) XRD pattern of La:YIG film and GGG substrate. (f) Hysteresis curve of a La:YIG sample.
As the film was too thick (>100 µm), it is difficult to detect the substrate across the epitaxial La:YIG films directly by XRD. The GGG and La:YIG was measured by XRD separately in the same test conditions, then draw their X-Ray diffraction pattern together as shown in Fig. 2(e). The diffraction peaks La:YIG (444) and GGG (444) are almost overlapping with each other, where the diffraction peaks of La:YIG is located at 51.038° and GGG at 50.007°. This good lattice matching has been further confirmed in Fig. 2(d). The La:YIG wafer has been cut into 10-mm square samples for testing and Fig. 2(f) shows the normalized VSM measurement of one sample. The saturation magnetic field in the perpendicular direction (out-of-plane) is ∼0.185 Tesla. This can be used as a reference value for EMF. It is easy to conclude that the wafer-scale thick epitaxial La:YIG films possess a pure single crystal garnet phase and a good lattice matching with the single crystal GGG substrate.
3.2 THz optical properties of La:YIG film
The time-domain pulse signals were measured to investigate the optical properties (refractive index and absorption) of La:YIG film by THz-TDS system when the THz polarizer is rotated to 0°. The transmitted time domain spectra of La:YIG/GGG as sample signal Es(t), the air and bare GGG substrate as reference signal Er(t) are obtained as shown in Fig. 3(a). Compared to the air, GGG’s transmission pulse is delayed by 4.5 ps, while the transmitted pulse delay of La:YIG/GGG is 7 ps. Therefore, the delay caused by La:YIG films is about 2.5 ps. Then the time domain spectra are processed by Fourier transform. The frequency domain information was obtained, including the amplitudes Er(ω), Es(ω) and phases δr(ω), δs(ω) of the reference and samples, correspondingly. The transmission coefficient T(ω) is
And the phase shift between the sample and the reference isFig. 3. (a) Experimentally measured time-domain THz pulses of air, bare GGG, and La:YIG film on GGG substrate. Experimentally measured effective refractive index (b) and absorption coefficient (c) of La: YIG and GGG substrate.
Therefore, the effective refractive index n(ω) and absorption coefficient α(ω) can be calculated by
The refractive index and absorption coefficient derived from Eqs. (3) and (4) are shown in Fig. 3(b) and 3(c). The refractive indices of GGG and La:YIG are approximately 3.55 and 4.09 in the range of 0.1 to 1.6 THz, respectively. The real part of permittivity of this MO film is as high as 16.8 with a very small dispersion in the whole THz frequency range. As Fig. 3(c) shows, the absorption coefficient of the substrate GGG is substantially below 10 cm−1, the overall is lower than La:YIG. When the frequency is lower than 0.8 THz, the absorption coefficient of La:YIG is about 10 cm−1. However, when the frequency is higher than 0.8 THz, La:YIG’s absorption coefficient increases rapidly, reaching 50 cm−1 at 1.6 THz. Therefore, the loss caused by material absorption in the low frequency THz band is acceptable. In general, this MO film has high dielectric function, low absorption and low dispersion for THz waves, which is very conducive to the preparation of THz integrated waveguide devices.
3.3 THz magneto-optical properties of La:YIG film
Next, we need to use the method of orthogonal polarization detection to study the MO polarization characteristics of the La:YIG film. To obtain the output polarization states, the +45° and –45° LP signals, E+45°(t) and E−45°(t), of 5 La:YIG samples stacked together were measured by THz-TDS system when the THz polarizer is rotated to +45° and –45°. As shown in Fig. 4(a), when there is no EMF applied, ±45° signals are nearly overlapped, which means that the polarization state of out waves is no changes compared to the input waves. When the EMF is applied in Fig. 4(b), the amplitudes of the ±45° signals become quite different, but the phase delay is nearly the same, which means that the output waves are still LP state, but rotate to a Faraday rotation angle. After Fourier transform, the T+45°(ω), T-45°(ω), and Δδ±45°(ω) = δ+45°(ω) – δ-45°(ω) can be obtained.
Fig. 4. Experimentally measured +45° and –45° LP time-domain THz pulses of 5 stacked La:YIG films under the EMF of (a) B = 0 T and (b) 0.155 T.
The Faraday rotation angle ψ(ω) can be derived as follows:
where $\tan \beta (\omega )\textrm{ = }{T_{ + {{45}^ \circ }}}(\omega )/{T_{ - {{45}^ \circ }}}(\omega )$. The Verdet constant V, describes the optical rotation of unit-thickness medium under a unit magnetic field, can be calculated by: where B is the magnetic flux density of EMF. The ellipticity ɛ(ω) of the output waves reflects the circular dichroism of MO material, which can be expressed as To express the complete polarization state information, the terminal trajectory equation of electric vector E, also called as polarization ellipse, is obtained as follows:Fig. 5. (a) Experimentally measured Faraday rotation angle spectra of five La:YIG samples (stacked together) under the EMF range from 0 to 0.155 T. (b) The Verdet constant spectrum of La:YIG calculated from the polarization rotation angle at a EMF of 0.155 T. (c) The curves of EMF v.s. rotation angle at 0.3 and 0.9 THz. (d) Experimentally measured polarization ellipticity spectra of La:YIG.
In order to represent the THz MO polarization conversion effect of La:YIG film more intuitively, the polarization states of the output waves at three different frequency points are plotted by Eq. (8) in Fig. 6. As the EMF increases, the output wave polarization direction of La:YIG rotates clockwise. It is worth mentioning that the polarization state always maintains a good LP light at 0.3 THz. However, for 0.9 THz, with the increase of EMF, the polarization state becomes an elliptically polarized light. This shows that in the higher THz frequency band, the La:YIG not only has the obvious Faraday rotation effect, but also has the weak circular dichroism effect. In general, this MO thin film shows remarkable MO polarization characteristics actively manipulate by the weak external magnetic field only up to 0.155 T, especially Faraday effect. It is a potential functional material for THz MO polarization converter, nonreciprocal phase shifter and isolator.
Fig. 6. Polarization states of the transmitted THz wave through La:YIG film at (a) 0.3 THz, (b) 0.6 THz and (c) 0.9 THz. The EMF range from 0 to 0.155 T.
Finally, we compared the performances of some MO materials reported in THz band as shown in Table 3. Some semiconductor gyroelectric materials, such as HgTe [10], InSb [8,11], and graphene [24,25], of which cyclotron resonance frequency is just in the THz band when an EMF is applied, shows a very strong Faraday rotation and circular dichroism effects near the cyclotron resonance frequency band. However, these materials often need to operate at low temperature and strong magnetic field, and show strong dispersion. In contrast, the last three MO materials shown in Table 3 (all the YIG materials) can work at room temperature and have a very low dispersion in the broadband frequency range. Our La:YIG show significant advantages compared to the two previously reported YIG. The Verdet Constant of SrFe12O19 is slightly smaller than that of La:YIG, but its absorption coefficient is about four times than that of La:YIG, because it is a polycrystalline material [12]. Tb3Sc2Al3O12 has a lower absorption coefficient, but its Verdet Constant is only <3 °/mm/T, which is much smaller than 100 °/mm/T of La:YIG [13]. Therefore, as a kind of large area, single crystal, thick film, the overall performances of our La:YIG are better than the YIG film previously reported in the THz regime.
Table 3. Comparison of Magneto-Optical Materials in the THz regime.
4. Conclusion
On summary, we fabricated a wafer-scale La:YIG single crystal film on a three-inch GGG substrate by LPE method. The THz optical properties of La:YIG film were demonstrated by THz-TDS system, which shows that a high refractive index of approximately 4.09 and a low absorption coefficient of 10–50 cm−1 from 0.1 to 1.6 THz. Moreover, the THz Faraday rotation effect in longitudinally magnetized La:YIG film was measured by the orthogonal polarization detection in THz-TDS system. With 5 samples stacked together, the Faraday rotation angle can be actively tuned linearly from −15° to 15° with the EMF up to 0.155 T. The Verdet constant of La:YIG is about 100 °/mm/T within the saturation magnetization. This MO single crystal thick film with large area shows low loss, high permittivity and strong MO effect in the THz regime, which will be widely used in MO polarization conversion, nonreciprocal phase shifter and isolator for THz waves.
Funding
National Natural Science Foundation of China (61831012); Science Challenge Project (TZ2018003); International Science and Technology Cooperation Programme (2015DFR50870).
Disclosures
The authors declare no conflicts of interest.
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