Faraday rotation and photoluminescence in heavily Tb3+-doped GeO2-B2O3-Al2O3-Ga2O3 glasses for fiber-integrated magneto-optics

We report on the magneto-optical (MO) properties of heavily Tb3+-doped GeO2-B2O3-Al2O3-Ga2O3 glasses towards fiber-integrated paramagnetic MO devices. For a Tb3+ ion concentration of up to 9.7 × 1021 cm−3, the reported glass exhibits an absolute negative Faraday rotation of ~120 rad/T/m at 632.8 nm. The optimum spectral ratio between Verdet constant and light transmittance over the spectral window of 400–1500 nm is found for a Tb3+ concentration of ~6.5 × 1021 cm−3. For this glass, the crystallization stability, expressed as the difference between glass transition temperature and onset temperature of melt crystallization exceeds 100 K, which is a prerequisite for fiber drawing. In addition, a high activation energy of crystallization is achieved at this composition. Optical absorption occurs in the NUV and blue spectral region, accompanied by Tb3+ photoluminescence. In the heavily doped materials, a UV/blue-to-green photo-conversion gain of ~43% is achieved. The lifetime of photoluminescence is ~2.2 ms at a stimulated emission cross-section σem of ~1.1 × 10−21 cm2 for ~ 5.0 × 1021 cm−3 Tb3+. This results in an optical gain parameter σem*τ of ~2.5 × 10−24 cm2s, what could be of interest for implementation of a Tb3+ fiber laser.

T he Faraday effect reflects the ability of a material to -in the presence of a magnetic field being parallel to the incident light beam -rotate the polarization plane of linear polarized light by a certain angle [1][2][3] . The material's magneto-optical (MO) performance is typically described by the Verdet constant V B , which represents the degree of rotation as a function of the acting magnetic field strength and the geometrical path length within the material. High performance can hence be achieved via large rotation efficiency or a long path length. Applications of MO materials range from magnetic field sensing and security encoding to optical modulators, diodes, isolators and switches [1][2][3][4][5][6] . Key for the design of an efficient, optically transparent (bulk) MO material is the incorporation of a high atom concentration of paramagnetic species while, at the same time, avoiding optical absorption to the highest possible degree. While some transition metals have also been considered for this purpose, at present, this calls for the use of rare earth species 7 . Here, due to the electronic transition of 4f 8 R 4f 7 5d 8,9 , the Tb 31 ion offers one of the highest paramagnetic susceptibilities (J 5 6, g 5 1.46) and magnetic moments (9.5-9.72 m eff ) of all rare earth ions. Consequently, the most promising bulk MO material is terbium aluminum garnet (Tb 3 Al 5 O 13 , TAG, V B , 180 rad/T/m) 10,11 , which is not yet available commercially, though. Instead, terbium gallium garnet single crystals (Tb 3 Ga 5 O 13 , TGG, V B , 134 rad/T/m) 12 are presently the most widely used commercial MO materials. But also all commercially available MO glasses rely on massive Tb 31doping 4, [13][14][15][16] . As an alternative to the MO crystals, glassy materials offer a much improved flexibility of forming and processing. Especially glass compositions which are suitable for fiber fabrication could enable fiber-integrated devices. In addition, the higher interaction length which can be achieved in fiber devices could further compensate eventual losses in Faraday rotation efficiency. In this regard, besides the primary optical properties, the thermo-physical stability and the rheological properties of the considered glass and its corresponding (supercooled) melt are key parameters: in order to avoid crystallization of the melt during fiber drawing, a certain crystallization stability is required. This is often expressed as the difference, DT, between the glass transition temperature T g and the onset temperature of crystallization T c , or through various other empirical stability indicators such as the Hrubý parameter which is derived from this difference, sometimes further relating it to the liquidus temperature of the melt or other properties 17,18 . Typically, a large value of DT is sought for two reasons: fiber drawing must be performed at a temperature sufficiently above T g so that a sufficiently low viscosity is reached and the interval of processing temperature must be sufficiently wide to tolerate a certain degree of processing-induced temperature variability. On the other hand, for many of the specialty (non-silica) compositions with often high liquid fragility, fiber drawing cannot be performed above the liquidus temperature (where there would not be any risk of crystallization) because then, the viscosity would be too low.
Here, we consider glass forming liquids of the type GeO 2 -B 2 O 3 -Al 2 O 3 -Ga 2 O 3 enabling high rare earth solubility. In this system, we achieve a Tb 2 O 3 doping concentration of up to 25 mol%. The glass stability parameters are controlled through tailoring the matrix composition in order to provide the possibility of fiber drawing. We then report on the MO and photoluminescence properties of this material.

Results
Magneto-optical properties. The chemical composition and physical properties of all samples are summarized in Tables 1-2. Figure 1a shows the room-temperature wavelength dependence of V B for the full series of GBAG-xTb (x 5 14, 18, 22 and 25). As expected, all samples exhibit paramagnetic behaviour over the full range of studied wavelengths, with a strong absolute increase towards the blue. Secondly, there is a notable increase with increasing Tb 31 dopant concentration, i.e., from ,48 to 119 rad/T/ m at 632.8 nm ( Fig. 1a and 1b). For similar Tb 31 ion concentration, the absolute value V B of GBAG-xTb glasses is in the order of that of other reported record values in Tb 31 -doped MO glasses, e.g, silicate 2,6 , phosphate 2 , borate 5,22 and borogermanate 23 glasses (Fig. 1b). For the maximum Tb 31 loading we report here, GBAG-25Tb, V B exceeds the rotation efficiency in most of the well-known MO glasses, e.g., 30Tb 2 O 3 -70B 2 O 3 (,103 rad/T/m) 22 and 25Tb 2 O 3 -15Al 2 O 3 -60SiO 2 (,102 rad/T/m) 6 , and is similar with that of 33Tb 2 O 3 -25GeO 2 -25B 2 O 3 -5SiO 2 -12Al 2 O 3 (,119 rad/T/m) 23 . For comparison, data for the single crystalline benchmarks of TAG and TGG are also shown in Fig. 1b 11,12 . In the framework of the Van Vleck-Hebb model of singleoscillator paramagnetic rare earth ions, the relationship between V and l 2 can be written as 24,25 In Eq. (1), g is the Landé factor, c the velocity of light, h is the Planck constant, C t is the effective transition probability, and l t is the effective transition wavelength. l t is a weighted average value which is taken as the origin of the paramagnetic Faraday rotation. In rare earth ions, it is close to the position of the electric transition of 4f n « 4f n21 5d 26 . Plotting V 21 over l 2 therefore yields a linear relationship (Fig. 1c). Here, l t is the intersection with the l 2 axis which results from extrapolation of the data. The value of l t is dependent on Tb 2 O 3 concentration (inset of Fig. 1c 27 , borosilicate (,259-280 nm) 28 , aluminoborate (,250 nm) 24 , sodium borate (,220 nm) 8 and fluorophosphate glasses (,217 nm) 26 . Fig. 1d shows the UV-NIR optical absorption spectra of GBAG-xTb (x 5 14, 18, 22 and 25). The absorption spectra consist of several strongly overlapping but sharp absorption bands in the 300 to 390 nm range, and another sharp band at ,484 nm. These bands can readily be assigned to the 4f 8 R 4f 8 electronic transitions of Tb 31 from the ground state of 7 F 6 to the labeled excited states (inset of Fig. 1d and Fig. 2e) 29,30 . The intensity of all bands follows well Lambert-Beer's power law. All glasses exhibit high transparency in the ,400 to 1500 nm range with a transmittance of ,58% (,95%) with a thickness of 1 cm (mm). The increasing absorption intensity with increasing Tb 31 content in the near-UV region results in a shift of the absorption edge and an apparent coloration under sunlight, gradually varying from colorless to brown (inset of Fig. 1e).
The MO figure of merit (FoM) which is an important parameter for practical applications results from the ratio of V B /a, where a is absorption coefficient 4 . As displayed in Fig. 1e, the spectral FoM exhibits a sharp dip at 484 nm, resulting from the 7 F 6 R 5 D 4 absorption band of Tb 31 . In the present case, the glass of GBAG-18Tb exhibits the best trade-off between V B and a over the whole spectrum. The highest FoM performance of ,20.049u/dB is found at Table 1 | Nominal and analyzed compositions of the studied glasses (data given in the form ''nominal/as-analyzed'', mol%)  ,435 nm, which matches the emission characteristics of various blue laser diodes.
Photoluminescence properties.  (Fig. 2b). For lower amounts of Tb 2 O 3 loading (x # 18), the intensity of all PL lines of Tb 31 decreases only slightly with Tb 2 O 3 concentration while for x $ 18, we observe strong concentration quenching 36,37 . This is related to an increasing probability for the formation of Tb-O-Tb entities in the first coordination shell of Tb 31 . 38 The concentration quenching effect is further confirmed by the decay data of the Tb 31 : 5 D 4 R 7 F 5 emission (Fig. 2c). All decay curves follow a single exponential function of the form I 5 I 0 exp(-t/t) (with time t and intensity I).
The effective lifetime t decreases with increasing Tb 31 concentration, ) over the square wavelength (l 2 ). The solid lines in (c) represents a linear fit of the data. The inset of (c) shows the value of the transition wavelength l t versus Tb 2 O 3 concentration. In (d), the UV-VIS-NIR optical absorption spectra are given, from which the spectral MO figure of merit is obtained (shown in (e)). The inset of (d) exemplarily shows a zoom at the absorption spectrum in the spectral region of 260-550 nm for GBAG-14Tb. i.e., from ,2.2 to ,1.2 ms when x # 18, and further to ,0.1 ms for x . 18 ( Fig. 2b and 2c). The lifetime of Tb 31 : 5 D 4 R 7 F 5 PL for GBAG-14Tb glass (,2.23 ms) is larger than what is found in similar B 2 O 3 -GeO 2 -Gd 2 O 3 glasses before concentration quenching, ,1.80 ms 39 . This further indicates that particularly weak concentration quenching occurs in the present case. The internal quantum efficiency g iQE for GBAG-14Tb is ,63%. This value is close to the highest reported g iQE of Tb 31 -based PL in literature, e.g., Tb 31 -doped phosphate glass (,78%) 40 and silicone hybrid materials (,68%) 41 . For higher doping concentration, it decreases to only 0.3% at x 5 25. The high Tb 31 loading results in a large absorption cross-section of incoming light and, hence, high photoconversion gain. That is, the absorbance of GBAG-14Tb at 350 nm is ,69%. Thus, the external quantum efficiency g eQE is ,43%, meaning that at the considered excitation wavelength, ,43% of the incoming photons are converted through photoluminescence.
PL of Tb 31 from the higher excited states, i.e., 5 D 3 R 7 F J (J 5 6, 5, 4, 3, 2 and 1) is almost fully quenched even in GBAG-14Tb (Fig. 2d). This is a result of the strong cross-relaxation processes which occur at the high doping levels used in this study. The cross relaxation process is caused by the closeness of the 5 D 3 and 5 D 4 (,5629 cm 21 ), and the 7 F 6 and 7 F 0 energy levels (,5791 cm 21 , Fig. 2e) 42 , The absorption cross-section s abs of Tb 31 at 350 (Tb 31 : 7 F 6 R 5 L 9 ) and 484 nm (Tb 31 : 5 F 6 R 7 D 4 ), and the stimulated emission crosssection s em of Tb 31 PL at 542 nm (Tb 31 : 5 D 4 R 7 F 5 ) can be estimated through McCumber's and Füchtbauer-Ladenburg's equation [43][44][45] , In Eqs.  40 . The product of s em *t, the optical gain parameter for laser applications, is proportional to the amplification gain and inverse laser oscillation threshold 45 . A relatively high value of ,2.5 3 10 224 cm 2 s is obtained for the GBAG-14Tb glass, what suggests a large amplification gain and low oscillation threshold and, hence, potential interest for further examination as a green laser gain material.
Thermal properties. The values of r, n d , T g , T c and DT of GBAG-xTb are summarized in Tab. 1. Density and refractive index increase from ,4.08 to 4.85 g/cm 3 and from 1.69 to 1.75 respectively with increasing Tb 2 O 3 concentration due to the much higher molar mass of Tb 2 O 3 (365.85 g/mol) as compared to Ga 2 O 3 (187.44 g/mol) (Fig. 3a). Figure 3b shows DSC curves of GBAG-xTb. Here, T g and T c gradually increase from 740 to 777uC and from 848 to 928uC, respectively, with increasing Tb 2 O 3 concentration (Fig. 3c). In order to empirically judge glass stability, DT 5 T c -T g is calculated from these data.
Generally speaking, larger values of DT reflect an improved stability against crystallization. Here, DT increases from 108 to 151 K with increasing of Tb 2 O 3 concentration (Fig. 3d). Overall, this suggests a comparably high crystallization stability of the glasses of this study.
The apparent activation energy E a of crystallization is calculated from the DSC data for varying heating rates by a Kissinger equation 46 , In Eq. (5), R is the ideal gas constant, T x is the temperature of crystallization, and w is the heating rate of the DSC experiment. E a can www.nature.com/scientificreports therefore be estimated from the slope of a linear fit of ln(w/T x 2 ) versus 1/T x plot. The obtained value depends on Tb 2 O 3 concentration. It reaches a maximum of ,593 kJ/(mol 3 K) at GBAG-18Tb and decreases to 482 kJ/(mol 3 K) for x 5 25 (Fig. 3e). Hence, while, GBAG-18Tb and GBAG-14Tb exhibit the highest MO FoM and the highest PL performance, they also exhibit large DT and comparatively high E a .

Conclusions
In summary, we reported on the magneto-optical (MO) properties of heavily Tb 31 -doped GeO 2 -B 2 O 3 -Al 2 O 3 -Ga 2 O 3 glasses towards fiberintegrated paramagnetic MO devices. For Tb 31 ion concentrations of up to 9.7 3 10 21 cm 23 , the reported glass exhibits an absolute negative Faraday rotation of ,120 rad/T/m at 632.8 nm. The underlying effective transition wavelength l t is close to the 4f 8 « 4f 7 5d transition of the Tb 31 ion, ,250 nm. The optimum FoM is found for a Tb 31 concentration of ,6.5 3 10 21 cm 23 (GBAG-18Tb), ,20.05u/dB at ,435 nm, matching the emission characteristics of blue light-emitting diodes. For this glass, the crystallization stability, expressed as the difference between glass transition temperature and onset temperature of melt crystallization exceeds 100 K, which is a prerequisite for fiber drawing. In addition, a high activation energy of crystallization is achieved using this composition. Optical absorption occurs in the NUV and blue spectral region, accompanied by Tb 31 photoluminescence. In the heavily doped materials, a UV/blue-to-green photo-conversion gain of ,43% is achieved. The Tb 31  crucibles, heating to 700uC at 5 K/min and to 1500uC at 10 K/min. Melting conditions were kept identical for all batches to ensure a homogenous dilution of Al 2 O 3 in the melt. Subsequently, melts were poured onto preheated brass plates, annealed for 1 h and finally cooled down to room temperature at the intrinsic furnace rate (,1 K/min). The obtained glass slabs were cut and polished on both sides for optical characterization.
Magneto-optical properties. Frequency-dependent MO analyses were done by using a series of laser diodes as light sources (405, 488, 635, 705 and 830 nm) and fitting the obtained data of Faraday rotation to a power function of the form V B 5 a(1-l) b with wavelength l. V B is calculated from the Faraday rotation angle h F , the strength of the external magnetic field B, and the length of the light path L in the sample, V B 5 h F /BL. 5,8,19 For this, the rotation of the polarization plane was measured with a polarimeter (PAX570VIST/PAX570IR-1T). In this set-up, the magnetic field was applied through a permanent magnet, achieving a constant magnetic flux of 0.23 T. In a second set of experiments, the value if V B was derived from the h F versus B dependencies in an iron-yoke magnet (20.1 T , B , 0.1 T), using a light-emitting diode with the central wavelength of 625 nm. For this, the magnetic flux was swept in the given range with a step-width of ,1 mT. Then, the obtained data on h F versus H were linearly extrapolated to obtain the slope dh F /dH, which was used to estimate V B . Error bars on the value of V were obtained from the comparison of those two experiments. UV-VIS-NIR absorption spectra were recorded over the spectral range of 200 nm to 2500 nm in a UV-NIR spectrophotometer (Perkin Elmer, Lambda 950).
Photoluminescence properties. Static photoexcitation (PLE) and luminescence (PL) spectra and dynamic decay curves of the Tb 31 -related photoluminescence were recorded with a high-resolution spectrofluorometer (Horiba Jobin Yvon Fluorolog FL3-22) at room temperature. PLE spectra were corrected over the lamp intensity with a silicon photodiode. PL spectra were corrected by the spectral response of employed photomultiplier tube. Absorbance (a), internal (g IQE ) and external quantum efficiency (g EQE ) of Tb 31 PL were obtained through recording all spectra on samples and on a blank reference, using a BaSO 4 -coated integration sphere 20,21 .
Thermal properties. The values of T g , T c and T x (peak temperature of crystallization) were obtained from differential scanning calorimetry (DSC, Netzsch DSC 404 F1), using a heating rate of 10 K/min. Non-isothermal crystallization dynamic were studied by DSC (Netzsch DSC 404 F1) on polished bulk glasses (,25-40 mg) at different heating rates of 5, 10, 15 and 20 K/min in order to evaluate the apparent activation energy of crystallization.
Other properties. The composition of all glasses was verified by wavelengthdispersive electron probe microanalysis (WD-EPMA, microprobe JXA-8800L; Jeol). The ion concentration of Tb 31 was calculated according to these compositions. Nominal and as-received compositions are given in Tab. 1. The absence of crystals from the as-made glasses was verified by X-ray diffraction analyses (XRD Siemens Kristalloflex D500, Bragg-Brentano, 30 kV/30 mA, Cu Ka) on bulk samples. The glass density r was determined in an Archimedes balance, using distilled water as the immersion liquid. The refractive index was determined at the d line (n d , l 5 587 nm) with a Pulfrich reactometer.