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High optical quality LiREF4 (RE = Tb3+, Dy3+, Ho3+, Er3+ and Yb3+), PrF3 and CeF3 single crystals have been grown by the Czochralski technique. Their magneto-optical properties have been measured and analyzed in detail in the ultraviolet-visible wavelength region, and their figures of merit as Faraday rotators have been determined. CeF3 presents superior properties above 300 nm, showing a figure of merit higher than that of the reference material, terbium-gallium-garnet, which is nowadays used in the visible-near infrared. PrF3 is the best rotator for the 220-300 nm range. Towards shorter wavelength and in the vacuum ultraviolet, it is shown that the LiREF4 crystals are unique rotators. Overall, the rare-earth fluoride single crystals studied here exhibit better properties than other materials considered so far, and therefore they have potential to cover the increasing demand for new and improved Faraday rotators in the ultraviolet-visible wavelength region.
©2012 Optical Society of America
1. Introduction
The Faraday rotation is one of the most important magneto-optical properties of materials due to its broad applications field. Since its discovery over hundred years ago, it has been widely utilized for sensors of electrical current and magnetic fields, beam splitters, optical modulators, optical isolators, etc [1]. The principle behind is the single rotation sense of the polarization plane of light, independently of the propagation direction of the light. A Faraday rotator (FR) can be a single crystal, a glass, a liquid or even a gas, placed inside a magnetic field. The angle of rotation θ is known to depend linearly on the magnetic flux density B, the length L of the FR, and the material dependent Verdet constant (V), i.e. θ = V∫BdL. FRs are mainly used as optical isolators in laser systems, guarantying an unidirectional light propagation. Here, the elimination of backreflections is very important for the performance and lifetime of the lasers. The main use is in the infrared (IR), for optical telecommunications at 1310 and 1550 nm [2] and for high-power fiber-laser machinery at 1080 nm. For the former application yttrium-iron-garnet (YIG), Y3Fe5O12, is used as FR, since it exhibits a high transparency above 1100 nm and an exceptionally high V value. For shorter wavelengths terbium-gallium-garnet (TGG), Tb3Ga5O12, is utilized. However, TGG presents technological disadvantages such as difficult and high-cost growth, as well as two physical drawbacks: increasing absorption losses in the visible (VIS), and an absorption edge at long wavelength, 400 nm [3]. This lack of high quality FRs in the VIS, together with the increasing use of VIS solid-state lasers and laser-diodes, as well as excimer lasers in the ultraviolet (UV), has led to an enhanced need to develop and supply new FRs for these wavelength regions.
The FR properties of UV-VIS transparent materials have been investigated since long. At the beginning the aim was to characterize common liquids and solids such as water [4], quartz [5,6], diamond, NaCl, etc [7]. In accordance with their diamagnetic character, these show quite small V values. Subsequently, the focus of attention was shifted to the rare-earth (RE) paramagnetic ions, mainly Ce, Tb, Dy and Pr doped oxide, fluoride and oxyfluoride glasses [8]. The V constant was found to correlate linearly with the RE concentration (NRE), but unfortunately (a) the NRE was critically constricted by the composition range for glass formation [9–11], and (b) the increase in V with the NRE is counteracted by enhanced absorption losses [12]. Further, the glasses exhibit an increasing absorption in the near UV region, with cutoffs around 300 nm [12,13]. RE-doped borate and phosphate glasses have been investigated for shorter wavelengths (>250 nm), however, these present a relatively high absorption coefficient α in this region [9,12]. Aiming at more transparent UV FRs, KH2PO4 (KDP) and its isomorphs single crystals with tetragonal symmetry have been investigated [14,15]. These are classified in two families, the phosphate (KDP, ADP, DKDP, etc) and the arsenates (ADA, KDA, and DKDA). The phosphates exhibit a wider transparency range (>180 nm) than the arsenates (>260 nm), however, their V values are almost half. KDP-isomorphs have higher V values than water or quartz, but they are hygroscopic and soft, so that they can neither be polished to high optical grade flatness nor coated with anti-reflection layers. Overall, materials investigated until now for UV-VIS FR applications present critical drawbacks from the physical (low V, high α, long cutoff) and/or chemical (low NRE, hygroscopicity, etc.) points of view.
The objective of our recent investigations has been to identify and characterize FR single crystals with a high V constant and a high transparency in the UV and VIS wavelength regions. From the technological view point, crystals that can be reproducibly grown and processed to high optical quality FRs have been considered. For this purpose our efforts have centered on fluoride single crystals with high concentration of efficient paramagnetic RE ions, i.e. Ce, Pr, Tb, Dy, Ho and Er, as well as the diamagnetic Yb ion. Fluorides are well known to exhibit wider transparency in the UV-IR than oxides. The highest NRE is achieved with RE-trifluorides. CeF3, PrF3, TbF3, DyF3, and HoF3 can be grown from the melt without undergoing any structural phase transition upon cooling to room temperature. The former two belong to the hexagonal system (tysonite), and therefore they are optically uniaxial. We have reported their V constant dispersions previously [16]. On the contrary, the latter three have been disregarded. Their crystalline structure is orthorhombic, and therefore they are optically biaxial. Consequently, the determination of the direction and temperature dependence of the optical axes is unpractical. We have also studied the FR properties of mixed crystals, Tb0.81Ca0.19F2.81 and Tb0.76Sr0.24F2.76 [17]. These have the same hexagonal structure as tysonite trifluorides. They are transparent in the VIS region, and due to the high Tb concentration they possess a V comparable to that of TGG.
In the present work, we focus on the further analysis of CeF3 and PrF3, as well as a new family of FRs, namely the binary LiREF4 (RE = Tb, Dy, Ho, Er, and Yb). This series is also uniaxial and possess a high NRE. As it will be seen below, some of them are transparent from the vacuum UV (VUV). High quality single crystals were grown by the Czochraski (Cz) technique. By means of transmittance and reflectance spectra the absorption coefficient was determined. The measured V constant dispersion was theoretically evaluated in terms of the effective magnetic moment, the transition probability and its wavelength. The potential as VUV-VIS FR of each compound was estimated with the figure of merit.
2. Experimental
All the fluoride compounds studied have been grown by the Cz technique using a resistive or a RF-heating furnace. The compounds of the LiREF4 series, except LiYbF4, undergo a peritectic reaction at temperatures about 1100 K [18]. LiYbF4, CeF3 and PrF3 melt congruently. The latter two have about 600 K higher melting points, at 1709 and 1674 K, respectively [19,20]. Taking into account the binary phase diagrams, REF3 and LiF were mixed to obtain following NRE in the melt: 37 mol% TbF3, 37.5 mol% DyF3, 36 mol% HoF3; 46 mol% ErF3 and 46 mol% YbF3. The powders (<99.99%) were loaded into a Pt-crucible, where they were subjected to a fluorination process. After that crystal growth was carried out under high purity CF4 (99.99%) atmosphere to effectively eliminate oxygen traces from the chamber. Single crystals were pulled using a-oriented LiYF4 seeds in the case of the LiREF4. CeF3 and PrF3 single crystals were grown using CeF3 seeds [21]. The rotation and pulling rates were fixed at 10 rpm and 1 mm/h, respectively.
LiREF4 compounds crystallize in the sheelite (CaWO4) structure, with tetragonal symmetry and space group I41/a [22]. CeF3 and PrF3 belong to the hexagonal system with space group P-3c1. All these compounds are optically uniaxial. In order to avoid birefringence in the magneto-optical measurements, crystals have been oriented along the optical axis, which is coincident with the crystallographic c-axis. Crystals were oriented by means of Back-Reflection Laue method using a Rigaku Geigerflex equipped with a tungsten-target as a radiation source. The acceleration voltage and current were set to 30 kV and 20 mA, respectively.
Transmittance spectra were measured in three ranges with different spectrometers: VUV (130-380 nm) with a Hitachi U-7000, UV-IR (200-2500 nm) with a PerkinElmer Lambda 900, and mid-IR (2.5-15 μm) with a PerkinElmer Spectrum One FT/IR. Additionally, reflectance spectra were obtained with a Jasco V570 spectrometer in the UV-IR (220-1500 nm). The ordinary no and extraordinary ne refractive indices were determined by the total reflection method using a glass prism at selected wavelengths: 440, 633, 1064 and 1545 nm. TE-mode (s-polarization) was used to measure no, TM-mode (p-polarization) for ne. FR measurements were performed on c-oriented bar-samples with fine polished front and rear sides. The length of the bars was 10, 15 or 20 mm, and a 10 mm TGG sample (Furuuchi Chemical Corp.) was used for comparison and calibration. Permanent magnets in Halbach configuration were utilized to achieve a large magnetic field, with a peak maximum over 2 T. The bars were placed in this magnetic field between two polarizers. As the magnetic field was not homogeneous, the calibration was done carefully, using equal size samples placed in the same position inside the magnet. The first approach was to introduce this setup inside the PerkinElmer spectrometer and measure the transmittance with the polarizers in parallel configuration. The wavelengths at which minima and maxima are observed correspond to 90 and 180 degrees rotations and their multiples (only odd in the case of minima), respectively. Additional data points were measured at particular wavelengths in the VIS (Xe-lamp plus monochromator) and in the UV (248 nm from a KrF excimer laser and 193 nm from a solid-state laser). For this purpose the rotation angle of the second polarizer respect to the first one to get a maximum light intensity was recorded. All measurements were performed at room temperature.
3. Results and discussion
The series of single crystals grown in this work is shown in Fig. 1 . As can be seen, the 10 mm long samples are transparent and homogeneous, exhibiting the typical coloration of the corresponding RE ion: Pr-green, Dy-yellow, Ho-red, and Er-pink. In the case of Ce, Tb, and Yb the crystals are colorless. All the samples are scattering free, indicating a high crystalline quality. Further, they are stable under ambient atmosphere and optical grade polishing can be carried out without any difficulty.
Fig. 1 Grown RE fluoride single crystals, from left to right: CeF3, PrF3, LiTbF4, LiDyF4, LiHoF4, LiErF4, and LiYbF4 (10 mm long, with front and rear fine polished sides).
Transmittance of CeF3, PrF3 and LiREF4 crystals from VUV to mid-IR is shown in Fig. 2(a) . As mentioned above, in comparison with oxides, fluorides exhibit extended transparency regions in the UV and IR. The mid-IR cutoffs of CeF3 and PrF3 lie at about 12 μm, while the LiREF4 cutoffs at about 10 μm. On the opposite side, LiYbF4 has the shortest cutoff at 158 nm, and CeF3 the longest at 282 nm. CeF3 and LiYbF4 (with 1 and 13 4f electrons, respectively) are the most transparent in the whole wavelength region, with a single absorption band in the IR. Instead, other compounds exhibit a rich collect of 4f-4f absorption lines, which confer the characteristic colors of these crystals. These electronic transitions are known [23,24] and will not be further discussed within the scope of this study.
Fig. 2 (a) UV-VIS-mid IR transmittance spectra of CeF3, PrF3, and LiREF4 single crystals without antireflection coating. (b) Measured and calculated reflectance spectra of LiErF4. (c) Schematic of the total reflectance R, approximated as the first reflections on the front and rear sides of a sample. Even though the arrows are drawn obliquely, a normal incident light is assumed.
Measured ordinary no and extraordinary ne refractive indices are given in Table 1 . CeF3 and PrF3 are negative uniaxial (no>ne), while the LiREF4 is positive uniaxial (ne>no). The wavelength dispersion of both indices was estimated by fitting the measured data to the standard Sellmeier equation:
whereas λ is the wavelength, and A, B, C, and D are the Sellmeier coefficients. The obtained coefficients are summarized in Table 2 . These have been used to estimate the reflectance of the LiREF4 series in the VUV wavelength region since this part of the spectra could not be measured with the available equipments. Taking into account that (a) on the c-plane the reflection of normal incident light is given by R0 = (no-1)2/(no + 1)2, calculated from Sellmeier equation, and (b) that the total reflectance rises in a good approximation from the first reflection at the front and back surfaces, the reflectance R can be estimated as R = R0 + (1-R0)2R0T2internal (see Fig. 2 (c)). The internal transmittance (Tinternal≈F´Tmeasured) was adjusted by the factor F, so that the calculated reflectance was coincident with the measured one in the UV-VIS range, which was about 7%. As an example, the measured and estimated reflectance spectra of LiErF4 are plotted in Fig. 2(b). In this way the missing reflectance in the VUV wavelength region could be extrapolated and the absorption coefficient calculated.
Table 1. Measured ordinary (no) and extraordinary (ne) refractive indices of CeF3, PrF3 and LiREF4 single crystals
Table 2. Sellmeier coefficients for the ordinary (no) and extraordinary (ne) refractive indices of CeF3, PrF3 and LiREF4 according to Eq. (1).
The FR of paramagnetic RE ions has been described by van Vleck-Hebb [25]. From quantum-mechanical considerations they deduced that the V constant dispersion is directly proportional to the magnetic susceptibility χ as follows:
whereas ν is the frequency of the incident light, νij is the transition frequency between electronic states, Cij is the transition probability of this, g is the Landé factor, μB is the Bohr magneton, c is the velocity of light, and h is the Planck constant. The considered RE ions obey very well Curie’s law, and therefore the magnetic susceptibility is estimated as [26]whereas NRE is the concentration of the RE ion, μo is the vacuum permeability (equal to 1 in CGS system), J is the angular momentum quantum number, p = g[J(J + 1)]1/2 is the effective number of Bohr magnetons, κB is the Boltzmann constant, T is the temperature, and TC the paramagnetic Curie temperature. As TC is much smaller than the room temperature of our experiments, the term Tc is negligible.The experimental data are described by a single electronic transition, and the V constant dispersion is given as a function of the wavelength λ in simplified form as:
whereas E includes all the constant terms, and λo is the transition wavelength, which is associated with the 4fn-4fn-15d electronic transition.An example of the FR measurements carried out with the transmittance spectrometer is given in Fig. 3(a) for the CeF3 case. First transmittance minimum in the IR corresponds to a 90 degrees rotation of the polarization plane. Towards shorter wavelengths maxima and minima are observed every further 90 degrees rotation. These measured points are plotted in Fig. 3(b) as inverse rotation versus wavelength square and fitted by a linear regression. The notable agreement between fit and experimental data indicates the validity of Eq. (2) to evaluate the FR measurements. In analogous way the rotation of other compounds were determined and subsequently calibrated with the TGG reference sample.
Fig. 3 FR measurements performed on a 20 mm long CeF3 sample. (a) Transmittance spectrum showing minima and maxima. (b) Inverse of measured minima and maxima rotation angles as a function of the wavelength square. The measured points are very well fitted by a single transition.
The VUV-VIS V constant dispersion of CeF3, PrF3, and the LiREF4 series is displayed in Fig. 4(a) . All compounds are paramagnetic except LiYbF4, which is diamagnetic. For the sake of comparison, from now on, the absolute V values of the paramagnetic compounds are considered. Here it can be seen as general tendency that the V values decrease as the UV transparency of the crystals increases. The V of CeF3 is close to that of TGG in the VIS, while it is remarkably higher than for any other crystal in the 300-400 nm range. LiTbF4 and PrF3 present a similar V dispersion, however, PrF3 has the advantage of a higher transparency in the 220-300 nm region. Our FR measurements on LiTbF4 are in good agreement with a previous report [27]. LiDyF4 has a high V in the narrow 200-220 nm interval. Below 200 nm there are only three crystals: LiHoF4, LiErF4, and LiYbF4. The first two possess comparatively higher V values, but they present 4f-4f absorption lines. On the contrary, LiYbF4 is widely transparent down to 170 nm, but its V is comparatively low. A sharp V increase is expected towards the absorption edge. The parameters used to fit the experimental data with Eq. (4) are given in Table 3 together with a more detailed evaluation by means of Eqs. (2)-(4). Table 4 summarizes the V values of all crystals at the specific wavelengths of common excimer lasers. In comparison with other FRs proposed for the UV region (water, quartz, ADA, etc.) our crystals show much higher V constants, indicating the high potential of these as alternative unique materials for UV FR applications. The V constants (in rad T−1m−1) of following compounds are noteworthy: CeF3 at 351 nm (XeF) has 653 and at 308 nm (XeCl) 1146; PrF3 at 248 nm (KrF) has 1658 and at 222 nm (KrCl) 2964; LiDyF4 and LiHoF4 at 193 nm (ArF) have 2885 and 974, respectively.
Fig. 4 (a) Verdet constant dispersion of CeF3, PrF3, and LiREF4 crystals in comparison with that of TGG. All compounds are paramagnetic except LiYbF4, which is diamagnetic. For the sake of comparison the absolute V values of the paramagnetic compounds are plotted. The dotted intervals indicate the part of the fittings extrapolated in the VUV. (b) Inverse Verdet constant as a function of the wavelength square for LiREF4 crystals. The experimental points are fitted by a single transition.
Table 4. Verdet constants (rad T−1m−1) comparison of FR materials at different excimer laser wavelengths (in nm).
The inverse V constant of the LiREF4 series as a function of the wavelength square is shown in Fig. 4(b). In analogy to Fig. 3(b), it is seen that the experimental data are well approximated by a single transition. Large V values are promoted by (1) a long λo and (2) a small slope (1/E). The estimated λo lie between the absorption edges of the crystals and the 4fn-4fn-15d transitions of the corresponding RE free ions, except for the case of LiHoF4 and LiErF4, whose λo are close to 100 nm. This correlation is visualized in Fig. 5(a) . Further, λo shows a decreasing tendency with the increase of 4f electrons of the RE ions. Back to Fig. 4(b), the slope of the fitting curves (1/E) diminishes with the 4f electrons. Taking into account that the NRE in the LiREF4 crystals does not vary significantly, the observed differences correlate with the χ in terms of the effective Bohr magneton p (Eq. (3)) and the transition probability of each RE ion CRE (Eq. (2)). These values were calculated (Table 3) and are displayed in Fig. 5(b). It is known that Tb, Dy, Ho, and Er possess a similarly large p, which contrasts with the relatively low one of Yb, Pr, and Ce. From the CRE point of view, the opposite relationship is found for Ce and Pr ions in these crystals, which have about six times higher CRE than the Tb ion in TGG reference. For the LiREF4 series the CRE are also higher, but more similar to that of TGG.
Fig. 5 Evaluation of the Verdet constant dispersion according to Eqs. (2)-(3). (a) Estimated transition wavelengths in comparison with absorption edge of crystals and 4fn-4fn-15d transition wavelengths of free RE ions. (b) Effective magnetic moments of the RE ions, and transition probabilities.
In order to evaluate the potential of each compound for FR applications, apart from the detail analysis of the V constant dispersion it is also necessary to determine the absorption losses. A high V constant and a high transparency are the major requirements; consequently the figure of merit (FM) is defined as the ratio between V and the absorption coefficient, V/α. The α dispersion was calculated using the Beer-Lambert law whereas d is the sample thickness, in our case 1 mm. The effective transmission was approximated by the sum of transmittance and reflectance spectra. The resulting α are shown in Fig. 6(a) .
Subsequently, the estimated FMs are plotted in Fig. 6(b) together with the TGG reference, which has about 10 rad T−1. CeF3 presents a much higher FM than TGG in the VIS. In the near UV, where TGG already absorbs strongly, CeF3 exhibits an outstanding high FM down to 300 nm. In the 220-300 nm interval, PrF3 is very transparent and possesses also a remarkably high FM. Below 220 nm, LiDyF4, LiHoF4, and LiErF4 are the potential FRs. Due to the occurrence of 4f-4f absorption lines, the crystal selection depends on the considered wavelength. The transmittance of LiDyF4 diminishes from 200 nm, while the other two crystals are transparent till about 170 nm. LiYbF4, with the absence of 4f-4f absorption lines, exhibits the highest transparency in the VUV-VIS range, however, its FM is strongly delimited by the low V value, so that at present its advantages as FR are noteworthy only at very short wavelengths, close to its absorption edge.
4. Conclusions
Summarizing, the potential of RE-fluoride single crystals for FR applications in the UV and VIS wavelength region is evaluated. CeF3, PrF3, and LiREF4 (RE = Tb, Dy, Ho, Er, and Yb) single crystals of high optical quality have been grown by the Cz technique. In comparison with previous candidates such as RE-doped glasses and KDP-isomorph compounds, we demonstrate that the synthesized crystals exhibit remarkably higher Verdet constants in a wider transmission range. All of them are paramagnetic, except the diamagnetic LiYbF4. CeF3 and PrF3 show outstanding FMs in the UV, from 300 and 220 nm, respectively. In the VIS range, CeF3 has a noteworthy larger FM than the one of commercially available TGG. LiDyF4 can be used above 200 nm, while LiHoF4 and LiErF4 can be utilized also in the VUV from 170 nm. Due to the presence of 4f-4f absorption bands, the selection of crystal depends on the wavelength needed. To date, compared with other materials the series of crystals investigated in current work present the highest potential for VUV-VIS FR applications.
Acknowledgment
Authors would like to express their gratitude to Dr. Norimasa Nukaga, Mr. Kenichi Muramatsu and Mr. Motoi Ueda from Nikon Corp. for the VUV transmittance measurements and the 193 nm laser source, and also to Dr. Tsuyoshi Ohnishi from NIMS for the support with the 248 nm laser source. This work has been partially supported by the Ministry of Education, Science, Sport and Culture, Grant-in-Aid for Scientific Research (C), 22560316, 2010.
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