Introduction

The 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 angle1,2,3. The material's magneto-optical (MO) performance is typically described by the Verdet constant VB, 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 switches1,2,3,4,5,6. 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 species7. Here, due to the electronic transition of 4f8 → 4f75d8,9, the Tb3+ ion offers one of the highest paramagnetic susceptibilities (J = 6, g = 1.46) and magnetic moments (9.5–9.72 μeff) of all rare earth ions. Consequently, the most promising bulk MO material is terbium aluminum garnet (Tb3Al5O13, TAG, VB ~ 180 rad/T/m)10,11, which is not yet available commercially, though. Instead, terbium gallium garnet single crystals (Tb3Ga5O13, TGG, VB ~ 134 rad/T/m)12 are presently the most widely used commercial MO materials. But also all commercially available MO glasses rely on massive Tb3+-doping4,13,14,15,16. 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, ΔT, between the glass transition temperature Tg and the onset temperature of crystallization Tc, 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 properties17,18. Typically, a large value of ΔT is sought for two reasons: fiber drawing must be performed at a temperature sufficiently above Tg 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 GeO2-B2O3-Al2O3-Ga2O3 enabling high rare earth solubility. In this system, we achieve a Tb2O3 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 VB for the full series of GBAG-xTb (x = 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 Tb3+ dopant concentration, i.e., from ~48 to 119 rad/T/m at 632.8 nm (Fig. 1a and 1b). For similar Tb3+ ion concentration, the absolute value VB of GBAG-xTb glasses is in the order of that of other reported record values in Tb3+-doped MO glasses, e.g, silicate2,6, phosphate2, borate5,22 and borogermanate23 glasses (Fig. 1b). For the maximum Tb3+ loading we report here, GBAG-25Tb, VB exceeds the rotation efficiency in most of the well-known MO glasses, e.g., 30Tb2O3-70B2O3 (~103 rad/T/m)22 and 25Tb2O3-15Al2O3-60SiO2 (~102 rad/T/m)6 and is similar with that of 33Tb2O3-25GeO2-25B2O3-5SiO2-12Al2O3 (~119 rad/T/m)23. For comparison, data for the single crystalline benchmarks of TAG and TGG are also shown in Fig. 1b11,12.

Table 1 Nominal and analyzed compositions of the studied glasses (data given in the form “nominal/as-analyzed”, mol%)
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Table 2 Experimental data of density ρ, Tb3+ ion concentration, refractive index nd, Verdet constant VB (at 632.8 nm), FoM (at 435 nm), τ, Tg, Tc, ΔT and Ea for the studied glasses
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Figure 1
figure 1

Magneto-optical properties of GBAG-xTb glasses.

(a) Variation of the Verdet constant with wavelength for GBAG-xTb glasses as a function of Tb2O3 concentration at room-temperature. The solid lines represent a fit of the data to the power function y = a(1-x)b. (b) Dependence of VB on Tb3+ ion concentration and comparison to other reported data glasses at a fixed wavelength of 632.8 nm. (c) Van Vleck-plot of the inverse VB (VB−1) over the square wavelength (λ2). The solid lines in (c) represents a linear fit of the data. The inset of (c) shows the value of the transition wavelength λt versus Tb2O3 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.

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In the framework of the Van Vleck-Hebb model of single-oscillator paramagnetic rare earth ions, the relationship between V and λ2 can be written as24,25

In Eq. (1), g is the Landé factor, c the velocity of light, h is the Planck constant, Ct is the effective transition probability and λt is the effective transition wavelength. λt 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 4fn ↔ 4fn−15d26. Plotting V−1 over λ2 therefore yields a linear relationship (Fig. 1c). Here, λt is the intersection with the λ2 axis which results from extrapolation of the data. The value of λt is dependent on Tb2O3 concentration (inset of Fig. 1c). It increases with Tb2O3 concentration, i.e., from ~225 to 300 nm when x ≤ 22. A decrease back to ~280 nm is observed for the highest Tb2O3 concentration. As expected, these values are close to the 4f8 ↔ 4f75d transition of the Tb3+ ion (~250 nm)5 and are also similar to other reported values, e.g., Tb3+-doped phosphate (~250 nm)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 = 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 4f8 → 4f8 electronic transitions of Tb3+ from the ground state of 7F6 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 Tb3+ 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).

Figure 2
figure 2

Photoluminescence of GBAG-xTb glasses.

Static (a) PLE and (b) PL spectra and (c) normalized dynamic decay curves of photoluminescence from GBAG-xTb as a function of Tb2O3 concentration at room-temperature. (d) is a zoom (by a factor of 3000) into the PLE spectra at the spectra region of 360–470 nm. (e) represents the energy level diagram of Tb3+. The labels in (a–b) indicate the respective band assignment.

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The MO figure of merit (FoM) which is an important parameter for practical applications results from the ratio of VB/a, where a is absorption coefficient4. As displayed in Fig. 1e, the spectral FoM exhibits a sharp dip at 484 nm, resulting from the 7F6 → 5D4 absorption band of Tb3+. In the present case, the glass of GBAG-18Tb exhibits the best trade-off between VB and a over the whole spectrum. The highest FoM performance of ~−0.049°/dB is found at ~435 nm, which matches the emission characteristics of various blue laser diodes.

Photoluminescence properties

Fig. 2a and 2b present static photoexcitation (PLE) and luminescence (PL) spectra of Tb3+ in GBAG-xTb (x = 14, 18, 22 and 25) at room temperature. Fully consistent with the optical absorption data (Fig. 1d), the PLE spectra of Tb3+ consist of a series of sharp overlapping PLE bands in the NUV region with maxima at 378, 368, 358, 350, 340, 325, 317 and 303 nm and another sharp PLE line in the blue with a maximum at 484 nm. These bands are attributed to the intra-configurational parity-forbidden 4f8 → 4f8 electronic transitions from the ground state 7F6 to the labeled excited states, also indicated in energy level diagram of Tb3+ (Fig. 2a and 2e)30,31,32,33,34. The strongest PLE band is the 7F6 → 5L9 at 350 nm, used in the following as excitation wavelength to record the PL spectra. Here, the five typical PL bands of Tb3+ are observed, i.e., at 488, 542, 585, 622 and 655 nm, deriving again from the intra-configurational parity-forbidden 4f8 → 4f8 transitions from 5D4 to the 7FJ (J = 6, 5, 4, 3 and 2) multiplet, Fig. 2b and 2e35. The green PL line of the magnetic dipole allowed transition (ΔJ = 1) Tb3+: 5D4 → 7F5 at 542 nm with a full width at half maximum (FWHM) of ~10 nm (~337 cm−1) dominates the PL spectra for all samples. As a result, the corresponding International Commission on Illumination (CIE) 1931 PL chromaticity coordinates of all samples are (~0.344 ± 0.002, ~0.592 ± 0.002), which are located in the green region. The aforementioned green PL band is Stark-split into two peaks due to the distorting effect of the disordered glass network on the Tb3+ ions (Fig. 2b). For lower amounts of Tb2O3 loading (x ≤ 18), the intensity of all PL lines of Tb3+ decreases only slightly with Tb2O3 concentration while for x ≥ 18, we observe strong concentration quenching36,37. This is related to an increasing probability for the formation of Tb-O-Tb entities in the first coordination shell of Tb3+.38 The concentration quenching effect is further confirmed by the decay data of the Tb3+: 5D4 → 7F5 emission (Fig. 2c). All decay curves follow a single exponential function of the form I = I0exp(-t/τ) (with time t and intensity I). The effective lifetime τ decreases with increasing Tb3+ concentration, 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 Tb3+: 5D4 → 7F5 PL for GBAG-14Tb glass (~2.23 ms) is larger than what is found in similar B2O3-GeO2-Gd2O3 glasses before concentration quenching, ~1.80 ms39. This further indicates that particularly weak concentration quenching occurs in the present case. The internal quantum efficiency ηiQE for GBAG-14Tb is ~63%. This value is close to the highest reported ηiQE of Tb3+-based PL in literature, e.g., Tb3+-doped phosphate glass (~78%)40 and silicone hybrid materials (~68%)41. For higher doping concentration, it decreases to only 0.3% at x = 25. The high Tb3+ loading results in a large absorption cross-section of incoming light and, hence, high photo-conversion gain. That is, the absorbance of GBAG-14Tb at 350 nm is ~69%. Thus, the external quantum efficiency ηeQE is ~43%, meaning that at the considered excitation wavelength, ~43% of the incoming photons are converted through photoluminescence.

PL of Tb3+ from the higher excited states, i.e., 5D3 → 7FJ (J = 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 5D3 and 5D4 (~5629 cm−1) and the 7F6 and 7F0 energy levels (~5791 cm−1, Fig. 2e)42,

The absorption cross-section σabs of Tb3+ at 350 (Tb3+: 7F6 → 5L9) and 484 nm (Tb3+: 5F6 → 7D4) and the stimulated emission cross-section σem of Tb3+ PL at 542 nm (Tb3+: 5D4 → 7F5) can be estimated through McCumber's and Füchtbauer-Ladenburg's equation43,44,45,

In Eqs. (3)–(4), N0 is the ion concentration of Tb3+, d is the sample thickness, λ0 is the emission wavelength, OD(λ) is the optical density, η is the internal quantum efficiency, n is the refractive index of the host material, τ is the emission lifetime and Δν1/2 is the FWHM of the transition. The σabs value of Tb3+ in GBAG-xTb glasses at 350 and 484 nm is calculated to be ~4.94 and 0.95 × 10−22 cm2, respectively. This value is comparable to that of phosphate glasses (~1.1 × 10−22 cm2)40. The σem value of Tb3+ in GBAG-xTb glasses at 542 nm is ~1.1 × 10−21 cm2, notably larger than in phosphate glasses (~7.4 × 10−22 cm2)40. The product of σem*τ, the optical gain parameter for laser applications, is proportional to the amplification gain and inverse laser oscillation threshold45. A relatively high value of ~2.5 × 10−24 cm2s 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 ρ, nd, Tg, Tc and ΔT of GBAG-xTb are summarized in Tab. 1. Density and refractive index increase from ~4.08 to 4.85 g/cm3 and from 1.69 to 1.75 respectively with increasing Tb2O3 concentration due to the much higher molar mass of Tb2O3 (365.85 g/mol) as compared to Ga2O3 (187.44 g/mol) (Fig. 3a).

Figure 3
figure 3

Thermal properties of GBAG-xTb glasses.

(a) Physical properties density and refractive index of GBAG-xTb as a function of Tb2O3 concentration. (b) DSC curves of GBAG-xTb as dependent on Tb2O3 concentration. From (b), the variation of the glass transition temperature Tg and the onset temperature of crystallization Tc are extracted (c). (d–e) show the glass stability parameter ΔT and the apparent activation energy of crystallization, respectively, of GBAG-xTb as a function of Tb2O3 concentration. Solid lines are drawn as guides for the eye.

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Figure 3b shows DSC curves of GBAG-xTb. Here, Tg and Tc gradually increase from 740 to 777°C and from 848 to 928°C, respectively, with increasing Tb2O3 concentration (Fig. 3c). In order to empirically judge glass stability, ΔT = Tc–Tg is calculated from these data.

Generally speaking, larger values of ΔT reflect an improved stability against crystallization. Here, ΔT increases from 108 to 151 K with increasing of Tb2O3 concentration (Fig. 3d). Overall, this suggests a comparably high crystallization stability of the glasses of this study.

The apparent activation energy Ea of crystallization is calculated from the DSC data for varying heating rates by a Kissinger equation46,

In Eq. (5), R is the ideal gas constant, Tx is the temperature of crystallization and ϕ is the heating rate of the DSC experiment. Ea can therefore be estimated from the slope of a linear fit of ln(ϕ/Tx2) versus 1/Tx plot. The obtained value depends on Tb2O3 concentration. It reaches a maximum of ~593 kJ/(mol × K) at GBAG-18Tb and decreases to 482 kJ/(mol × K) for x = 25 (Fig. 3e). Hence, while, GBAG-18Tb and GBAG-14Tb exhibit the highest MO FoM and the highest PL performance, they also exhibit large ΔT and comparatively high Ea.

Conclusions

In summary, we reported on the magneto-optical (MO) properties of heavily Tb3+-doped GeO2-B2O3-Al2O3-Ga2O3 glasses towards fiber-integrated paramagnetic MO devices. For Tb3+ ion concentrations 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 underlying effective transition wavelength λt is close to the 4f8 ↔ 4f75d transition of the Tb3+ ion, ~250 nm. The optimum FoM is found for a Tb3+ concentration of ~6.5 × 1021 cm−3 (GBAG-18Tb), ~−0.05°/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 Tb3+ photoluminescence. In the heavily doped materials, a UV/blue-to-green photo-conversion gain of ~43% is achieved. The Tb3+ ions are well dispersed in GBAG-xTb glasses without notable concentration quenching of photoluminescence up to a dopant concentration of ~14 mol% of Tb2O3 (GBAG-14Tb). The lifetime of photoluminescence is ~2.2 ms with 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.

Methods

Synthesis of Glasses

Precursor glasses with nominal compositions of 16.5GeO2-21.5B2O3-37Al2O3-(25–x)Ga2O3-xTb2O3 (GBAG-xTb with x = 14, 18, 22 and 25 mol%) were prepared by conventional melting and quenching. Batches of ~50 g of GeO2 (99.99%), H3BO3 (99.99%), Ga2O3 (99.99%) and Tb4O7 (99.99%) were thoroughly mixed and melted in a resistive heating furnace at 1500°C for 3 h in Al2O3 crucibles, heating to 700°C at 5 K/min and to 1500°C at 10 K/min. Melting conditions were kept identical for all batches to ensure a homogenous dilution of Al2O3 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 VB = a(1-λ)b with wavelength λ. VB is calculated from the Faraday rotation angle θF, the strength of the external magnetic field B and the length of the light path L in the sample, VB = θF/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 VB was derived from the θF versus B dependencies in an iron-yoke magnet (−0.1 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 θF versus H were linearly extrapolated to obtain the slope dθF/dH, which was used to estimate VB. 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 Tb3+-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 (ηIQE) and external quantum efficiency (ηEQE) of Tb3+ PL were obtained through recording all spectra on samples and on a blank reference, using a BaSO4-coated integration sphere20,21.

Thermal properties

The values of Tg, Tc and Tx (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 wavelength-dispersive electron probe microanalysis (WD-EPMA, microprobe JXA-8800L; Jeol). The ion concentration of Tb3+ 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 Kα) on bulk samples. The glass density ρ was determined in an Archimedes balance, using distilled water as the immersion liquid. The refractive index was determined at the d line (nd, λ = 587 nm) with a Pulfrich reactometer.