Thin films of BixCe3-xFe5O12 with x = 0.7 and 0.8 compositions were prepared by using pulsed laser deposition. We investigated the effects of processing parameters used to fabricate these films by measuring various physical properties such as X-ray diffraction, transmittance, magnetization and Faraday rotation. In this study, we propose a phase diagram which provides a suitable window for the deposition of BixCe3-xFe5O12 epitaxial films. We have also observed a giant Faraday rotation of 1-1.10 degree/µm in our optimized films. The measured Faraday rotation value is 1.6 and 50 times larger than that of CeYIG and YIG respectively. A theoretical model has been proposed for Faraday rotation based on density matrix method and an excellent agreement between experiment and theory is found.
©2012 Optical Society of America
There is a considerable interest in the study of Faraday rotation in garnet thin films at communication wavelengths [1–24]. High transmittance, low optical absorption and high Faraday rotation are key properties that make garnet materials as a suitable candidate for integrated optics [1–4]. It is known that the Faraday rotation in garnet materials is studied using transmission geometry. In this method, the garnet materials are magnetized along the direction of the light propagation and the final output of the light is not similar as the original input; instead it rotates two times the Faraday rotation angle. In double pass geometry, light is reflected from a dielectric mirror behind the film and passes twice through the magneto optical medium . Thus, the property of non reciprocity has an immense technological importance and can be exploited to produce fundamental optical components such as rotators, and isolators [1,2]. Garnet materials with extremely high Faraday rotation are required for the miniaturization of optical isolator devices. Cerium and bismuth substituted iron garnet materials have a wide range of applications including magneto optical devices and magneto photonic crystals [1–20]. The performance of these devices depends strongly on the physical properties of garnets, such as magnetization, transmittance, Verdet constant and Faraday rotation. Magneto optical properties of a garnet material also depend on the preparative conditions which can be controlled or by proper substitution of various lanthanide elements .
Garnet materials that have shown giant Faraday rotation are yttrium iron garnet Y3Fe5O12 (YIG) and bismuth iron garnet Bi3Fe5O12 (BiIG) with 3-5 x103 cm−1 and 8.09°/μm respectively at visible wavelengths (633 nm) . These materials have applications in magneto optical imaging [3–5]. The highest Faraday rotation in visible spectral regimes is obtained in the composite film (BiDy)3(FeGa)5O12:Bi2O3 with values 10°/μm, 2.6°/μm, and 1.9°/μm for wavelengths 532 nm, 635 nm and 670 nm respectively. In this composite film, it has been demonstrated that as the wavelength of incident light increases, the Faraday rotation decreases . Similarly, at the telecommunication wavelength 1.55 µm, the Faraday rotation measured in CeYIG, Co-doped CeO2-δ films, CeFeO3 films, YbIG, Sc doped EuIG, scandium substituted EuIG films were found to be 0.44, 0.60, 0.60 −0.0420, −0.0450 and −0.0500 deg/μm respectively [14, 16, 20]. These materials are employed in the fabrication of communication devices [14–16] but their other potential applications are limited due to high absorption and stoichiometric problems (either lower Bi content or excessive Fe content). In order to shrink the device dimensions further, it is necessary to search for new garnet materials which exhibit a high Faraday rotation. In the fabrication of new garnet materials, it is crucial to study the effect of various process parameters such as the partial pressure of different gases, temperature, laser fluency, repetition rate, and the distance from the target to substrate. All these parameters significantly influence magneto optical properties of these garnet epitaxial films.
Faraday rotation of pure and doped yttrium iron garnet materials depend on the selection of suitable substrates as well as doping of the lanthanide elements. In garnet thin films, the choice of substrate plays a key role in determining the films magneto optical properties (i.e. Faraday rotation) and minimization of losses associated with absorption . Several garnet materials, such as certain lanthanide- doped yttrium iron garnet (YIG) materials, have been proposed to improve Faraday rotation [19–21] at the telecom wavelength 1.55µm. Despite their ability to exhibit a high degree of Faraday rotation, the YIG and other doped materials have severe transmission losses and other compatibility issues with optical integration schemes. The integration of optical isolators and other issues are mentioned in the following.
Optical isolators are bulky and require expensive optics and alignment. Integration of these devices and other non reciprocal devices on a single chip is challenging. The magneto optical materials cannot be implemented as a wave guide core layers on semiconductor wafers due to lower refractive index. Another difficulty arises due to the phase velocity mismatch inherent in the waveguide geometry (structural birefringence). These problems can be minimized by using III-V semiconductor with a non reciprocal and reciprocal mode converter in an asymmetric waveguide, which will avoid mode matching problems . The non reciprocal mode converter is formed from a III-V semiconductor waveguide core with a magneto optic layer as the upper cladding material so that the Faraday rotation occurs through the interaction of the evanescent tail of a guided mode. The phase velocity mismatch due to the waveguide birefringence can be prevented using a quasi-phase-matching approach . However, this solution may complicate the fabrication process.
In another report , it was explained about non linear optical processes in magneto optical devices such as electro-optic modulators where the isolation occurs at specific power levels only . To circumvent this problem, it was reported in the literature  that non reciprocal (complete) isolation can be achieved by spatial and temporal refractive index modulations where photon states can go through interband transitions similar to the electronic transition in semiconductors. Most importantly, this method of modulation has no impact on the backward propagation of light. These structures can absorb incident light traveling in one direction while transmitting light in the opposite direction; in this way the method of isolation is achieved . Recently, this concept was demonstrated on monolithic integration of isolators with a foot length of 290 µm fabricated on a cerium doped yttrium iron garnet material using YIG buffer layer on an SOI platform [24, 25].
Another approach to optical integration which has been intensively explored using waveguide –isolators, which involve nonreciprocal phase shifts as a “blocking” mechanism, have been intensively explored [26–30]. This arrangement usually employed in a Mach-Zehnder interferometer (MZI) configuration with nonreciprocal and reciprocal phase shifters as both active and passive components [26–30]. The waveguide –isolator approach is appealing because it is less sensitive to fabrication errors and there is no need for phase matching between orthogonally polarized modes. To produce an optical isolator with complete isolation, it is necessary to minimize all the problems mentioned above. This requires keeping both the active and passive isolator components on a single platform.
In our investigation, considerable effort has been placed in the development of new magneto optical materials with controlled processing parameters such as temperature and pressure. The aim of this research is to produce new bismuth-cerium iron garnet BixCe3-xFe5O12 films that exhibit higher transmittance and giant Faraday rotation at communication wavelengths. We synthesized several batches of BixCe3-xFe5O12 films on gadolinium and gallium garnet substrates using the pulsed laser deposition. The advantage of using this deposition is the transfer of the target stoichiometry to the film [31–37]. In the fabrication of these films, we investigated the role of processing parameters such as distance between the laser beam and the target, laser fluency, partial pressure of gases, temperature, and choice of substrate. We found that all of the above processing parameters play a prominent role in influencing the degree of Faraday rotation. Furthermore, we proposed a phase diagram for the processing parameters which can be used in the fabrication of these epitaxial thin films. This phase diagram provides detailed knowledge in achieving a giant Faraday rotation in garnet thin films. We show that BixCe3-xFe5O12 epitaxial films can be used to fabricate optical isolators with a dimension of 45µm. This is an important device that can be used to protect from unwanted reflected light that causes noise and instability in the laser system.
2. Experimental results and data analysis
We prepared BixCe3-xFe5O12 material with stoichiometric ratios with x = 0.7 and 0.8 and which were sent to praxair-USA for the preparation of dense-ceramic targets with a material purity of 99.99%. After receiving the right stoichiometry of BixCe3-xFe5O12, target was ablated with a pulsed excimer KrF laser (λ=248 nm) in the pulsed laser deposition chamber. The laser was set with a repetition rate of 20 Hz and focused onto the target. We used a Gd3Ga5O12 substrate in the fabrication of all epitaxial thin films. The choice of this material as a substrate was driven by the need to minimize both the lattice parameter and thermal expansion mismatch to enable epitaxial growth. We took precautions to avoid any strain and cracking in the film that arises due to thermal expansion mismatch between the film and the substrate [3, 6, 10, 11, 14, 21, 22] in order to obtain smooth deposition of these films. To circumvent the misfit dislocations which are caused by lattice parameter mismatch between the film and substrate, which would worsen the film properties [20, 34–36], we chose gadolinium and gallium garnet substrate for the deposition of the BixCe3-xFe5O12 epitaxial films. In the deposition of these epitaxial films, the substrate to film lattice mismatch is about 1.9% which can be calculated from the lattice constants of all these garnets (yttrium iron garnet =12.377Å, Gd3Ga5O12 =12.378Å and Bi3Fe5O12 =12.63 Å). The thermal expansion mismatch is below 10% (thermal expansion constants: yttrium iron garnet = 10.4 x 10−6/°C, Gd3Ga5O12=9.2x 10−6/°C). In addition, this substrate has an excellent transparency and low contribution to the Faraday rotation (0.002deg/μm) [20, 38].
Before the deposition, the substrate was heated to 500°C for thermal cleaning of the surface. For the depositing the films on the substrate background gasses (such as oxygen, argon, and argon + hydrogen) are introduced in the deposition chamber separately. The interaction of the gases with the target produces the molecular species such as cerium and bismuth and further helps in the formation of proper crystalline phase [3, 10, 11, 14, 21, 22]. Introduction of the gases further reduce the kinetic energy of the molecular species (impinging particles) on the substrate and the growing film.
In the deposition of films, we used three gases, namely oxygen, reduced atmosphere and argon and varied the pressure of these gases in the range of (50-500 m.Torr). After film deposition using pulsed laser deposition, the ramping process was completed in three stages. In the first step, the samples were cooled at a rate of 10°C/min until the temperature reached 400°C. In the second stage, the samples were maintained at this temperature for 40 minutes of in situ annealing. In the last stage, the temperature was reduced to room temperature at the same cooling rate as in the first step. We found a deposition rate of 0.25-0.36 nm/sec to achieve 0.9-1 μm thick BixCe3-xFe5O12 epitaxial films.
2.1 Optimization of process parameters in fabricating BixCe3-xFe5O12 epitaxial films
In depositing epitaxial garnet films, we studied the role of substrate temperature and different partial pressure of gases for the formation of epitaxial films. First, we studied the role of the oxygen gas. We varied the pressure of oxygen in the range 50-300 m.torr. The substrate temperature was varied between 680 and 720°C. The X- ray diffraction and energy dispersive X –ray spectroscopy were performed on these films. We only show the experimental details on the X –ray diffraction in Fig. 1 . From these experiments, we found that these films suffer from oxygen deficiency in their stoichiometry and have a multiphase structure. Subsequently we increased the oxygen partial pressure during the deposition of these films, which resulted in structural degradation (multiphase) after 400 m.Torr. Therefore, oxygen pressure is not useful in providing the appropriate stoichiometry and the crystal structure at those partial pressures. In the next step, we studied the effect of reduced atmosphere. The reduced gas consists of Ar + H2 with a ratio of 1:5. The pressure was varied from 100 to 200m.Torr and the substrate temperature varied between 680 and 720°C. The X-ray diffraction results are shown in Fig. 1. Note that there are clearly resolved film and substrate peaks observed at 2θ = 50° and 51° respectively. These peaks represent the crystallographic structure of BixCe3-xFe5O12 phase.
After gradual increase in the partial pressure of reduced atmosphere (Ar + H2), in the range of 200-350 m.Torr and using similar temperatures, we found a cubic structure and high Faraday rotation. Further increase in partial pressures of reduced atmosphere (Ar + H2), resulted in black color samples which exhibited poor transmittance.
Finally, we studied the effect of argon gas and varied the pressure between 200 and 400m.Torr and temperature between 680 and 720°C which is shown in Fig. 1. Here we observed cubic crystal structure with clearly resolved peaks in film and substrate peaks. Figure 2 shows the results of energy dispersive X –ray spectroscopy for argon treated films. Here, we find an optimized region for the deposition of the epitaxial films in the presence of different argon pressure and temperature. Furthermore, in Fig. 2 (a), it was shown that argon between 200 and 375 m.Torr is the appropriate and optimized atomic concentration range to produce higher quality of the BixCe3-xFe5O12 epitaxial films. From energy dispersive X-ray spectroscopy, we confirmed the correct stoichiometry of thesefilms (note that the film composition should conform to the target stoichiometry of bismuth 4%, cerium 11%, iron 25%, and oxygen to be 60% in all the deposited BixCe3-xFe5O12 epitaxial films). We analyzed the target composition CBi/CFe = 0.14, CCe/CFe = 0.46 for both compositions, which is close to the target stoichiometry. We have also compared the stoichiometry of argon treated films where both the compositions and the ratio appeared to be slightly deviating from the target. The values obtained from energy dispersive X –ray spectroscopy for x = 0.7 and x = 0.8 are ~0.50, 0.51 respectively for the argon treatment. This variation in composition is more or less similar for all the BixCe3-xFe5O12 samples. Figure 2(b) shows the actual temperature regions where the high quality BixCe3-xFe5O12 samples are found. In both the conditions (pressure and temperature variation) using argon, enhancement of magneto optical response is exhibited, i.e. transmittance and Faraday rotation. We have also shown the appropriate regions of stoichiometry of BixCe3-xFe5O12 samples and both the compositions have displayed similar trends observed in energy dispersive X-ray spectroscopy. Figure 2(a)-2(b) shows color regions of blue, green, red and white symbols correspond to the constituent elements of bismuth, cerium, iron and oxygen respectively. Also, the vertical lines clearly state the optimized argon pressure and temperature regions (where it points on the x axis) to find the right stoichiometry in BixCe3-xFe5O12 epitaxial films.
To summarize this section, the crystalline state of the film is significantly related with the argon gas pressure used. The argon gas controls the energy of plasma particles, which affect the film growth. Hence, poorly crystallized films resulted from low argon pressures. Therefore, among all the partial pressure of gases, argon is the right choice when depositing garnet epitaxial films. Finally, during the deposition of BixCe3-xFe5O12 epitaxial films, a fluency of 3J/cm2 was maintained. The dense target (6.56 gm/cc) of BixCe3-xFe5O12 was set at a distance of 5.5 cm from the gadolinium gallium garnet (111 orientation) single crystal substrate (dimensions of 10 mm x10 mm x 0.5mm). The phase diagram can be used to produce new BixCe3-xFe5O12 magneto optoelectronic devices, which is one of the interesting discoveries of the paper. Using argon ambient, it was achieved a target stoichiometry (Fig. 2(c)) as well as cube on cube epitaxial relationship in BixCe3-xFe5O12 films and the details are presented in the following section. Further deposition parameters from PLD are given in Table 1 for producing BixCe3-xFe5O12 epitaxial films.
2.2 X-ray diffraction
X-ray diffraction measurements were carried out using Xpert panalytical (Philips) 3373/10 diffractometer attached with a copper Cu-Kα radiation source (with a λ Cu-Kα = 1.54056 Ǻ MRD) operating at 45 kV and 40 mA in a θ-2θ arrangement. Figure 3 shows details of the X- ray diffraction for both out of plane (θ-2θ) and in plane (Φ) patterns of BixCe3-xFe5O12 epitaxial films. We obtained similar diffraction patterns for both the compositions (x = 0.7, 0.8) studied here.
Figure 3 shows crystallographic structure of BixCe3-xFe5O12 epitaxial films. The θ-2θ scan shows only reflections from the planes which are integer multiples of the 111 plane, proving that the film is only (111) oriented in the growth direction.
The broadened XRD (444) film peak and Gd3Ga5O12 substrate peaks (444) are clearly defined with X-ray diffraction measurements. The lattice constants of (111) oriented BixCe3-xFe5O12 epitaxial films were found to be 12.47Å for film and 12.42 Å for GGG. The BixCe3-xFe5O12 epitaxial films and GGG substrate have the full width at half maximum of 0.2 and 0.020 respectively (Fig. 3). In every BixCe3-xFe5O12 film structural analysis, no other crystalline material other than BiCeIG phase was observed. Further to prove cube on cube relationship, we extended our measurements to scan in plane (ϕ-scan) orientation of the samples. Figure 3(a) represents the ϕ-scan of the 640 reflections of the film and gadolinium and gallium garnet substrate. Basically, this analysis gives information about azimuthal orientation of the grains in the film plane. Therefore, the ϕ-scan of the BixCe3-xFe5O12 (640) reflection displays six equally spaced peaks (six-fold symmetry) at the similar angles for the film and the substrate, suggesting that the film is epitaxial and properly oriented in the substrate plane. This was also confirmed with other in plane orientations such as (642) and (420) which were performed on these films to ensure their structural symmetry. From Fig. 3, it is clear that these films crystallize in a cubic –pervoskite type structure. The structures of these BixCe3-xFe5O12 materials depend on the magnetic anisotropy and magnetization of the material, the sample shape, defects, the temperature, surface treatment, and the history of the sample . Bismuth was used to enhance the lattice constant of the films over that of the gadolinium and gallium garnet substrate so that films were in compression state as evident from X-ray diffraction measurements. After verifying the structure in these compositions, it is important to determine the passage of light through these samples by studying the transmittance measurements.
The transmittance spectrums of BixCe3-xFe5O12 epitaxial films were obtained using ultraviolet-visible spectrophotometer in the range of 190-2000 nm with a resolution wavelength of 1nm. Figure 4 shows the transmittance spectrum as a function of the wavelength for garnet epitaxial films. We measured the transmittance as a function of wavelength at an argon partial pressure of 300 m.Torr. We observed the transmittance up to 62% for x = 0.7 and 80% for x = 0.8 epitaxial films. The increased transmittance for x = 0.8 composition may be attributed to the importance of processing parameters especially temperature and partial pressure of argon. Using other partial pressures (oxygen and reduced atmosphere) for the deposition of films, we found a decreased transmittance due to porosity that may affect the propagation of light due to scattering. We have also observed slightly lower Faraday rotation in x = 0.7 composition in comparison with the x = 0.8 composition. The oscillation in Fig. 4 (a) are attribute to theelectron transitions from 5d excited level to the 4f ground state of Ce3+ (2F5/2, 2F7/2) . The absorption edge for both of the compositions is observed between 370 and 420 nm. Furthermore, absorption decreases with an increase in transmittance at infrared wavelengths (>1600 nm) and garnet materials become fully transparent.
2.4 Morphology and topographical studies
The scanning electron microscope (SEM) images were obtained with JEOL-JSM, for BixCe3-xFe5O12 epitaxial films. The SEM is used for viewing topological (surface), morphological (bulk-structure) and grain distribution at high magnifications. The accelerating voltage was varied from 0.2 to 5 KV in 0.1 increments and from 5 to 30 kV in 1 kV increments. The basic SEM is connected to an energy dispersive X-ray analysis unit, which displays the characteristic X-ray spectrum. The images were collected on both the compositions and are displayed in Fig. 5 . To measure the surface roughness of the films Atomic Force Microscope (AFM) was employed using a Veeco enviroscope equipped with Co/Cr coated cantilevers (NSC 36) from MicroMasch. We employed thetapping mode to collect images of the surface topography. In this mode, the cantilever oscillation amplitude of the AFM is kept constant by a feedback loop. When the tip attached to the cantilever passes over a surface of the sample, the cantilever oscillates at its resonance. The amplitude of the cantilever tends to change according to the surface features. Finally, these amplitude variations are used to identify the surface profile (imaging). Figure. 5 show details on SEM and AFM topography of BixCe3-xFe5O12 epitaxial films.
We measured the thickness of the BixCe3-xFe5O12 epitaxial films from the cross sectional SEM image and stylus profilometer. From the cross sectional image, we found a thickness of 1 μm for the BixCe3-xFe5O12 films and this thickness is in agreement with the one measured from profilometer within the error of ± 0.5%. We also measured the thickness of the films from ellipsometric data for all these garnet films and found similar agreement when in comparison with the above measurements. The grain distribution was found to be dense without any cracks observed from SEM images, as shown in Fig. 5(b). The topographic nature of BixCe3-xFe5O12 epitaxial films are shown in AFM Figs. 5(c)-5(e). From these measurements, we found that the lateral dimension of the grain varies from 110 to 200 nm for films deposited at temperatures 690-700°C. We evaluated the root mean square (rms) surface roughness for all films over areas of 2 x 2μm2 from the AFM measurements. These values are in the range of 1.3-2.6 nm. The dimensions and topographic features are similar in all the films studied. The Faraday rotation is strongly influenced by the film topography due to surface roughness. The decrease in roughness parameter relates to the improvement with the film epitaxy which is also supported by X-ray diffraction observation.
Furthermore, lower roughness values are useful (Table 2 ) in waveguide fabrication. As we increased film thickness we did not observe any increase in the roughness of these films. There was no drastic increase in these values due to change in partial pressure of gases. The physical parameters extracted from PLD, profilometer, EDX, AFM, and Faraday rotation measurements are displayed in Table 2.
The magnetization measurements of the samples were made using Superconducting Quantum Interference Device (SQUID). The system employs a probe located in a helium gas exchange cryostat for measuring the field dependence of magnetization. The system is equipped with a DC magnet for fields up to 50 Gauss. The cryostat is surrounded by a µ-metal shield, which keeps the remnant field up to 20 milli-Guass. Figure 6 displays magnetization behaviour of the BixCe3-xFe5O12 epitaxial films. The magnetic field was applied in the film plane. Both the electron spin and the orbital angular momentum contribute to the magnetization which leads to a positive susceptibility. To obtain the exact magnetic susceptibility of the film, the substrate paramagnetic susceptibility has been removed . After correcting the magnetization data, the obtained spectra for
BixCe3-xFe5O12 epitaxial films from SQUID consist of paramagnetic type transition. In these measurements; we did not observe any loop in the BixCe3-xFe5O12 spectrums that show a clear signature of paramagnetic type transition. Another evidence for paramagnetism is shown in the inset of Fig. 6(b), where the variation of inverse susceptibility with temperature follows a Curie-Weiss law with a linear dependence in a broad temperature range. It is also known that yttrium iron garnet has a ferrimagnetic structure with Curie temperature of 500-600 K . In pure yttrium iron garnet at a specific substitution level, both the tetrahedral and octahedral sublattices are equivalent and they compensate each other. Hence, in this case magnetization is one of the dodecahedral substituting ion/ions . Similarly, magnetization spectra were obtained for BixCe3-xFe5O12 epitaxial films with other treatments and compositions using argon, implying that these samples were displaying paramagnetic type in the entire temperature range studied. These results are very promising for developing a magneto optical device. Further processing features identified in this investigation are presented in the following section.
2.6 Phase diagram
In this section, we summarize the results presented in the previous sections. Figure 7 shows a phase diagram for the processing parameters of the BixCe3-xFe5O12 epitaxial films, and the optimized Faraday rotation region is displayed. In the dotted region between 400 and 500 m.Torr (irrespective of temperature used), we observed a poor transparency. In this region, we could not measure any optical properties due to light scattering. The dotted and dashed region between 500 and 600°C and 790-850°C represents unsuitable crystallographic areas (irrespective of partial pressures used in the deposition of these garnet films) and compositions. In these regions, the transmittance and Faraday rotation measured is weak. In the region of substrate temperature between 600 and 620°C and partial pressures between from 200 to 350 m.Torr, we found a weak magneto optic response. Similarly, in other regions of the phase diagram, between 725 and 790°C (partial pressures between 200 and 350m.Torr) we found a poor Faraday rotation. This is because of the multiphase as evident from XRD, which may be attributed to the differences in oxygen impurities and vacancies. Apparently, we also found depositing above the optimized temperature (750°C) results in an excessive vaporization of the volatile constituents, especially Bi elements substitution in iron garnet materials. After, optimization in argon we reached a near stoichiometry of the elements present in the target. This is evident from energy dispersive X – ray analysis.
In this study the repeated measurements are very important to know the overall magneto optical response of the films and to determine the optimized window for several physical properties associated in achieving a giant Faraday rotation. The phase diagramclearly explains the efforts in producing excellent epitaxial BixCe3-xFe5O12 films with a narrow window (rectangle-region) of deposition. We also confirmed that argon pressure between 200 and 375 m.Torr and the temperature 690-720°C is the main influencing parameters in depositing these epitaxial films on GGG substrates.
2.7 Faraday rotation
We designed an optical setup with the magnet supplied by GMW-USA for measuring Faraday rotation @ 1.55 µm wavelengths. The sample was placed between the two poles of an electromagnet and an optical beam from a laser diode, with wavelength λ= 1550 nm was transmitted through the sample, parallel to the magnetic field axis. In our experiments, a quarter wave plate and a polarizer facilitated the scan of all the possible input linear polarization states. A polarizing beam splitter was used to collect the sample output intensities of the two polarization components, parallel (p-component) and orthogonal (s-component) to the propagation plane. The differential signal, chopped at 1.5 kHz, is obtained from two photodiodes connected to the Lock-in amplifier. When a magnetic field is applied, a polarization rotation is induced in the magneto optical material and the powers of the ‘s’ and ‘p’ components are different resulting in a “nonzero” differential signal recorded by the lock-in amplifier.
The differential arrangement has been chosen because it allows for a 3dB signal to noise ratio increment with respect to the one-channel detection. In this experiment, Lock-in integration times exceeding 1000 chopping cycle periods were adopted to remove the background noise.
Figure 8 shows the Faraday rotation measurements on our 1μm BixCe3-xFe5O12 thick sample and the rotation 1.00 & 1.10 degree/µm has been recorded together with a saturation field of 0.5 Tesla. Note that these values are 1.6 times higher than the existing cerium doped yttrium iron garnet and 50 times higher than pure yttrium iron garnet materials.
In the following, we present a theory on Faraday rotation using the density matrix method  to correlate with experiment. It is considered that the BixCe3-xFe5O12 sample contains N (number density) per unit volume, and an external laser field with frequency and amplitude is propagating in the sample. Note that the garnet material considered here exhibits paramagnetic behavior. Therefore, the electronic transitions which are responsible for the Faraday rotation in the presence of magnetic field B, denoted as and [2, 6]. The energy levels and are denoted as and respectively. The levels for states and have energies and respectively. The energy difference between and is = (ħeB)/m* where, e and m* are the charge and the effective mass of the charge carriers, respectively.
The Faraday rotation is defined as,2]. The refractive index is related to the susceptibility () as. Replacing the refractive index by the susceptibility in Eq. (1), we have
Expressions for susceptibility can be written in terms of the density matrix element as
Using density matrix method for the three level model given in the inset of Fig. 8 and using Eqs. (1-2), we obtained the following expression for the Faraday rotation after rigorous mathematical treatment:
Numerical calculations were performed for the Faraday rotation using Eq. (3) with MAPLE software. The parameters appearing in this theory are taken from reference . Only the optimal parameter N was used in fitting, since we do not know the N (number density) of the present materials. The numerical calculations are plotted in Fig. 8 along with experimental data. Note we find an excellent agreement between theory and experiment. Based on our extensive characterization of these epitaxial films, we believe that the major contribution to the Faraday rotation enhancement comes from an increase in the concentration of Ce3+ induced by the substitution of Bi3+. Detailed calculations on Monte-Carlo methods using X-ray photoelectron spectroscopy are in progress.
In summary, we successfully prepared high quality epitaxial films of BixCe3-xFe5O12 using pulsed laser deposition. The quality of the deposited films were optimized using various laser growth parameters, including different partial pressure conditions and gases such as oxygen, argon, intermixing of argon, and hydrogen. It was found that high quality epitaxial films could be produced only in an argon pressure. The crystalline state of the film is significantly related to the argon gas used, since the latter controls the energy of the plasma particles. Furthermore, we have constructed a phase diagram which shows the appropriate window of deposition for fabricating superior quality BixCe3-xFe5O12 epitaxial films which give a giant Faraday rotation. In addition, AFM images show a lower roughness values (about 1.3-1.6 nm) for the BixCe3-xFe5O12 samples treated in argon. The measurements are reproducible under the growth conditions mentioned. We have correlated the experimentally measured Faraday rotation with theory and find an excellent agreement. The films exhibit a Faraday rotation of ~1.10 degree/µm (104 degree/cm) at @1.55 µm. The measured value is 1.6 times and 50 times higher than that of CeYIG and pure YIG garnets respectively, which is higher than the Faraday rotation reported so far for garnet materials at the telecommunication wavelength. The BixCe3-xFe5O12 thin films can be utilized as a potential candidate for a new generation of integrated optics. Our method of processing can produce cost effective and reliable magneto-optoelectronic devices with smaller dimensions.
MCS thanks the Institute de la National Recherché Scientifique, QC for using some of the facilities. Thanks to Stefan Lauroche, Ecole de Polytechnique, QC for useful discussions on transmittance measurements. Authors thank Joel Cox for editing the manuscript. Also, MCS thanks, Brain Richter GMW –Associates USA for valuable tips to setup the magneto optical measurements.
References and links
1. M. Levy, “The on-chip integration of magnetooptic waveguide isolators,” IEEE J. Sel. Top. Quantum Electron. 8(6), 1300–1306 (2002). [CrossRef]
2. A. K. Zvezdin and V. A. Kotov, Modern magneto-optics and magneto optical materials, (IOP publishing, Bristol, 1997).
3. S. Kahl, S. I. Khartsev, A. M. Grishin, K. Kawano, G. Kong, R. A. Chakalov, and J. S. Abell, “Structure, microstructure, and magneto-optical properties of laser deposited Bi3Fe5O12/Gd3Ga5O12 (111) films,” J. Appl. Phys. 91(12), 9556–9560 (2002). [CrossRef]
4. Z. C. Xu, “Magnetooptic caracteristiques of BiTbGaIG film/TbYbBiIG bulk crystal composite structure in 1550 nm band,” Appl. Phys. Lett. 89(3), 032501 (2006). [CrossRef]
5. R. G. David, Fiber Optic Reference Guide, 3rd ed. (Boston Focal Press, 2002), p. 5.
6. G. B. Scott and D. E. Lacklison, “Magnetooptic properties and applications of bismuth substituted iron garnets,” IEEE Trans. Magn. 12(4), 292–311 (1976). [CrossRef]
7. T. Okuda, N. Koshizuka, K. Hayashi, T. Takahashi, H. Kotani, and H. Yamamoto, “Epitaxial growth of Bi-substituted yttrium iron garnet films by ion beam sputtering,” Advances in magneto-optics, Proceedings. Int. Symp. Magneto-optics, J. Magn. Soc. Jpn. 11, Supplement S1, 179–182 (1987).
8. B. Teggart, R. Atkinson, and I. W. Salter, “Enhancement of the polar Kerr effect in bismuth-substituted DyGa iron garnet thin films,” J. Phys. D Appl. Phys. 31(19), 2442–2446 (1998). [CrossRef]
9. M. Inoue, K. Arai, T. Fuji, and M. Abe, “One-dimensional magneto photonic crystals,” J. Appl. Phys. 85(8), 5768–5770 (1999). [CrossRef]
10. Y. H. Kim, J. S. Kim, S. I. Kim, and M. Levy, “Epitaxial growth and properties of Bi-substituted yttrium-iron garnet films grown on (111) gadolinium-gallium-garnet substrates by using rf magnetron sputtering,” J. Korean Phys. Soc. 43(3), 400–405 (2003).
11. S. I. Khartsev and A. M. Grishin, “[Bi3Fe5O12/Gd3Ga5O12] magneto-optical photonic crystals,” Appl. Phys. Lett. 87(12), 122504 (2005). [CrossRef]
12. R. Lux, A. Heinrich, S. Leitenmeier, T. Korner, M. Herbort, and B. Stritzker, “Pulsed-laser deposition and growth studies of Bi3Fe5O12 thin films,” J. Appl. Phys. 100(11), 113511 (2006). [CrossRef]
13. M. Vasiliev, K. E. Alameh, V. A. Kotov, and Y. T. Lee, “ Nanostructured engineered materials with high magneto-optic performance for integrated photonics applications,” in Proceedings. IEEE Photonics Global @Singapore, (IPGC 2008).
14. T. Shintaku, A. Tate, and S. Mino, “Ce-substituted yttrium iron garnet films prepared on Gd3Sc2Ga3O12 garnet substrates by sputter epitaxy,” Appl. Phys. Lett. 71(12), 1640–1642 (1997). [CrossRef]
15. L. Bi, H. S. Kim, G. F. Dionne, S. A. Speakman, D. Bono, and C. A. Ross, “Structural, magnetic, and magneto-optical properties of Co-doped CeO2-δ films,” J. Appl. Phys. 103(7), 07D138 (2008). [CrossRef]
16. M. Bolduc, A. R. Taussig, A. Rajamani, G. F. Dionne, and C. A. Ross, “Magnetism and magneto optical effects in Ce-Fe Oxides,” IEEE. Trans. Mag. 42(10), 3093–3095 (2006). [CrossRef]
17. D. C. Hutchings, “Prospects for the implementation of magneto-optic elements in optoelectronic integrated circuits: a personal perspective,” J. Phys. D. 36(18), 2222–2229 (2003). [CrossRef]
18. T. Körner, A. Heinrich, M. Weckerle, P. Roocks, and B. Strizker, “Integration of magneto-optical active bismuth iron garnet on nongarnet substrates,” J. Appl. Phys. 103(7), 07B337 (2008). [CrossRef]
19. J. Ostorero and M. Guillot, “Magneto-optical properties of Sc-substituted dysprosium iron garnet single crystals,” J. Appl. Phys. 91(10), 7296–7298 (2002). [CrossRef]
20. M. Chandra Sekhar, J. Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett. 94(18), 181916 (2009). [CrossRef]
21. J. Y. Hwang, R. Morandotti, and A. Pignolet, “Strong Faraday rotation in Ce and Bi comodified epitaxial iron garnet films: valence control through strain engineering,” Appl. Phys. Lett. 99(5), 051916 (2011). [CrossRef]
22. B. M. Holmes and D. C. Hutchings, “Demonstration of quasi-phase-matched nonreciprocal polarization rotation in III-V semiconductor waveguides incorporating magneto-optic upper claddings,” Appl. Phys. Lett. 88(6), 061116 (2006). [CrossRef]
23. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009). [CrossRef]
24. L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011). [CrossRef]
25. J. Fujita, M. Levy, R. M. Osgood Jr, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76(16), 2158 (2000). [CrossRef]
26. T. Mizumoto, K. Oochi, T. Harada, and Y. Naito, “Measurement of optical nonreciprocal phase shift in a Bi-substituted Gd3Fe5O12 film and application to waveguide-type optical circulator,” J. Lightwave Technol. 4(3), 347–352 (1986). [CrossRef]
27. H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, P. Hertel, and A. F. Popkov, “Application of magneto-optical waveguides in integrated optics,” J. Opt. Soc. Am. B 22, 240–253 (2005). [CrossRef]
28. H. Y. Wong, W. K. Tan, A. C. Bryce, J. H. Marsh, J. M. Arnold, A. Krysa, and M. Sorel, “Current injection tunable monolithically integrated InGaAs-InAlGaAs asymmetric Mach-Zehnder interferometer using quantum well intermixing,” IEEE Photon. Technol. Lett. 17(8), 1677–1679 (2005). [CrossRef]
29. H. Yokoi, T. Mizumoto, N. Shinjo, N. Futakuchi, and Y. Nakano, “Demonstration of an optical isolator, with a semiconductor guiding layer that was obtained by use of a nonreciprocal phase shift,” Appl. Opt. 39(33), 6158–6164 (2000). [CrossRef] [PubMed]
30. Y. Shoji, T. Mizumoto, H. Yokoi, I. W. Hsieh, and R. M. Osgood Jr., “Magneto optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett. 92(7), 071117 (2008). [CrossRef]
31. D. B. Chrisey and G. K. Hubler, Pulsed Laser Deposition of thin films (Wiley Interscience, 1994).
32. A. Ohtomo and A. Tsukazaki, “Pulsed laser deposition of thin films superlattices based on ZnO,” Semicond. Sci. Technol. 20(4), S1–S12 (2005). [CrossRef]
33. R. Eason, Pulsed Laser Deposition of Thin Films: Applications-led Growth of Functional Materials, (John Wiley & Sons, Inc, 2007), Chap. 1.
34. M. Chandrasekhar, “Structural and dielectric properties of Ba0.5Sr0.5TiO3 thin films grown on LAO with homo-epitaxial layer for tunable applications,” Int. J. Mod. Phys. B 18(15), 2153–2168 (2004). [CrossRef]
35. M. Zaezjev, M. Chandrasekhar, M. Ferrera, L. Razzari, B. Holmes, M. Sorel, D. Hutchings, A. Pignolet, and R. Morandotti, “Crystallization of yttrium –iron garnet (YIG) in thin films: nucleation and growth aspect” in Proceedings of Materials and Hyperintegration Challenges in Next-Generation Interconnect technology, MRS proceedings (2007), 1036–M04–19.
36. M. Zaezjev, M. Chandrasekhar, M. Ferrera, L. Razzari, A. Pignolet, R. Morandotti, B. Holmes, M. Sorel, and D. Hutchings, “Effect of the Foreign Phases on the crystallization and Growth of Magnetooptic garnet Films, in conference on Lasers and Electro-Optics/Quantum Electronics and Laser science Conference and Photonic Applications Systems Technologies, OSA technical digest (CD) (Optical Society of America, 2008) paper CThM5.
37. W. K. Lee, H. Y. Wong, K. Y. Chan, T. K. Yong, S. S. Yap, and T. Y. Tou, “Effects of laser fluence on the structural properties of pulsed laser deposited ruthenium thin films” Appl. Phys. A. Mater. Sci. Process. 100(2), 561–568 (2010). [CrossRef]
38. S. Kang, S. Yin, V. Adyam, Q. Li, and Y. Zhu, “Bi3Fe4Ga1O12 Garnet properties and its application to ultrafast switching in the visible spectrum,” IEEE Trans. Magn. 43(9), 3656–3660 (2007). [CrossRef]
39. S. Geller and M. A. Gilleo, “The crystal structure and ferrimagnetism of yttrium–iron garnet Y3Fe2(FeO4)3,” J. Phys. Chem. Solids 3(1–2), 30–36 (1957). [CrossRef]
40. M. O. Scully and M. S. Zubary, Quantum optics, (Cambridge University Press, 1997).