Growth, anisotropy, and spectroscopy of Tm³⁺ and Yb³⁺ doped MgWO₄ crystals

Abstract

We report on an improved crystal growth process, reassessment of the orientation of the optical ellipsoid, and polarized spectroscopy of doped monoclinic magnesium monotungstate (MgWO₄) in a new dielectric frame. A set of crystals, including undoped, Yb³⁺-doped, and Tm³⁺-doped MgWO₄, were grown by the top-seeded solution growth (TSSG) method with K₂W₂O₇ as a solvent. This approach resulted in high-quality crystals with a significantly reduced growth time compared to those grown using Na₂WO₄. The crystal structures were confirmed by powder X-ray diffraction, and the lattice parameters were determined using Le Bail fitting. We review the growth methodology and emphasize the revision of the principal optical axes orientation in this biaxial crystal which differs substantially from previous reports. Polarized Raman spectroscopy was conducted based on this revised orientation. The absorption and stimulated emission cross-sections of the studied ions were derived for the principal light polarizations, comparing these findings with existing results to validate the new dielectric frame orientation.

---

1. Introduction

The divalent metal monotungstates, denoted as M²⁺WO₄, find applications as scintillators¹ and, when doped with rare-earth ions (RE³⁺), in solid-state lighting and lasers.^2–4 Historically the primary focus has been on their tetragonal scheelite-type phase, which occurs when M²⁺ = Ca²⁺, Sr²⁺, Ba²⁺, or Pb²⁺. Besides as laser hosts such crystals have proven to be highly suitable for Raman shifters. Their thermal conductivity (κ) is moderate, approximately 3 W m⁻¹ K⁻¹.⁵ In the tetragonal MWO₄ crystals, the RE³⁺ dopant ions replace the M²⁺ cations, however, the doping level is limited due to the mismatch of ionic radii and the need for charge compensation. Unfortunately, the tetragonal structure does not offer substantial transition cross-sections of the RE³⁺ ions for efficient lasing. Furthermore, the negative thermo-optic coefficients (dn/dt) for tetragonal M²⁺WO₄ crystals typically cannot be offset by thermal expansion. Consequently, RE³⁺-doped tetragonal M²⁺WO₄ monotungstates garnered more attention for applications as phosphors, nano- and microcrystals.⁶

Besides the tetragonal scheelite structure family of divalent metal monotungstates, there has been a growing interest in recent years in laser applications of the monoclinic structure, which occurs for M²⁺ = Mg²⁺, Zn²⁺, Cd²⁺, etc.⁷ These compounds feature a crystal symmetry known as wolframite [(Fe,Mn)WO₄] type, which falls within the monoclinic class with the space group P2/c.⁸ They exhibit a high degree of order with a single crystallographic site for the M²⁺ cations of six-fold oxygen coordination (site symmetry: C₂).⁹ Two noteworthy representatives of this crystal family are magnesium monotungstate (MgWO₄), recognized as huanzalaite in its natural mineral state, and zinc monotungstate (ZnWO₄), alternatively named sanmartinite.

These crystals are optically biaxial, offering strong optical anisotropy. Due to their appealing optical and thermal properties, introducing RE³⁺ ions to enable laser operation has been under consideration. The crystal structure of the undoped MgWO₄ has been documented in ref. 10. As a host material, it is characterized by a relatively high thermal conductivity of κ ∼8.7 W m⁻¹ K⁻¹,¹¹ as measured for a random crystal orientation. In recent years, significant efforts have been directed towards synthesizing nanocrystals and ceramics based on monoclinic M²⁺WO₄ phases.^12–14 Initially, single-crystal MgWO₄ was explored as a scintillator.^14–16 Later, it was studied as a promising host for transition-metal ions such as Cr³⁺, showing broad emission spectra in the near-infrared spectral range.¹⁷ However, achieving laser operation with Cr³⁺:MgWO₄ remains an ongoing challenge.

Previous research with RE³⁺ dopants primarily concentrated on the 1 μm spectral range by incorporating ytterbium (Yb³⁺)^3,18–20 and the 2 μm spectral range by incorporating thulium (Tm³⁺).^21–26 Notably, a diode-pumped high-power laser based on Yb³⁺:MgWO₄ was demonstrated,²⁰ delivering impressive 18.2 W near 1056 nm in a linearly polarized output with a slope efficiency of ∼89%. Pulses as short as 125 fs at 1065 nm were obtained by semiconductor saturable absorber (SESAM) mode-locking (ML) of a Yb³⁺:MgWO₄ laser at 117 Hz.¹⁹ A continuous-wave (CW) diode-pumped Tm³⁺:MgWO₄ laser generated an output power of 3.09 W in the 2022–2034 nm wavelength range with a slope efficiency of 50%.²⁰ Employing graphene for ML such a laser at a repetition rate of 76 MHz produced 86 fs pulses at 2017 nm with a bandwidth of 53 nm (ref. 21) while using single-walled carbon-nanotubes (SWCNTs), pulses as short as 76 fs could be generated at 2037 nm with a bandwidth of 64 nm for a repetition rate of 86.5 MHz.²⁵

Previous studies have revealed various favorable spectroscopic characteristics of MgWO₄ crystals doped with RE³⁺ ions. These properties include significant anisotropy of the transition cross-sections for polarized light, relatively large Stark splitting of the ground states, and the presence of unevenly broadened spectral bands. These characteristics result from the low symmetry of the RE³⁺ site, where dopant ions replace the Mg²⁺ host-forming cations, and the significant difference in ionic radii between Mg²⁺ (0.72 Å)²⁷ and the RE³⁺ dopant (e.g., the ionic radii of Tm³⁺ and Yb³⁺ for VI-fold coordination amount to 0.88 and 0.868 Å, respectively²⁷), as well as the valence state difference between the dopant and host-forming cations, leading to distortion in the local crystal field. Charge compensation occurs by M²⁺ vacations or various valence impurity cations entering the interstitial positions.^28,29 Additionally, it was suggested that incorporation of monovalent alkali-metal cations (e.g., Na⁺ from the flux in the case of MgWO₄), play a crucial role in the modification of the spectroscopic properties of these crystals.^7,23

Growing MgWO₄ crystals using the conventional Czochralski method is challenging due to their high-temperature phase transition. Instead, the top-seeded solution growth (TSSG) method is a well-documented and effective alternative for obtaining high-quality MgWO₄ crystals.^3,11 Early studies have shown that MgWO₄ crystals may exhibit notable defects affecting their optical properties.^3,30 These color centers and other defects may prevent the desired laser operation with Yb³⁺ and Tm³⁺ doped MgWO₄ crystals. Additionally, the growth duration of these crystals is a critical consideration (30 days of growth³). It can be improved by fine-tuning the growth parameters such as the choice of solvent (with lower viscosity, offering sufficient solubility of MgWO₄ and a wide enough crystallization region of monoclinic MgWO₄), solute/solvent ratio, seed orientation, cooling rate, and angular rotation velocity of the growing crystal.

In this work, high quality undoped MgWO₄ and Tm³⁺ and Yb³⁺ doped crystals were grown by the TSSG method with optimized growth time. For the first time to our knowledge, K₂W₂O₇ was used as a flux instead of Na₂WO₄. No additional post-growth annealing was applied. We provide a comprehensive analysis of the orientation of the optical indicatrix (dielectric frame) with respect to the crystallographic frame, measurements of the principal refractive indices and precise polarization-resolved spectroscopy. The present study revealed an unexpected deviation from the previously reported orientation of the optical ellipsoid used in earlier spectroscopic characterization of doped MgWO₄. The polarization-resolved spectroscopy of Tm³⁺ and Yb³⁺ doped MgWO₄ samples and the polarized Raman spectroscopy were performed according to the newly determined orientation of the principal optical axes.

2. Experimental

2.1 Crystal growth

Single crystals of MgWO₄ were grown using the TSSG method under similar conditions. The starting growth involved undoped MgWO₄ crystals, followed by two doped crystals with different RE³⁺ ion dopants, Tm³⁺ and Yb³⁺.

All samples were grown in a vertical tubular furnace, using a Kanthal wire as the heating element and an Eurotherm 903P temperature controller/programmer connected to a thyristor. A type S thermocouple, located near the heater, was used to control the furnace temperature. For the undoped crystal, K₂W₂O₇ was used as a solvent with a molar ratio of the solution composition K₂W₂O₇/MgWO₄ = 75/25. The starting materials, K₂CO₃, K₂O, MgO and WO₃, were mixed in the appropriate ratios, weighting about 240 g, and placed in a platinum (Pt) crucible with a diameter of 40 mm and a height of 52 mm. The crucible was then positioned in the center of the furnace to maintain an axial temperature gradient of 1 °C cm⁻¹, ensuring that the bottom was hotter than the surface. The mixture was homogenized by maintaining the solution at 50 °C above the expected saturation temperature (T_SA) for 9 h. The T_SA was determined with a b-oriented MgWO₄ seed in contact with the solution surface. After accurately determining T_SA by monitoring the growth and dissolution of the seed, the growth process began with the same b-oriented MgWO₄ seed, while the solution temperature was gradually decreased by 40 °C at a rate of 0.12 °C h⁻¹. The crystal was rotated at 60 rpm. Subsequently, it was removed from the solution and cooled slowly to room temperature (RT) at a rate of 40 °C h⁻¹. The obtained crystals were transparent and free from defects, with typical dimensions of 11.3 × 10.6 × 14.9 mm³ along the a* × b × c directions, see Fig. 1(a). Several identical crystal growth attempts were carried out, resulting in crystals with very similar dimensions and quality.

Fig. 1 Photographs of the crystals grown along the [010] direction: (a) undoped MgWO₄, (b) Tm³⁺:MgWO₄, and (c) Yb³⁺:MgWO₄.

For the doped crystals, a Pt crucible with a length of 47 mm and a diameter of 45 mm was used due to availability. The same starting materials were mixed. For the Tm-doped crystal, Tm₂O₃ was added according to the formula Tm_0.1Mg_0.9WO₄, with the mixture weighting 150 g. A growth approach similar to that used for the undoped crystal was applied, including growth direction, rotation speed, cooling rate, thermal gradient, and speed. The dimensions of the obtained crystals were 9.1 × 14.8 × 10.3 mm³ (a* × b × c). The as-grown crystals were transparent, as shown in Fig. 1(b). Similarly, the Yb-doped crystals were grown by adding Yb₂O₃ to the starting material, assuring a starting concentration of 10 at% of Yb³⁺ relative to Mg²⁺ in the solution. The 10% dopant concentration in the solution was chosen to reproduce the crystals reported in the literature.^3,24 The resulting crystals typically measured 6.1 × 7.7 × 12.9 mm³ (a* × b × c). These crystals were transparent, free of cracks and inclusions as shown in Fig. 1(c). All the crystals exhibited a wine-brown coloration. We attribute the coloration in our crystals to the presence of oxygen vacancies. In order to remove them, we have treated the crystals thermally in air, under some conditions of temperature and time. Because of the large volume of the crystals, the oxygen did not penetrate significantly to remove those vacancies. For that reason, after the thermal treatment we still observe the coloration.

Growing the crystals took less than 15 days each, which is twice as fast compared to previously reported growth rates for the Yb-doped MgWO₄ crystals, amounting to 30 days to achieve similar dimensions.³ This improved growth rate is attributed to the use of K₂W₂O₇ as the solvent, which facilitates faster mass and heat transport for nucleation and growth due to the lower viscosity of the solution, resulting from the higher WO₃ content.

Microprobe analysis using wavelength dispersive spectroscopy, conducted with a Cameca Camebax SX-100 analyzer, determined the actual doping levels in the crystals. The Tm³⁺ doping level was found to be 0.78 at% (ion density: N_Tm = 1.2 × 10²⁰ cm⁻³), resulting in a segregation coefficient K_Tm = C_crystal/C_solution of 0.078. For the Yb³⁺ ion, the doping level was determined to be 1.11 at% (ion density: N_Yb = 1.69 × 10²⁰ cm⁻³) with a segregation coefficient K_Yb of 0.111.

2.2 Characterization methods

To study the changes in unit cell parameters due to Yb³⁺ and Tm³⁺ doping and to calculate the linear thermal expansion tensor, small MgWO₄ single crystals were grown on a Pt rod immersed in the solution. After the crystals were cleaned, they were ground in an agate mortar and pestle for X-ray diffraction (XRD) measurements.

The unit cell parameters of the three crystals were determined from powder XRD analysis using a Bruker-AXS D8 Advance diffractometer equipped with a vertical θ–θ goniometer and Cu Kα radiation. Diffracted X-ray were detected using a LynxEye-XE-T position-sensitive detector (PSD) featuring an opening angle of 2.94°. Data were acquired over the 2θ range of 10° to 80°, with a step size of 0.02° and a step time of 2 s. The obtained XRD patterns were analyzed using Le Bail fitting, facilitated through Topas V6 software. The initial model for the Le Bail fitting was based on the crystal structure of undoped MgWO₄ (Powder Diffraction File™ (PDF®), PDF card #73-0562, The International Centre for Diffraction Data (ICDD®), ICSD code 22357).

To determine the linear thermal expansion tensor of MgWO₄, powder XRD measurements were conducted at temperatures ranging from 30 to 600 °C. The heating rate was 10 °C min⁻¹, with a delay time of 300 s before each measurement. The powder sample was placed inside an MCT-HIGHTEMP chamber with a Pt heating element. Data were collected for the same settings except for the step time which was 1 s.

In order to compare the crystalline quality when doping, a 2θ/ω scan of the (030) reflection (rocking curve) of the MgWO₄ and Yb:MgWO₄ single crystals was recorded with the same X-ray equipment used for the previous measurements. The rocking curves were obtained by scanning within a range of ±1.2° ω width by taking 120 frames at a step size of 0.02° and 10 s per frame.

The refractive indices were systematically determined for polarization along the three principal optical axes for each crystal investigated using a prism-film coupler, specifically a Metricon 2010 instrument. The samples used were 2 mm thick in the b direction, enabling the measurement of the refractive index for the three principal polarizations.

A Varian CARY 5000 spectrophotometer equipped with a Glan–Taylor polarizer was used to measure the polarized absorption spectra of cubic samples oriented in the dielectric frame for the ³H₆ → ³H₄ Tm³⁺ electronic transition and the ²F_7/2 → ²F_5/2 Yb³⁺ electronic transition.

Luminescence measurements were performed by exciting the same samples with a laser diode emitting at 966 nm for Yb³⁺ and 793 nm for Tm³⁺. The emitted light was collected in a 90° configuration. A Glan–Taylor polarizer was employed to discriminate the polarization of the luminescence.

The decay time of the luminescence was quantified using an optical spectrum analyzer (OSA, Yokogawa, model AQ6375B) in conjunction with a 2 GHz digital oscilloscope (Tektronix DPO5204B). The excitation was performed at very low power and directed towards the edge of the sample to mitigate reabsorption effects.

The Raman spectra were acquired using polarized light in conjunction with a Renishaw Via Raman confocal microscope equipped with a 50× objective. The excitation wavelength used was 633 nm, generated by a He–Ne laser, and the spectral resolution was approximately 1 cm⁻¹.

3. Results and discussion

3.1 Phase structure and lattice parameters

The crystal structure and phase were confirmed through XRD analysis. The RT XRD patterns for the 0.78% Tm:MgWO₄, 1.11% Yb:MgWO₄ and undoped MgWO₄ are presented in Fig. 2. The diffraction peaks exhibited by the crystals grown in this work, in terms of both relative intensity and position, closely align with those outlined in the crystallographic database for undoped MgWO₄, see Fig. 2. The crystal structure of MgWO₄ is monoclinic (centrosymmetric point group 2/m, space group – P2/c, No. 13). It is important to emphasize that for the crystallographic frame we adopt the a < c setting with b corresponding to the monoclinic axis according to the P2/c space group, and in addition the convention of β > 90° for the monoclinic angle^8,10 as well as righthandedness of the frame for univocal correspondence with other reference frames.

Fig. 2 Measured powder X-ray diffraction (XRD) results for the Tm-doped, Yb-doped, and undoped MgWO₄, and theoretical pattern for undoped MgWO₄ based on PDF card #73-0562.

In the pursuit of comprehending the structural modifications, the unit cell parameters of the three crystals were determined using the Le Bail method, Fig. 3.³¹ Initial unit cell parameters for the Le Bail refinement were extracted from.³² As anticipated, the obtained unit cell parameters and volume in Table 1 were larger for the doped crystals due to the larger ionic radii of the doping ions compared to Mg²⁺.²⁷

Fig. 3 Le Bail refinement of (a) Yb doped MgWO₄ (b) Tm doped MgWO₄ (c) undoped MgWO₄ crystals: experimental (black), calculated (magenta) and differential (green), vertical dashes mark the Bragg reflections.

Table 1 The unit cell parameters using Le Bail refinement

Crystal	a (Å)	b (Å)	c (Å)	β (°)	Volume (Å^3)
MgWO4	4.686(7)	5.674(1)	4.927(8)	90.710(7)	131.036(5)
0.78%Tm:MgWO4	4.693(1)	5.677(1)	4.931(6)	90.741(6)	131.382(9)
1.11%Yb:MgWO4	4.695(1)	5.677(9)	4.932(7)	90.753(7)	131.492(3)

---

The analysis of the rocking curves of the (030) reflection of MgWO₄ and Yb:MgWO₄ single crystals consists of two peaks for each crystal, corresponding to the K_α1 and K_α2 radiation from the X-ray source. For the evaluation of the crystals, we fitted both peaks to pseudo-Voigt functions. We have focused on K_α1 to extract conclusions from the measurements because of its higher intensity and found a full width at half maximum (FWHM) of the reflection to be 0.036° for MgWO₄ and 0.031° for Yb:MgWO₄, indicating the absence of significant difference between them and, due to the very small values, the high crystals quality.

3.2 Linear thermal expansion tensor

The thermal expansion of undoped MgWO₄ was studied by recording XRD patterns at temperatures of 30, 50, 100, 200, 300, 400, 500 and 600 °C. The unit cell parameters (a, b, c, and β) were determined for each temperature using the Le Bail method. All lattice constants increased linearly with temperature (see Fig. 4). The volume of the unit cell (V) showed the same behaviour of increasing with temperature.

Fig. 4 (a–e) Linear dependence of lattice constants a, b, c, and β, and the volume of the unit-cell V of undoped MgWO₄ crystal on temperature.

The coefficients of the linear thermal expansion tensor of MgWO₄ in the crystallophysic frame were obtained from the slope of the linear fits of the thermal evolution of the normalized unit cell parameters of this phase (see Fig. 5). This tensor is presented below:

with parallel to a axis, parallel to b axis and parallel to c* direction (c* = a × b), defining an orthogonal auxiliary frame.

Fig. 5 Normalized unit cell parameters of MgWO₄versus temperature, (L = a, b, c, and c × cos(β − 90°)).

By diagonalizing the previous tensor, the linear thermal expansion tensor of MgWO₄ in the eigenframe is obtained:

with the principal axis X₁ located at 35.9° (counterclockwise) from the a axis, X₂ parallel to the b axis, and X₃ at 36.6° (counterclockwise) from the c axis when the b axis shows towards the observer. The thermal expansion ellipsoid is depicted in Fig. 6.

Fig. 6 Thermal expansion ellipsoid of MgWO₄.

The above values can be compared with our previous results obtained for Ho:MgWO₄:⁷ the corresponding principal values were very close, 14.8, 8.09, and 5.07 × 10⁻⁶ K⁻¹, respectively, and the rotation angle for the X₁ axis was 37.35° for a monoclinic angle of β = 90.74°. This good agreement shades more doubt in the accuracy of the thermal expansion results reported in ref. 11 for Cr³⁺:MgWO₄ using a dilatometer.

3.3 Orientation of the optical indicatrix

The monoclinic MgWO₄ crystal is optically biaxial and as such possesses three principal optical directions (axes of the optical indicatrix) forming an orthogonal frame, which are known as N_g, N_m and N_p, according to the notation of the corresponding refractive indexes n_g > n_m > n_p, where the subscript g denotes the highest refractive index, and p denotes the lowest one. One of the principal optical axes (in this case N_m) aligns with the C₂ symmetry axis (the b axis), while the other two axes (N_p and N_g) lie in the orthogonal mirror plane (the a–c plane). These principal axes define the principal planes and light polarized in or perpendicular to these planes does not experience polarization rotation upon propagation.

Initially, the orientation of the principal optical axes for 1.25 at% Yb:MgWO₄ was studied using transmission measurements with a polarizing microscope without information on the refractive index, hence they were denoted in a neutral manner, e.g. as XYZ.³ In this work, the rotation of the two principal optical axes lying in the a–c plane around the b-axis of the quasi-orthogonal abc frame was measured to be in the 36.4–37.1° range with an obvious error seen comparing with the monoclinic angle β given (see Fig. 2 in ref. 3). This error was rectified in ref. 23 in terms of rotation of the dielectric frame relative to the abc frame in the opposite direction with the two angles in the a–c plane being the same. The refractive indices were estimated then in this new frame from transmission measurements near 1.2 μm: n_p = 1.97, n_m = 2.03, and n_g = 2.13 with an error of ± 0.02 which enabled the assignment of N_g, N_m and N_p.

Apart from the above controversial assignment of the orthogonal dielectric frame N_pN_mN_g, notable disparities surfaced between the respective spectroscopic studies, encompassing variations not only in the absolute values of absorption and stimulated emission (SE) cross-sections for the three polarizations but also in the spectral shape, with similarities observed in absorption cross-sections and marked dissimilarity in SE cross-sections.^3,20,23,24 The uncertainties led to the study and presentation of the Ho- and Er-doped MgWO₄ spectroscopy in the crystallographic frame abc.^7,30 For laser applications, however, spectroscopy in the orthogonal dielectric frame is desirable, because although this does not guarantee that cross-sections are maximized, more important is to ensure that polarization–rotation (waveplate) effects are absent in a laser emitting polarized radiation. The above discrepancies raised concerns, prompting a reassessment of the orientation of our doped MgWO₄ crystals. Initial attempts using the dielectric frame orientation from²³ yielded inaccurate results for our samples, Tm:MgWO₄ and Yb:MgWO₄, further justifying a thorough investigation into the relative frame orientation.

Subsequent to orienting our samples in the crystallographic abc frame through XRD, an examination of the principal optical axes was conducted using a crossed polarizers setup. The 2 mm thick samples, precisely cut perpendicular to the b direction, were positioned between two crossed Glan–Taylor polarizers. Through systematic rotation (with a goniometer with a precision of better than 1°), we successfully identified the principal optical axes in the a–c plane. Remarkably, one principal optical axis deviated by 6 ± 1° from the c direction (easily detectable as a natural edge of the grown crystal and confirmed by XRD), while the other was found to be exactly at 90° from the first zero transmission position. This consistent observation was replicated across all examined samples. The substantial deviation from the previously reported positions of these axes^3,23 solidified our suspicions, creating the need for an additional confirmation.

To substantiate our findings, the next investigative step involved determining the refractive index at various angles using the same goniometer relative to the c crystallographic axis for our undoped MgWO₄. The refractive index was measured with the prism coupler instrument using linearly polarized light at 633 nm and rotating the 2 mm thick polished plate around the b-axis. As shown in Fig. 7, knowing that N_g aligns with the highest refractive index while N_p corresponds to the lowest refractive index, our measurements corroborated that N_g is located at 5° from the c direction when rotating the crystal clockwise, as depicted in Fig. 7(a) and (b). Importantly, these refractive index measurements align closely with the results obtained through the crossed polarizers setup, providing further confirmation for the revised orientation of the dielectric frame of our crystal.

Fig. 7 Refractive index of MgWO₄ crystal at 633 nm for different angles φ of the polarization relative to the c crystallographic axis: (a) for the N_g principal optical direction, and (b) for the N_p principal optical direction. Inset – rotation direction of the crystal.

Based on the reproducible results obtained with different samples, we confidently assert that the dielectric frame orientations reported in earlier studies on MgWO₄-based crystals were inaccurate. Our proposed orientation, supported by a comprehensive study, diverges from previous reports. Earlier assertions placed N_g at 36.4° from the a direction,^3,23 whereas our findings conclusively determine that N_g is located at 5 ± 1° from the c direction as shown in Fig. 8. Similarly, N_p was previously reported at 37.1° from the a direction, but our results definitively place N_p at 6 ± 1° from it. Thus, the previously reported substantial angles for MgWO₄ between the crystallographic and optical axes are likely inaccurate. Fig. 8 illustrates the correct orientation we propose for the monoclinic MgWO₄ crystal.

Fig. 8 Orientation of the optical indicatrix axes (N_p, N_m, N_g) forming the orthogonal dielectric frame with respect to the crystallographic frame (a, b, c) in monoclinic MgWO₄.

Since laser elements are cut for propagation within one of the principal planes in order to avoid waveplate like polarization rotation effects, it is of practical interest to calculate the thermal expansion along the three dielectric axes of the newly determined frame. Matrix transformation gives α_p = 12.71 × 10⁻⁶ K⁻¹, α_m = 8.26 × 10⁻⁶ K⁻¹, and α_g = 7.62 × 10⁻⁶ K⁻¹.

3.4 Refractive index measurements

The refractive indices of the three different samples were measured with the prism coupler device at various angles relative to the crystallographic axes to confirm the consistency of the angle between the principal optical and crystallographic axes.

As previously mentioned, using a 633 nm He–Ne laser, we verified that the N_g axis, which is associated with the highest refractive index, is located at an angle of 5 ± 1° from the c direction. Similarly, the N_p axis, with the lowest refractive index, is situated at an angle of 95 ± 1° from the c direction, while the N_m axis is aligned parallel to the b direction. Table 2 presents the refractive indices along the three principal optical axes for the grown crystals at 633 nm.

Table 2 Refractive index for light polarization along N_p, N_m, and N_g for the undoped, Tm³⁺ doped, and Yb³⁺ doped MgWO₄ at 633 nm

Crystal	n p	n m	n g
MgWO4	1.9880	2.0478	2.2027
Tm:MgWO4	1.9889	2.0478	2.2002
Yb:MgWO4	1.9894	2.0476	2.2011

---

3.5 Polarized Raman spectroscopy

Polarized Raman spectra of MgWO₄ were previously presented in ref. 23 for Tm doping and in ref. 20 for Yb doping. To further characterize the doped crystals in the newly determined dielectric frame, we measured the polarized Raman spectra for both Tm³⁺:MgWO₄ and Yb³⁺:MgWO₄ at RT, as illustrated in Fig. 9. We used Porto's notation m(nk)l̄, where ‘m’ and ‘l̄’ indicate the propagation directions of the excitation and scattered light, respectively, while ‘n’ and ‘k’ represent the corresponding polarization states.

Fig. 9 Polarized Raman spectra for g(_)ḡ, m(_)m̄, and p(_)p̄ of (a–c) Tm doped MgWO₄ crystal and (d–f) Yb doped MgWO₄ crystal. The excitation wavelength was 633 nm.

In the monoclinic structure of MgWO₄, there are two unit formulas per unit cell (Z = 2). According to factor group theory, 36 lattice modes are predicted at the centre of the Brillouin zone: Γ(k = 0) = 8A_g + 10B_g + 8A_u + 10B_u. Of these, 18 modes are Raman-active (even modes A_g and B_g), and 18 are IR-active (odd modes A_u and B_u). All the modes for MgWO₄ were assigned in ref. 33.

In the Tm³⁺:MgWO₄ and Yb³⁺:MgWO₄ crystals, the most intense mode, occurring around 918 cm⁻¹, corresponds to symmetric stretching W–O vibrations (ν₁ mode, A_1g symmetry) within the WO₆ octahedra, while modes around 813 cm⁻¹ and 711 cm⁻¹ are assigned to asymmetric stretching (ν₂ mode, E_g symmetry). Notably, a trend in peak intensities is evident. For instance, the peak at approximately 918 cm⁻¹ (an A_g mode) is prominent in the pp, mm, and gg polarizations for different directions of excitation and scattered light, while it is less pronounced in other polarizations. This pattern is observed for several A_g mode peaks. Conversely, B_g modes, such as those around 813 cm⁻¹ and 102 cm⁻¹, are less pronounced in the pp, mm, and gg polarizations and clearer in other polarizations.

When comparing our Raman spectra of Yb:MgWO₄ crystal with those reported in ref. 20 for m(_)m̄ configuration, notable differences in peak intensities are observed, particularly for the m(pg)m̄ polarization configuration. In this work, m(pg)m̄ shows unexpectedly high intensities across several A_g modes, comparable to m(pp)m̄, while in the present measurements, m(pg)m̄ yields much lower intensities. This discrepancy may indicate possible differences in crystal orientation but one cannot rule out the effect of different actual doping levels as well.

3.6 Optical spectroscopy

Polarized optical absorption measurements of Tm³⁺:MgWO₄ and Yb³⁺:MgWO₄ at RT were performed in the newly determined dielectric frame. Fig. 10 depicts the obtained absorption cross-sections (σ_abs) for the Tm³⁺ and Yb³⁺ doped MgWO₄ crystals, derived as σ_abs = α_abs/N_Tm/Yb, where α_abs is the measured absorption coefficient, and N_Tm and N_Yb are the actual Tm³⁺ and Yb³⁺ ion density respectively. The polished cubic samples had dimensions of 4.74 × 6.04 × 5.34 mm³ for Tm:MgWO₄ and 2.86 × 3.57 × 2.56 mm³ for Yb:MgWO₄, both aligned along the principal optical directions N_p, N_m, and N_g, respectively.

Fig. 10 Absorption cross-sections, σ_abs, for light polarizations E||N_g, N_m, and N_p for: (a) Tm³⁺ doped MgWO₄ crystal and (b) Yb³⁺ doped MgWO₄ crystal.

High-brightness Ti–sapphire lasers or high-power AlGaAs diode lasers, emitting at approximately 800 nm, are suitable for pumping Tm³⁺-doped crystals due to the ³H₆ → ³H₄ transition of the Tm³⁺ ion. The maximum absorption cross-section (σ_abs) of Tm³⁺:MgWO₄ amounts to 2.42 × 10⁻²⁰ cm² at 803 nm, for light polarization E||N_g, and the corresponding absorption bandwidth (FWHM) is 15.5 nm, see Fig. 10(a). The σ_abs values are lower for the other principal polarizations. For E||N_p, σ_abs = 0.45 × 10⁻²⁰ cm² at 802 nm, and for E||N_m, σ_abs = 1.59 × 10⁻²⁰ cm² at 807 nm. Notably for E||N_m, the absorption bandwidth is superior, FWHM = 20 nm. The absorption bands around 800 nm are in general significantly wider than what is typically observed in monoclinic double tungstates such as Tm³⁺:KLu(WO₄)₂. In the latter, for E||N_m the absorption cross-section (σ_abs) reaches a value of 5.95 × 10⁻²⁰ cm² at 802 nm, yet the absorption bandwidth is 4 nm.³⁴ Such broadband absorption behavior significantly simplifies the task of wavelength stabilization for AlGaAs pump laser diodes.

Fig. 10(b) shows the polarized absorption cross-section of Yb³⁺:MgWO₄ around 1 μm, associated with the ²F_7/2 → ²F_5/2 electronic transition. Yb³⁺:MgWO₄ features strongly anisotropic absorption properties. The maximum σ_abs amounts to 6.1 × 10⁻²⁰ cm² at 974 nm, corresponding to a FWHM of 6 nm, for light polarization E||N_g, and this peak is associated with the so-called zero-phonon-line (ZPL) in absorption for the Yb³⁺ ion. When compared to Yb:KLu(WO₄)₂ with its σ_abs = 1.47 × 10⁻¹⁹ cm² at 981.1 nm (E||N_m), the absorption in Yb³⁺:MgWO₄ is roughly two times lower but has a broader FWHM (6 vs. 3.5 nm).³² For the other two polarizations, the absorption at this wavelength is lower: σ_abs = 2.24 × 10⁻²⁰ cm² for E||N_m, and σ_abs = 0.94 × 10⁻²⁰ cm² for E||N_p. Notably, these maximum σ_abs values are almost twice as high as those reported for the isostructural Yb³⁺:ZnWO₄, for which a maximum σ_abs of 2.73 × 10⁻²⁰ cm² at 973.5 nm was measured with a FWHM = 6 nm, for E||N_g.³⁵

In the case of Tm-doping, the results obtained in the XYZ frame^22,24 are very close to our present results. Comparing with previously published absorption spectra, the difference is stronger for Yb-doping: the cross-sections obtained in ref. 3 in the XYZ frame are much lower although the spectral shapes look similar. The results in ref. 20 are very close to the present ones since they were obtained after an independent alignment in the dielectric frame N_pN_mN_g between crossed polarizers and were thus independent of the exact frame location relative to the crystallographic frame.

The SE cross-section, σ_SE, was calculated using a combination of two methods. The first method employed the Füchtbauer–Ladenburg (F–L) equation³⁶ based on the measured luminescence intensity W(λ):

where λ denotes the luminescence wavelength, 〈n〉 is the refractive index at the average emission wavelength; τ_rad is the radiative lifetime associated with the ³F₄ state of Tm³⁺ and the ²F_5/2 state of Yb³⁺, c is the speed of light; and the subscripts i and j = p, m, g indicate the polarization state.

The second approach used was based on the reciprocity method (RM),³⁷ using the Stark splitting data determined in ref. 23 for the Tm³⁺ ion and in ref. 20 for the Yb³⁺ ion:

where σⁱ_abs is the absorption cross-section for the i-th polarization, h is Planck's constant, k is the Boltzmann constant, T is the crystal temperature (RT), E_ZPL is the energy difference between the lowest Stark sub-levels of the two multiplets involved in the transition (ZPL), and Z_l are the partition functions of the lower (l = 1) and upper (l = 2) manifolds.

The maximum SE cross-section (σ_SE) for Tm³⁺:MgWO₄ is observed at 1876 nm for E||N_m, amounting to 3.33 × 10⁻²⁰ cm², see Fig. 11(a). For Yb³⁺:MgWO₄, the maximum σ_SE reaches 6.63 × 10⁻²⁰ cm² at 1058 nm, again for E||N_m, while for E||N_g and E||N_p, σ_SE at the same wavelength drops to 1.98 × 10⁻²⁰ and 0.54 × 10⁻²⁰ cm², respectively. Notably, for E||N_g, maximum σ_SE occurs at 974 nm, reaching 5.93 × 10⁻²⁰ cm², which is close to the maximum value observed for E||N_m, see Fig. 11(b). For both dopant ions, a strong anisotropy of the SE cross-section is observed, implying a natural selection of a linear polarization for laser emission.

Fig. 11 Stimulated emission cross-sections, σ_SE, for the principal light polarizations E||N_p, N_m, and N_g of (a) Tm³⁺ doped MgWO₄ crystal and (b) Yb³⁺ doped MgWO₄ crystal.

The obtained SE cross-sections for Tm³⁺:MgWO₄, are higher for the two dominating polarizations (E||N_g and E||N_m) than the previously obtained values in what was thought to be the dielectric frame, both when denoted as XYZ²⁴ and as N_pN_mN_g.²³ For Yb³⁺:MgWO₄, the difference compared to the XYZ assumption³ is much larger, showing in roughly two times higher values and very different shapes, whereas minor discrepancies are observed comparing with results reported in ref. 20 in the N_pN_mN_g frame.

For quasi-3-level laser systems the expected oscillation wavelength can be estimated from the corresponding gain cross-sections, σ_gain. The gain profiles for Tm³⁺ and Yb³⁺ doped MgWO₄ were calculated using the relation σ_gain = β_iσ_SE − (1 − β_i)σ_abs, where β_i = N₂/N_RE represents the population inversion ratio, i.e. the ratio of dopant ions in the excited state, N₂, to the total ion density N_RE. Here, N₂ corresponds to the upper laser states ³F₄ for Tm³⁺ and ²F_5/2 for Yb³⁺.

The gain spectra associated with the ³F₄ → ³H₆ transition in Tm³⁺:MgWO₄ are displayed in Fig. 12(a)–(c) for the three principal light polarizations E||N_g, N_m, N_p. The maximum σ_gain is observed for the E||N_m polarization, with a local maximum at ∼2020 nm at lower inversion ratios (β_i < 0.3), which suggest a linearly polarized laser output along N_m at wavelengths exceeding 2 μm. This wavelength range is accessible due to the pronounced Stark splitting of the Tm³⁺ ground-state (³H₆) in MgWO₄, ΔE(³H₆) = 633 cm⁻¹,²³ an important advantage over the monoclinic double tungstates such as Tm³⁺:KLu(WO₄)₂ when it comes to mode-locking in the sub-100 fs regime in relation to structured water vapor air absorption below 2 μm.^21,25 No such local maximum is seen for the other strong polarization E||N_g. One of these two polarizations will be naturally selected for any principal cut of the laser element. All previous laser studies have been based on the strongest E||N_m output polarization (sometimes designated as E||Y).

Fig. 12 Gain cross sections, σ_gain, for (a–c) Tm³⁺-doped and (d–f) Yb³⁺-doped monoclinic MgWO₄ for polarizations along the principal optical axes E||N_g (a and d), N_m (b and e), and N_p (c and f), respectively.

The polarized σ_gain spectra corresponding to the ²F_5/2 → ²F_7/2 transition in Yb³⁺:MgWO₄ are shown in Fig. 12(d)–(f). Again, the E||N_m polarization yields the highest σ_gain centered around 1057 nm. This is consistent with previously reported linear output polarization from Yb:MgWO₄ lasers. The only occasion when E||N_g was utilized was in a mode-locked laser,²¹ just to confirm that its performance is inferior notwithstanding the superior absorption efficiency, cf.Fig. 11(b). Note that the weakest polarization E||N_p has never been studied in a Tm or Yb lasers based on MgWO₄. It can be only imposed by a Brewster angle of the laser element surfaces and is potentially interesting only in Q-switched lasers to obtain higher output energies and peak powers.

Compared to previously reported σ_gain calculations for both Tm³⁺ and Yb³⁺ doped MgWO₄ crystals, our results are higher^20,22,24 or much higher and different compared to ref. 3 where the XYZ frame was used; note also that there shall be typographical errors in Fig. 3 of ref. 20 where these cross-sections for Yb³⁺:MgWO₄ shall be actually ten times higher.

The luminescence lifetimes (τ_lum) of the ³F₄ state of Tm³⁺ and the ²F_5/2 state of Yb³⁺ in MgWO₄ were determined through temporal decay measurements. For Tm³⁺ ions excited at 793 nm, the luminescence decay at 1878 nm was monitored, see Fig. 13(a), revealing a lifetime of 1.81 ms. This value is comparable to the previously reported lifetime for Tm³⁺:MgWO₄, τ_lum = 1.93 ms (ref. 24) and Tm³⁺,Li⁺:ZnWO₄, τ_lum = 2.08 ms.³⁸ For Yb³⁺:MgWO₄, the lifetime was derived by exciting Yb³⁺ at 966 nm and monitoring the luminescence at 1057 nm, see Fig. 13(b), yielding a decay constant of 388 μs. This result aligns with earlier measurements for Yb³⁺:MgWO₄ (366 μs),³ and Yb³⁺,Li⁺:ZnWO₄ (367 μs).³⁹ Notably, the decay curves exhibited a single exponential pattern, consistent with the presence of a single site for both Tm³⁺ and Yb³⁺ ions in MgWO₄.

Fig. 13 Decay curves of (a) the Tm^{3+ 3}F₄ state and (b) the Yb^{3+ 2}F_5/2 state in MgWO₄: symbols – experimental data, solid lines – single-exponential fits.

Conclusions

In summary, we have successfully grown monoclinic MgWO₄ crystals, both undoped and doped with Tm³⁺ and Yb³⁺ ions, using K₂W₂O₇ as a solvent for the first time. This method significantly reduced the growth time to 15 days, which is half the duration reported in previous studies for crystals of similar size. We also determined the orientation of the principal optical axes relative to the crystallographic axes and obtained polarized absorption, stimulated emission, and gain cross-section spectra for the relevant transitions of the Tm³⁺ and Yb³⁺ ions, as well as polarized Raman spectra.

Our analysis revealed that the angle between the principal optical axis N_g, corresponding to the highest refractive index, and the crystallographic axis c is only 5 ± 1°. This finding corrects a recurring error in prior studies regarding the orientation of MgWO₄ crystals. The partial consistency of our absorption and stimulated emission cross-section data with some of the literature further supports that previous misidentifications were likely due to incorrect crystallographic axes orientation. However, it is difficult to evaluate the impact of wrong active element orientation in previous laser experiments carried out with Tm³⁺:MgWO₄ and Yb³⁺:MgWO₄ crystals. They were all based on the best E||N_m polarization.^3,7,18–26 The direction N_m is in fact easy to identify since in MgWO₄ it is perpendicular to a natural crystal surface, however, the crystal cut utilizing this polarization might be still erroneous. A wrong cut for the propagation direction might result in lower gain cross-sections even though the propagating beam in the crystal is an eigen polarization, when this happens in a principal plane containing the N_m principal optical axis.

Summarizing, the doped MgWO₄ crystals exhibit broad spectral bands and pronounced polarization anisotropy in their transition cross-sections, and both with Tm and Yb active ions are very promising for high-power sub-100 fs pulse generation from mode-locked lasers.

Data availability

The data supporting our findings are available from the corresponding author upon reasonable request.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was financially supported by project PID2022-141499OB-100, funded by MICIU/AEI/10.13039/501100011033/ and by FEDER/UE.

References

1. J. Zhang, J. Pan, J. Yin, J. Wang, J. Pan, H. Chen and R. Mao, Structural investigation and scintillation properties of Cd1−xZnxWO4 solid solution single crystals, CrystEngComm, 2015, 17, 3503–3508.
2. X. Wang, Z. Fan, H. Yu, H. Zhang and J. Wang, Characterization of ZnWO₄ Raman crystal, Opt. Mater. Express, 2017, 7, 1732–1744.
3. L. Zhang, W. Chen, J. Lu, H. Lin, L. Li, G. Wang, G. Zhang and Z. Lin, Characterization of growth, optical properties, and laser performance of monoclinic Yb:MgWO₄ crystal, Opt. Mater. Express, 2016, 6, 1627–1634.
4. J. Chen, L. Dong, F. Liu, H. Xua and J. Liu, Investigation of Yb:CaWO4 as a potential new self-Raman laser crystal, CrystEngComm, 2021, 23, 427–435.
5. P. A. Popov, S. A. Skrobov, E. V. Zharikov, D. A. Lis, K. A. Subbotin, L. I. Ivleva, V. N. Shlegel', M. B. Kosmyna and A. N. Shekhovtsov, Investigation of the thermal conductivity of tungstate crystals, Crystallogr. Rep., 2018, 63, 111–116.
6. D. Kumar, B. P. Singh, M. Srivastava, A. Srivastava, P. Singh, A. Srivastava and S. K. Srivastava, Structural and photoluminescence properties of thermally stable Eu³⁺ activated CaWO₄ nanophosphor via Li⁺ incorporation, J. Lumin., 2018, 203, 507–514.
7. L. Zhang, P. Loiko, J. M. Serres, E. Kifle, H. Lin, G. Zhang, E. Vilejshikova, E. Dunina, A. Kornienko, L. Fomicheva, U. Griebner, V. Petrov, Z. Lin, W. Chen, K. Subbotin, M. Aguiló, F. Díaz and X. Mateos, Growth, spectroscopy and first laser operation of monoclinic Ho³⁺:MgWO₄ crystal, J. Lumin., 2019, 213, 316–325.
8. E. Cavalli, A. Belletti and M. G. Brik, Optical spectra and energy levels of the Cr³⁺ ions in MWO₄ (M=Mg, Zn, Cd) and MgMoO₄ crystals, J. Phys. Chem. Solids, 2008, 69, 29–34.
9. P. F. Schofield, K. S. Knight and G. Cressey, Neutron powder diffraction study of the scintillator material ZnWO₄, J. Mater. Sci., 1996, 31, 2873–2877.
10. V. B. Kravchenko, Crystal structure of the monoclinic form of magnesium tungstate MgWO₄, J. Struct. Chem., 1969, 10, 139–140.
11. L. Zhang, Y. Huang, S. Sun, F. Yuan, Z. Lin and G. Wang, Thermal and spectral characterization of Cr³⁺:MgWO₄—a promising tunable laser material, J. Lumin., 2016, 169, 161–164.
12. E. N. Sota, F. Che Ros and J. Hassan, Synthesis and characterisation of AWO₄ (A = Mg, Zn) tungstate ceramics, J. Phys.: Conf. Ser., 2018, 1083, 012002.
13. S. Wannapop, T. Thongtem and S. Thongtem, Photoemission and energy gap of MgWO₄ particles connecting as nanofibers synthesized by electrospinning–calcination combinations, Appl. Surf. Sci., 2012, 258, 4971–4976.
14. J. Meng, T. Chen, X. Wei, J. Li and Z. Zhang, Template-free hydrothermal synthesis of MgWO₄ nanoplates and their application as photocatalysts, RSC Adv., 2019, 9, 2567–2571.
15. F. A. Danevich, D. M. Chernyak, A. M. Dubovik, B. V. Grinyov, S. Henry, H. Kraus, V. M. Kudovbenko, V. B. Mikhailik, L. L. Nagornaya, R. B. Podviyanuk, O. G. Polischuk, I. A. Tupitsyna and Y. Y. Vostretsov, MgWO₄–A new crystal scintillator, Nucl. Instrum. Methods Phys. Res., Sect. A, 2009, 608, 107–115.
16. V. B. Mikhailik, H. Kraus, V. Kapustyanyk, M. Panasyuk, Y. Prots, V. Tsybulskyi and L. Vasylechko, Structure, luminescence and scintillation properties of the MgWO₄–MgMoO₄ system, J. Phys.: Condens. Matter, 2008, 20, 365219.
17. L. Li, Y. Yu, G. Wang, L. Zhang and Z. Lin, Crystal growth, spectral properties and crystal field analysis of Cr³⁺:MgWO₄, CrystEngComm, 2013, 15, 6083–6089.
18. J. Lu, H. Lin, G. Zhang, B. Li, L. Zhang, Z. Lin, Y.-F. Chen, V. Petrov and W. Chen, Direct generation of an optical vortex beam from a diode-pumped Yb:MgWO₄ laser, Laser Phys. Lett., 2017, 14, 085807.
19. H. Lin, G. Zhang, L. Zhang, Z. Lin, F. Pirzio, A. Agnesi, V. Petrov and W. Chen, Continuous-wave and SESAM mode-locked femtosecond operation of a Yb:MgWO₄ laser, Opt. Express, 2017, 25, 11827–11832.
20. P. Loiko, M. Chen, J. M. Serres, M. Aguiló, F. Díaz, H. Lin, G. Zhang, L. Zhang, Z. Lin, P. Camy, S.-B. Dai, Z. Chen, Y. Zhao, L. Wang, W. Chen, U. Griebner, V. Petrov and X. Mateos, Spectroscopy and high-power laser operation of a monoclinic Yb³⁺:MgWO₄ crystal, Opt. Lett., 2020, 45, 1770–1773.
21. Y. Wang, W. Chen, M. Mero, L. Zhang, H. Lin, Z. Lin, G. Zhang, F. Rotermund, Y. J. Cho, P. Loiko, X. Mateos, U. Griebner and V. Petrov, Sub-100 fs Tm:MgWO₄ laser at 2017 nm mode locked by a graphene saturable absorber, Opt. Lett., 2017, 42, 3076–3079.
22. P. Loiko, J. M. Serres, X. Mateos, M. Aguilo, F. Diaz, L. Zhang, Z. Lin, H. Lin, G. Zhang, K. Yumashev, V. Petrov, U. Griebner, Y. Wang, S. Y. Choi, F. Rotermund and W. Chen, Monoclinic Tm³⁺:MgWO₄: a promising crystal for continuous-wave and passively Q-switched lasers at ∼2 μm, Opt. Lett., 2017, 42, 1177–1180.
23. P. Loiko, Y. Wang, J. M. Serres, X. Mateos, M. Aguiló, F. Díaz, L. Zhang, Z. Lin, H. Lin, G. Zhang, E. Vilejshikova, E. Dunina, A. Kornienko, L. Fomicheva, V. Petrov, U. Griebner and W. Chen, Monoclinic Tm:MgWO₄ crystal: Crystal-field analysis, tunable and vibronic laser demonstration, J. Alloys Compd., 2018, 763, 581–591.
24. L. Zhang, H. Lin, G. Zhang, X. Mateos, J. M. Serres, M. Aguiló, F. Díaz, U. Griebner, V. Petrov, Y. Wang, P. Loiko, E. Vilejshikova, K. Yumashev, Z. Lin and W. Chen, Crystal growth, optical spectroscopy and laser action of Tm³⁺-doped monoclinic magnesium tungstate, Opt. Express, 2017, 25, 3682–3693.
25. L. Wang, W. Chen, Y. Zhao, Y. Wang, Z. Pan, H. Lin, G. Zhang, L. Zhang, Z. Lin, J. E. Bae, T. G. Park, F. Rotermund, P. Loiko, X. Mateos, M. Mero, U. Griebner and V. Petrov, Single-walled carbon-nanotube saturable absorber assisted Kerr-lens mode-locked Tm:MgWO₄ laser, Opt. Lett., 2020, 45, 6142–6145.
26. E. Kifle, P. Loiko, J. R. Vazquez De Aldana, C. Romero, V. Llamas, J. M. Serres, M. Aguilo, F. Diaz, L. Zhang, Z. Lin, H. Lin, G. Zhang, V. Zakharov, A. Veniaminov, V. Petrov, U. Griebner, X. Mateos and W. Chen, Low-loss fs-laser-written surface waveguide lasers at >2 μm in monoclinic Tm³⁺:MgWO₄, Opt. Lett., 2020, 45, 4060–4063.
27. R. D. Shannon and C. T. Prewitt, Revised values of effective ionic radii, Acta Crystallogr., Sect. B, 1970, 26, 1046–1048.
28. A. Lupei, V. Lupei, C. Gheorghe, L. Gheorghe and A. Achim, Multicenter structure of the optical spectra and the charge-compensation mechanisms in Nd: SrWO₄ laser crystals, J. Appl. Phys., 2008, 104, 083102.
29. W. Kolbe, K. Petermann and G. Huber, Broadband emission and laser action of Cr³⁺ doped zinc tungstate at 1 μm wavelength, IEEE J. Quantum Electron., 1985, 21, 1596–1599.
30. L. Zhang, L. Basyrova, P. Loiko, P. Camy, Z. Lin, G. Zhang, S. Slimi, R. M. Solé, X. Mateos, M. Aguiló, F. Díaz, E. Dunina, A. Kornienko, U. Griebner, V. Petrov, L. Wang and W. Chen, Growth, structure, and polarized spectroscopy of monoclinic Er³⁺:MgWO₄ crystal, Opt. Mater. Express, 2022, 12, 2028–2040.
31. A. Le Bail, Whole powder pattern decomposition methods and applications: A retrospection, Powder Diffr., 2005, 20, 316–326.
32. N. J. Dunning and H. D. Megaw, The crystal structure of magnesium tungstate, Trans. Faraday Soc., 1946, 42, 705–709.
33. J. Ruiz-Fuertes, D. Errandonea, S. López-Moreno, J. González, O. Gomis, R. Vilaplana, F. J. Manjón, A. Muñoz, P. Rodríguez-Hernández, A. Friedrich, I. A. Tupitsyna and L. L. Nagornaya, High-pressure Raman spectroscopy and lattice-dynamics calculations on scintillating MgWO₄: Comparison with isomorphic compounds, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 83, 214112.
34. V. Petrov, M. C. Pujol, X. Mateos, Ò. Silvestre, S. Rivier, M. Aguiló, R. M. Solé, J. Liu, U. Griebner and F. Díaz, Growth and properties of KLu(WO₄)₂, and novel ytterbium and thulium lasers based on this monoclinic crystalline host, Laser Photonics Rev., 2007, 1, 179–212.
35. G. Z. Elabedine, K. Subbotin, P. Loiko, Y. Zimina, S. Pavlov, A. Titov, P. Camy, A. Braud, R. M. Solé, M. Aguiló, F. Díaz, W. Chen, X. Mateos and V. Petrov, Monoclinic Yb³⁺,Li⁺:ZnWO₄ – efficient broadly emitting laser material, Proc. SPIE, 2024, 12864, 128640K.
36. B. F. Aull and H. P. Jenssen, Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections, IEEE J. Quantum Electron., 1982, 18, 925–930.
37. S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway and W. F. Wyers, Infrared cross-section measurements for crystals doped with Er³⁺, Tm³⁺, and Ho³⁺, IEEE J. Quantum Electron., 1992, 28, 2619–2630.
38. G. Z. Elabedine, K. Subbotin, P. Loiko, Z. Pan, Y. Zimina, K. Kuleshova, A. Titov, A. Nady, P. Camy, A. Braud, R. M. Solé, M. Aguiló, F. Díaz, W. Chen, W. Chen, X. Mateos, X. Mateos and V. Petrov, Monoclinic Tm³⁺:ZnWO₄: Novel 2 μm laser crystal, Advanced Solid State Lasers Conference, Tacoma (WA), USA, Oct 8, 2023, vol. 12, OPTICA Online Technical Digest, paper AW1A.5.
39. A. Volokitina, S. P. David, P. Loiko, K. Subbotin, A. Titov, D. Lis, R. M. Solé, V. Jambunathan, A. Lucianetti, T. Mocek, P. Camy, W. Chen, U. Griebner, V. Petrov, M. Aguiló, F. Díaz and X. Mateos, Monoclinic zinc monotungstate Yb³⁺,Li⁺:ZnWO₄: Part II. Polarized spectroscopy and laser operation, J. Lumin., 2021, 231, 117811.

---

Footnote

† Serra Húnter Fellow, Spain.

---