8. A Spectrally Broadened Disordered Crystal for ... - ACS Publications

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Crystal Growth and Physical Characterization of Monoclinic Li3Lu3Ba2(MoO4)8. A Spectrally Broadened Disordered Crystal for Ultrafast Mode-Locked Lasers Xiumei Han, Rocío Calderón-Villajos, Fátima Esteban-Betegón, Concepción Cascales, and Carlos Zaldo* Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, c/Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain

Andrzej Jezowski and Piotr Stachowiak Institute of Low Temperature and Structure Research, Polish Academy of Sciences, 2 Okolna Street, 50-422 Wroclaw, Poland S Supporting Information *

ABSTRACT: Undoped Li3Lu3Ba2(MoO4)8 monoclinc (C2/c) single crystals, as well as crystals doped with Tm or Ho and codoped with Tm and Ho, have been grown by the top seeded solution growth method using Li2MoO4 as the solvent. A convenient growth flux was found for the solute/ solvent molar composition of 1:5; for this, the growth temperature interval was ≈1073−1053 K, with a cooling rate of 0.05 K/h. The crystal shape is controlled by the seed orientation, and a- and b-oriented seeds give rise to near rectangular cross sections while c-oriented seeds produce rhombohedral cross sections. The grown crystals are deficient in Li with regard to the nominal formula. Li and Lu (Tm, Ho) ions share the same 8f crystal site with occupancy factors near 0.2 and 0.8, respectively. The relationships between the crystallographic and physical frames of some crystal properties (thermal expansion, refractive indices, and optical absorption) are determined as well as the specific heat and thermal conductivity (along a- and b-crystal axes). Perspectives for application of these disordered crystals as mode-locked ultrafast laser media are discussed.

1. INTRODUCTION Ultrafast solid state lasers require the use of optical gain media with large optical bandwidths (Δν). While such large bandwidths are intrinsic for d−d electronic transitions of transition metal ions due to coupling with lattice vibrations, that is, in Ti3+ (3d1), trivalent lanthanides (Ln) are characterized by spectrally narrow bands due to the shielding of 4fn valence electrons by the outer though less energetic 5s and 5p orbitals. However, the use of Tm3+ or Yb3+ as lasants is desirable because of their large absorption cross sections at the emission of AlGaAs (at λ ≈ 800 nm) and InGaAs (at λ ≈ 980 nm) diode lasers, respectively. Coincidentally, Tm3+ (4f12) and Yb3+ (4f13) have the largest number of electrons among the optically active 4fn lanthanides (Ln) and therefore are less shielded from the crystalline environment than other Ln3+ lasants, such as Nd3+ (4f3), Ho3+ (4f10), or Er3+ (4f11). This leads to comparatively larger bandwidths for Tm3+ and Yb3+ absorption and emission bands. Yb3+-doped traditional laser crystals, such as YAG,1 LiYF4,2 or Lu2O3,3 have been widely tested in fs mode-locked solid state lasers. It was soon realized that the laser pulse duration was limited by the time-bandwidth product (Δν × Δt, Δt is the pulse duration) of these crystals. Pulses of ∼340 fs were obtained from a semiconductor saturable absorption mirror (SESAM) ended oscillator © XXXX American Chemical Society

when a large gain cross section but narrow (fwhm < 10 nm) λ = 1030 nm emission of Yb-doped YAG was used1 and 35 ps was obtained under similar conditions for Tm-doped YAG.4 In the particular case of Yb-doped YAG shorter pulses ( 20σ(I). The calculations have been performed using the SHELXTL program.20 Further details of the data collection and analytical treatment were similar to those previously described for the isostructural monoclinic C2/c Yb:Li3Gd3Ba2(MoO4)8 single crystal.15 Rocking curves were collected at room temperature by using a Bruker four circles texture diffractometer equipped with a Cu anode. Thermal expansion coefficients were obtained from X-ray powder diffraction (XRPD) scans collected by using a Panalytical X′Pert PRO MPD diffractometer system, with a PW3050/60 goniometer in θ−θ scan configuration and a X′Celerator detector, equipped with an Anton Paar HTK-1200 high temperature chamber. Monochromatic Cu K α1 radiation (λ = 1.540560 Å) from a PW3373/00 X-ray tube was used, and the generator was set to 45 kV and 40 mA. The samples were disposed in alumina holder disks, and the scans cover the 2θ range between 5 and 70°, in continuous scan mode with an angular step size of 0.0334° and a counting step time of 2 s. Specific heat (Cp) was measured at room temperature with a Quantum Design Physical Property Measurement system and above room temperature (300−573 K) by using a DSC apparatus. The thermal conductivity coefficient (κ) was measured in the temperature range 4−330 K by the steady-state longitudinal heat-flow method.21,22 For these measurements, a liquid helium cryostat enabling control over this temperature range was used. A crystal bar with rectangular 4.050(b) × 2.967(c) mm2 cross section and 7.998(a) mm of length was mounted in the above cryostat and used for the study of heat propagation along the direction with the largest dimension (a-axis). During the measurements the temperature gradient along the sample did not exceed 0.02 K/mm, and extreme care was taken to eliminate parasitic heat flow between samples and their surrounding. Further, κ was calculated in the 300− 573 K range from crystal density (Ω), Cp and the thermal diffusion constant (D) as κ(T)= Ω(T) × Cp(T) × D(T). Ω(T) was obtained from the thermal expansion measurements, and D(T) was measured by the laser flash method23 by using a Holometric equipment, model Thermaflash 2200. In the latter measurements, a 10 atom %Tm:0.2 atom %Ho:Li3Lu3Ba2(MoO4)8 crystal with dimensions 8(a) × 8(a) × 0.95(b) mm3 was coated with gold and carbon and heated in Ar atmosphere for measurements along the b-axis. The refractive indices were determined by the minimum deviation angle method using three crystal prisms, in each case with the a′, b′, and ́ c′ indicatrix principal axes vertical, and by propagation of light polarized parallel to these axes. The uncertainty of the measured refractive index is ±0.003. Optical absorption spectra were collected with a Varian spectrophotometer, model Cary 5E, at room and cryogenic temperatures using a closed cycle He cryostat. The spectrophotometer light was polarized with a Glan-Taylor prism and the sample was rotated in situ using a goniometer.

Recently, the Ln-doped Li3T3Ba2(MoO4)8 crystal family was suggested for these laser purposes.12,13 Li3Gd3−xYbxBa2(MoO4)8 crystals were shown to belong to the monoclinic C2/c (No. 15) space group, but contrary to previous crystallographic determinations,14 it was shown that only a 8f site is shared by Li, Gd (and Yb) with occupancy factors of 0.215, 0.725 (and 0.060), respectively.15 Since then, a few studies have reported isostructural crystals with T = Y (Nd-doped),13 La (Nd-doped),16 Gd (Nd-16 or Yb-17doped), and Lu (Tm-doped).18 These studies provided spectroscopic information of Nd3+, Yb3+, and Tm3+ ions, but very little information is available on the crystal growth details or about the structural and physical properties of the crystals. This is particularly needed to guide the laser applications of these crystals since the monoclinic symmetry implies biaxial crystals, and therefore crystallographic and physical frames do not coincide. The present work addresses this lack of information by establishing for Li3Lu3Ba2(MoO4)8 crystals the details of the crystal growth, crystal morphology, and crystallography. Moreover, the principal directions of the thermal expansion, refractive index, and Tm3+ and Ho3+ optical absorption/emission properties are determined along with results of the specific heat and thermal conductivity. The Tm and Ho dopant ions are selected on the basis of the strong energy transfer between them leading to an efficient emission at λ ≈ 2.06 μm, a combination that has been used previously to obtain the shortest (191 fs) mode-locked laser pulses at this wavelength in a solid state crystalline laser using the also disordered Tm:Ho:NaY(WO4)2 crystal.19

2. EXPERIMENTAL SECTION Differential scanning calorimetry (DSC) experiments were performed with a Setaram system, model SetSys Evolution 1700 DTG-DSC. DSC experiments were made in Ar atmosphere using platinum crucibles with a heating/cooling rate of 10 K/min. Crystal growth was carried out using vertical tubular furnaces with heating elements made of Kantal A1. Powdered 99% Li2CO3, 98% BaCO3, and 99.5% MoO3 from Alfa Aesar, as well as 99.99% Lu2O3, Ho2O3, and Tm2O3 powders purchased through Shanghai Zimei International Trade Co. Ltd. were used as raw materials. The raw oxides and carbonates powders were mixed to achieve the desired amounts of solute, Li3Lu3−x−yTmxHoyBa2(MoO4)8, and solvent, Li2MoO4, and held in platinum crucibles of 75 mL of volume. The crucible was heated at 100 K/h up to ≈50 K above the melting temperature of the mixture. The melt was held at this temperature for 12 h to allow melt homogenization, and afterward the crucible temperature was decreased to obtain melt supersaturation. The crystallization was induced by a crystal seed in contact with the melt surface and proceeded upon cooling from the saturation temperature to the final growth temperature. Afterward, the crystal was removed slowly from the melt and cooled to room temperature. The concentrations of Tm and Ho in the grown crystal were determined by inductively coupled plasma (ICP) emission spectrometry by using a Perkin-Elmer (Optima 2100 DV) equipment. For this purpose, the samples with 10 atom % of nominal Tm or Ho concentrations were dissolved in 37% HCl by heating at 363 K with stirring, and the ICP signal intensity was quantified from the comparison with Li, Ba, Lu, Tm, and Ho standards. Moreover, the actual concentration of the Li, Lu, Ho, and Tm in the crystal was further corrected by a calibration curve obtained independently for each ion with the mixture of the precursor oxides and carbonates used for crystal growth. For samples with lower nominal Tm or Ho dopant levels, the concentrations were calculated by the comparison of the room temperature integrated optical absorption. For this purpose the transitions 3H6 → 3H4 (λ = 760−830 nm, c-polarized) of Tm3+ and the 5I8 → 5S2 + 5F4 (λ = 510−560 nm, c-polarized) of Ho3+ were selected on the basis that these transitions are free of overlap with other Tm or Ho transitions.

3. RESULTS 3.1. Crystal Growth. Previous studies on the growth of Li3T3Ba2(MoO4)8 isostructural monoclinic C2/c crystals have reported the decomposition of these compounds upon melting. In particular, DSC analyses of Yb:Li3Gd3Ba2(MoO4)8 showed a melt with decomposition at 1256 K, and in addition some phase transition is observed both upon heating and cooling at 953 and 874 K, respectively.15 A similar behavior was reported for Nd:Li3Y3Ba2(MoO4)8,13 although the melting temperature was higher and the phase transition feature was not so evident. B

dx.doi.org/10.1021/cg300105g | Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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molar ratios higher than one evidence of solute decomposition is observed; that is, the amount of used solvent is not able to completely dissolve the present solute. Below this ratio, the endothermic melting peak of Li3Lu3Ba2(MoO4)8 weakens and broadens, and resolidification peaks at temperatures higher than that corresponding to the solute melting disappear. Both facts indicate a progressive dissolution of the Li3Lu3Ba2(MoO4)8 solute in the Li2MoO4 solvent. The saturation temperature of the Li 3 Lu 3 Ba 2 (MoO 4 ) 8 (solute)/Li2MoO4 (solvent) mixture has been monitored through the resolidification temperature of the mixture observed in the DSC curve. Figure 2 shows the evolution of onset and peak

As a preliminary information to guide the crystal growth, we present a DSC study of the 10 atom %Tm:Li3Lu3Ba2(MoO4)8 ground crystal. Figure 1 shows the results of two consecutive

Figure 1. DSC heating/cooling cycles in Ar atmosphere (heating/ cooling rate 10 K/min) of a 10 atom % Tm-doped Li3Lu3Ba2(MoO4)8 ground crystal. (a) First cycle. (b) Second cycle.

Figure 2. Evolution of the resolidification temperature measured by DSC of several Li3Lu3Ba2(MoO4)8 (solute)/Li2MoO4 (solvent) mixture compositions. The symbols are the experimental onset (◊) and maximum heat flow (○) resolidification temperatures. The line is a visual help.

heating/cooling cycles. During the first heating cycle no endothermic peaks were observed before melting. Melting starts at about 1133 K with maximum heat flow at 1168 K, and exothermic peaks observed upon cooling at 1289 and 1207 K correspond to product resolidification. Further DSC peaks appear below the melting temperature either in the cooling run of the first cycle or upon heating (787 K) and cooling (799 K) in successive cycles. These results show the crystal decomposition and therefore prevent the use of the Czochralski method for crystal growth. DSC studies have been extended to Li3La3Ba2(MoO4)8 powders prepared by solid state reaction. In this case the melting onset is at about 1190 K and the maximum heat flow was measured at 1202 K. Clear evidence of product decomposition upon melting was derived by the presence of a peak at 1241 K, that is, at a higher temperature than the observed Li3La3Ba2(MoO4)8 melting temperature. The melting temperatures so far found for Li3T3Ba2(MoO4)8 crystals are 1277 K for 4.77 atom %Nd:Li3Y3Ba2(MoO4)8,13 1190−1202 K for Li3La3Ba2(MoO4)8, 1223−1253 K for Li 2.86 Gd 2.90 Yb 0.24 Ba 2 (MoO 4 ) 8 , 15 and 1160−1168 K for Li2.44Lu2.78Tm0.35Ba2(MoO4)8. It can be observed that the Lubased compound has the lowest melting temperature. Two different solvents have been used in previous works for the growth of Li3T3Ba2(MoO4)8 crystals, namely, Li2MoO4 and Li2Mo2O7. The former has a lower melting temperature and therefore was preferred as solvent for growth. As a preliminary guide for the growth process described later, we have studied by DSC the evolution of the saturation temperature of the Li3Lu3Ba2(MoO4)8 (solute)/Li2MoO4 (solvent) mixtures using products synthesized by solid state reaction. For solute/solvent

temperatures of this resolidification. For crystal growth, a moderate change of the solute/solvent composition upon cooling is desirable; therefore on the basis of Figure 2 results we have selected a 1:5 molar ratio for the TSSG method further used. Undoped, Tm-doped, Ho-doped, and Tm,Ho-codoped Li3Lu3Ba2(MoO4)8 crystals were grown in platinum crucibles using Li2MoO4 as the solvent. The required amounts of precursor oxide and carbonate products were mixed to produce the solute to solvent molar ratio of 1:5. The saturation temperature was further determined by monitoring the grow/ dissolution of the seed in the melted flux and simultaneous measurement of the flux temperature with a thermocouple immersed in the liquid phase; results for the different grown crystals are summarized in Table 1. Crystal growth proceeded upon melt supersaturation during cooling at 0.05 K/h down to the final temperature (see Table 1). At this final temperature the crystal was pulled out of the melt, cooled to 943 K, and further cooled to room temperature, most often at a faster cooling rate (see Table 1 for used cooling rates). Crystallization was carried out using a, b, and c-oriented seeds of crystals previously grown; some of them by spontaneous nucleation on a platinum wire. The crystals obtained do not present mechanical damage associated to stress produced by the possible phase transition monitored in the DSC study (Figure 1). It could be advanced that Li3Lu3Ba2(MoO4)8 crystals are free of structural phase transitions from the room temperature to the melting point. This is a significant advantage over Li3Gd3Ba2(MoO4)8, which has a narrow thermal window for the growth below its phase transition at 953 K.15 C



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Table 1. A = Nominal Dopant Concentrations of Li3Lu3−x−yTmxHoyBa2(MoO4)8 (Tm:Ho:LLBM) Crystal in the Melt, B = Solute(Tm:Ho:LLBM)/Solvent (Li2MoO4) Molar Ratio, C = Saturation Temperature (K), D = Growth Cooling Rate (K/h), E = Final Growth Temperature (K), F = After Growth Cooling Rates down to 943 K, and from 943 K to Room Temperature (K/h), G = Seed Orientation, Seed Composition, H = Tm Concentration (1020 cm−3), Crystal Composition of Analysed Elements, I = Ho Concentration (1020 cm−3), Crystal Composition of Analysed Elements, J = Occupancy Factors for (Lu + T)/Li1 A

C

D

E

1:5 1:5

1072 1073

0.05 0.05

1053 1053

10 atom %Tm

∼1:5

1058

0.05

1033

10 atom %Ho

1:5

1071

0.04

1057

∼1:5

1076

0.05

1060

∼1:5

1068

0.05

1038

undoped 5 atom %Tm

5 atom %Tm and 0.5 atom %Ho 10 atom %Tm and 0.2 atom %Ho a

B

F

G

H

10, 10 ∼c, LLBM 6, 6 random, 5 atom %:LLBM 5, 10 b, 5 atom % Tm:LLBM 5, 10 ∼b, 10 atom % Ho:LLBM 6, 10 a, 10 atom %Tm: LLBM 5, 10 b, Tm:LLBM

I

J

0, Li2.80Lu3.20b 2.95, Tm0.177c

0.800/0.200

5.65, Li2.44Lu2.78Tm0.35a Li2.82(LuTm)3.18b

0.795/0.205

2.41, Tm0.1493c

7.32, Ho0.454a Li2.85(LuHo)3.15b 0.27, Ho0.017c

5.79, Tm0.359c

0.19, Ho0.011c

0.787/0.213

Inductively induced plasma emission spectrometry analysis. bSingle crystal X-ray diffraction refinements. cOptical absorption results.

Figure 3. Characteristic crystal growth shapes of Li3Lu3Ba2(MoO4)8 single crystals: First and second rows, photographs of characteristic (a) 5 atom % Tm:0.5 atom %Ho:Li3Lu3Ba2(MoO4)8 grown from an a-oriented seed, (b) 10 atom %Tm:Li3Lu3Ba2(MoO4)8 crystal grown from a b-oriented seed, (c) Li3Lu3Ba2(MoO4)8 grown from a c-oriented seed. Third row, simulated morphology schemes showing developed faces and axes of single crystals in a−c, respectively.

{101} and {110} faces grow fast while {100}, {010}, or {001} faces are little developed. These crystals develop {021} faces that give rise to corners along the b-direction (Figure 3a). Crystals grown from b-oriented seeds reproduce the facets of the seed

Figure 3 shows photographs of the characteristic morphologies of grown crystals, along with SHAPE24 simulations of their corresponding crystal growth habit, indicating developed faces and crystal axes. For crystals obtained from a-oriented seeds, D



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Li concentration in the grown crystals always lower than the nominal one; for instance, the undoped Li3Lu3Ba2(MoO4)8 must be written as Li2.80Lu3.20Ba2(MoO4)8, confirming the Li deficiency determined by the ICP analysis described above. Similarly determined compositions of doped crystals can be also found in Table 1. Positions of peaks and their relative intensities in the XRPD profile generated using the above refined single crystal X-ray data agree with those of the XRPD pattern of the ground crystal; see Figure SI1, which confirms the experimental procedure. The cationic distribution achieved in the current refinement indicates a disordered local environment around Tm3+ or Ho3+ optical centers derived from the coexistence of Lu3+ and Li+ cations over one 8f crystal site. Further XRD analyses of undoped, 10 atom % Tm-doped, and 10 atom % Ho-doped Li3Lu3Ba2(MoO4)8 grown crystals provided the following unit cell parameters a(Å) = 5.1605(6), 5.1672(4), 5.1717(19), b(Å) = 12.5717(16), 12.5858(10), 12.604(5), c(Å) = 19.055(2), 19.0744(15), 19.068(7), and β (°) = 91.559(2), 91.521(1), 91.521(6), respectively. The substitution of Lu3+ by the larger Tm3+ or Ho3+ ions induces the expected expansion of the crystal unit cell. 3.3. Thermal Expansion. The evaluation of the thermal expansion of a laser crystal is important in order to estimate its mechanical resistance upon heating by the pump beam, and it is also required for the calculation of the thermo-optic coefficients. Crystals with low thermal expansion anisotropy are desired for laser applications. Thermal expansion coefficients were calculated from XRPD data above 300 K made in air on 5 atom %Tm:Li3Lu3Ba2(MoO4)8 ground crystal. XRPD patterns were collected at temperatures of 298, 323, 348, 373, 398, 423, 448, 573, 523, 573, 623, 673, 723, 773, 873, and 973 K. This range of temperature is large enough to adequately describe the behavior of crystals under cooling from the growth temperature and under heating by optical pumping. These XRPD scans, shown as Supporting Information (see Figure SI2), indicate that the crystal symmetry remains the same in the whole range of measured temperatures. Crystal lattice parameters of the 5 atom %Tm:Li3Lu3Ba2(MoO4)8 crystal at each measured temperature were determined from the Rietveld refinement25 of the corresponding XRDP profile using as starting data those from previous X-ray single crystal structure determination. The complete list of unit cell parameters is included as Supporting Information in the Table SI10. Thermal expansion defined as α = ΔL/L0 × ΔT is a second rank tensor, αij, connecting the lattice expansion, ΔL, upon heating ΔT, with the original lattice length, L0. In the monoclinic point symmetry the tensor is characterized in the orthogonal crystallo-physical frame (a, b, c*) by four nonvanishing components, α11, α22, α33, α13. The diagonal components (i = j) can be obtained from the ΔL/L0 vs ΔT plots shown in Figure 5 as α11 = 1.48 ± 0.01 × 10−5 K−1, α22 = 1.73 ± 0.02 × 10−5 K−1, α33 = αc* = 2.004 ± 0.01 × 10−5 K−1. α13 is determined taking into account the expansion along the crystallographic c-axis also given in Figure 5, αc = 2.001 ± 0.01 × 10−5 K−1, and the fact that the value for an arbitrary direction is related to the α ij components by αn = ninjαij, where ni and nj are the director cosines of the given direction with the axes of the crystallophysical frame. By this procedure, whose details can be found in previous works,26 we obtained α13 = α31 = −0.063 ± 0.01 × 10−5 K−1. It is worth noting at this point that the presently calculated α11, α22, αc set are quite close to that calculated by dilatometry in a Nd-doped Li3Gd3Ba2(MoO4)8 crystal, namely, α11 = 1.62 × 10−5 K−1, α22 = 1.73 × 10−5 K−1, αc = 2.15 × 10−5 K−1.27

with a large development of the {010} face. They exhibit a platelike growth habit; that is, they have a rectangle cross section, and the growth is preferentially confined to the ac plane (Figure 3b). Finally, crystals grown from c-oriented seeds have a pseudorhombohedral shape with the largest dimension along the b crystal direction (Figure 3c), the shape of these latter crystals being more three-dimensional than in the previous cases. They have a large {001} face but the sides are controlled by the growth of {110} faces which limits the presence of {100} and {010} faces. The crystalline microstructural quality of the grown crystals has been studied by a rocking curve of the 200 Bragg reflection. Figure 4 shows the results obtained. The full width at half of the

Figure 4. Rocking curve of the 200 X-ray reflection of a 5 atom %Tm:0.5 atom %Ho:Li3Lu3Ba2(MoO4)8 crystal. The inset shows the rocking direction.

intensity maximum (fwhm) was 0.015°, which indicates a high crystalline quality in terms of the low level of crystal domain twining. The chemical ICP analysis of the 10 atom %Tm:Li3Lu3Ba2(MoO4)8 crystal shows a deficiency in the Li composition with respect to the nominal chemical formula; see Table 1. This Li deficiency is further confirmed by the crystal composition derived from the refinement of the single crystal XRD analysis presented later. Inversely, an excess of Ln3+ composition is observed. The Tm and Ho segregation coefficients, S = [Ln composition in crystal]/[Ln composition in melted solvent], were S = 1.18 and 1.51, respectively. The segregation coefficient tends to unity as the ionic radius difference between the substituted Lu and the dopand ion decreases. 3.2. Structural Characterization. From the analysis of single crystal XRD data of undoped, 10 atom % Tm-doped and 10 atom % Ho-doped Li3Lu3Ba2(MoO4)8 crystals, the following conclusions can be drawn: In the structure of the crystals, Li occupies two lattice sites (Li1 and Li2), Lu (and Tm and Ho dopants), and Li1 share a same 8f crystal site with the total population assumed to be 1, Ba and Li2 fully occupy each one a different 4e site, and Mo1, Mo2, and the eight types of O are located in different 8f sites. Structure refinements, which included the 8f site occupancy factors (OF) for Lu(Tm/Ho) and Li cations, yielded low discrepancy R1 factors, with anisotropic displacement parameters for all atoms. Details of the refinements can be consulted in the Supporting Information (Tables SI1, SI4, and SI7). Final atomic coordinates, refined OF for Lu(Tm or Ho) and Li over the 8f crystal site, as well as isotropic displacement parameters appear in Tables SI2, SI5, and SI8. Selected bonds lengths are given in Tables SI3, SI6, and SI9. The crystallographic refinements yield a E



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Resonant pumping at cryogenic temperatures, particularly at liquid nitrogen temperature (77 K), is recently envisaged as a very effective method to overcome crystal limitations associated with the low value of the thermal conductivity coefficient (κ). In fact lasers of 100 kW of power class are developed under this concept. The most extended example of this laser operation scheme is the 2F7/2 ↔ 2F5/2 transition of Yb3+ (λ ≈ 1.06 μm),32 and more recently the 5I8 ↔ 5I7 transition of Ho3+ (λ ≈ 2.07 μm),33 the 3F3 ↔ 3H4 of Pr3+ (λ ≈ 1.65 μm),34 and the 4I15/2 ↔ 4I13/2 transition of Er3+ (λ ≈ 1.60 μm)35,36 are receiving increasing attention. The knowledge of the thermal conductivity evolution upon cooling is a parameter required for the design of such lasers. Figure 6a shows the evolution of κ with temperature T of the 5 atom %Tm:Li3Lu3Ba2(MoO4)8 crystal along the a-axis.

Figure 5. Evolution of the thermal expansion of the lattice parameters of the crystallographic (a, b, c) and crystallo-physical (a, b, c* = c × cos(β-90)) frames of 5 atom %Tm:Li3Lu3Ba2(MoO4)8.

Once α13 is known we can write the thermal expansion tensor in the crystallo-physical frame as ⎛ 1.48 0 − 0.063⎞ ⎜ ⎟ αij = ⎜ 0 1.73 0 ⎟ × 10−5 K−1 ⎜ ⎟ ⎝−0.063 0 2.00 ⎠

(1)

The principal frame of the physical property (a′, b′, c′) is such that the tensor can be expressed by a diagonal second order matrix. According to the matrix diagonalization procedures, the angle ρ between the a crystallo-physical (or crystalline) and a′ principal axes is given by ρ=

⎛ 2α13 ⎞ 1 arctan⎜ ⎟ 2 ⎝ α13 − α11 ⎠

Figure 6. Temperature dependence of the thermal conductivity (κ) along (a) the a-axis of 5 atom %Tm:Li3Lu3Ba2(MoO4)8 crystal, and (b) the b-axis of 10 atom %Tm:0.2 atom %Ho:Li3Lu3Ba2(MoO4)8 crystal.

(2)

From this expression, ρ = −6.72°. The minus sign of ρ means clockwise rotation, that is, contrary to the direction of the β angle between the a and c crystallographic axes. Thus, following the development in ref 26 (here not given in detail for brevity), the α′ij tensor in the principal frame is written as ⎛1.47 0 0 ⎞ ⎜ ⎟ αij = ⎜ 0 1.73 0 ⎟ × 10−5 K−1 ⎜ ⎟ ⎝ 0 0 2.01⎠

The dependence displays a maximum at T = 20 K (κ = 1.85 W/m × K), typical for a dielectric crystal, which is a result of an interplay between the increase with temperature of the crystal phonon energy and a growing intensity of the resistive phonon−phonon scattering. What distinguishes the thermal conductivity of this crystal from a typical one is a relatively small change over the investigated temperature range, which in this case does not exceed 100%, while typically the coefficient of thermal conductivity changes by 2−3 orders of the value. The conductivity change from T = 77 K (κ = 1.58 W/m × K) to 300 K (κ = 1.50 W/m × K) is small. It should be also noted that the thermal conductivity of the Li3Lu3Ba2(MoO4)8 crystal is lower than in the case of other well established laser crystals, like YAG (κ ≈ 11 W/m × K), YVO4 (κ ≈ 7 W/m × K), or KY(WO4)2 (κ ≈ 3 W/m × K).37 This reduced value of κ could be related to an increased phonon−phonon scattering probability associated with the crystal disorder; in fact the also disordered NaGd(WO4)2 laser crystal also have rather low thermal conductivity (κ ≈ 1.1 W/m × K).38 In order to make a first estimation of the κ anisotropy and due to the limited number of samples available with proper quality and dimensions, we have compared the above κ measurements with those obtained by the laser flash method on a 10 atom % Tm: 0.2 atom %Ho:Li3Lu3Ba2(MoO4)8 crystal. Figure 6b shows the κ(T) results obtained from the crystal density, heat capacity, and diffusion coefficient results summarized in Table SI11. Ignoring the difference in dopand concentrations between both samples, at room temperature the ratio κa/κb ≈ 1.17 is obtained

(3)

From the above results it can be seen that the maximum thermal expansion anisotropy of 5 atom %Tm:Li3Lu3Ba2(MoO4)2, α′33/α′11= 1.37, is lower than those of other laser crystals successfully used in mode-locked fs laser oscillators. In particular, for monoclinic KLu(WO4)2 crystal α′33/α′22 = 4.99,28 for tetragonal NaY(WO4)2 α33/α11 = 2.2,29 for tetragonal CaGdAlO4, α33/α11 = 1.60,30 and for apatite oxysilicates SrLn2(SiO4)3O, α33/α11 = 1.35−1.40.31 3.4. Specific Heat and Thermal Conductivity. The specific heat of the 5 atom %Tm:Li3Lu3Ba2(MoO4)8 crystal measured at 323 K was Cp = 0.42 J/g × K (205.2 cal/mol K). For laser applications a large value of the specific heat means lower temperature changes upon optical pumping. In terms of energy required per mole, the Cp value of the Li3Lu3Ba2(MoO4)8 crystal is similar to that of NaGd(WO4)2 laser crystal, that is, Cp = 236.58 cal/(mol × K), and larger than those of standard laser hosts, like YAG, Cp = 83.7 cal/mol × K, or YVO4, Cp = 24.6 cal/mol × K. Further characterization of Cp above room temperature was made for 10 atom %Tm:0.2 atom %Ho:Li3Lu3Ba2(MoO4)8 crystal; Table SI11 summarizes the results. F



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provides the parameters, A, B, C (μm), and D (μm−2) given in the inset of Figure 8. It is concluded that ng corresponds to the b′ principal

as a first approximation. Above 20 K κ decreases continuously with increasing temperature; this shows that the thermal conductivity of Li3Lu3Ba2(MoO4)8 crystal behaves closer to that observed for ordered crystals39 than for glasses,40,41 or disordered crystals.23 In the former κ decreases with temperature due to the reduction of the phonon mean free path induced by the increase of the phonon−phonon scattering, while in the latter the phonon mean free path saturates to a constant value and κ becomes proportional to Cp; therefore from a certain threshold it increases with temperature. This behavior is consistent with the relatively low lattice disorder found in Li3Lu3Ba2(MoO4)8 crystal, as explained previously, only one lattice site is shared and ∼80% of it is filled with Lu while Li1 only fills the ∼20% remaining. 3.5. Optical Indicatrix. Crystals of the monoclinic system are biaxial and the optical indicatrix describing the refractive indices is again a second rank tensor with the same form as the thermal expansion tensor above. The crystallographic b axis and principal b′ axis of the indicatrix are parallel, but the crystallophysical (a, c) frame and principal (a′, c′) axes of the indicatrix are in the same plane but rotated. To determine the rotation angle (ρ) between these two frames we examined the light intensity transmitted by crossed polarizers when the sample is rotated around the b axis, while the latter is parallel to the propagation direction of the light. Figure 7 shows the evolution

Figure 8. Dispersion of the room temperature refractive indices (symbols) of 5 atom % Tm:0.5 atom % Ho:Li3Lu3Ba2(MoO4)8 crystal. The lines are the fits to the Sellmeier law with the A, B, C (μm), and D (μm−2) parameters summarized in the inset.

axis, while nm and np correspond to the a′ and c′ principal axes, respectively. It is worth noting that ng ≈ nm, and this could be related to the fact that the crystallographic β parameter is near 90° (β = 91.521°, see Table SI4); that is, the crystal is near to uniaxial. The optical axes of the crystal, that is, the propagation directions for which the refractive index is independent of the polarization orientation, are found in the npng plane at an angle Vg to the ng axis: 1/2 ng ⎛ nm2 − n p2 ⎞ ⎜ ⎟ sin Vg = nm ⎜⎝ ng2 − n p2 ⎟⎠

from the data of Figure 8 for the examined 5 atom %Tm:0.5 atom % Ho:Li3Lu3Ba2(MoO4)8 crystal at λ= 1 μm Vg= 71.52°. The crystal is negative biaxial (Vg > 45° or nm−np < ng−nm) and the angle between the optical axes is 2V = 18.47°. 3.6. Optical Absorption. In biaxial crystals the real and imaginary parts of the complex dielectric permittivity tensor do not have parallel reference axes (with the exception of b and b′axes), and as a consequence the directions for maximum optical absorption (or emission) must be specifically investigated. Moreover, it has been shown that the orientation of the a′ and c′principal axes of the imaginary permittivity tensor does not follow a simple spectral dispersion law.42 This has a direct impact in the crystal orientation in order to optimize the laser performance of Ln-doped Li3Lu3Ba2(MoO4)8 monoclinic crystals. A promising application of this crystal is related to Tm and Ho codoping. The (a′c′) frame orientation of the 3H6 → 3H4 Tm3+ transition (the pumping channel) has been determined previously as anticlockwise rotated by ρ ≈ 20° with respect to the (a,c*) crystallo-physical frame.18 Here we shall focus on the determination of the (a′, c′) principal frame orientation of the 5 I8 → 5I7 Ho3+ absorption (the emission channel). Figure 9a shows the room temperature polarized spectra of the 5 I8 → 5I7 Ho3+ optical absorption. Several overlapped bands characterize this absorption, and the largest absorption of these bands occurs for two peaks at λ = 1950.9 nm and λ = 2050.5 nm, respectively. The intensity of the first peak depends little on the polarization, but the second peak is significantly more intense for

Figure 7. Evolution of the light intensity transmitted along the b-axis of 5 atom % Tm:0.5%Ho:Li3Lu3Ba2(MoO4)8 crystal when it is rotated around this axis between crossed polarizers (symbols). The red line is a fit to a cos2 θ law. The relative position of the crystallographic (a, c) and principal (a′, c′) axes is shown.

of the light intensity at 633 nm, which follows a cos2 θ law. We observed that minimum transmission is obtained when the light polarization is anticlockwise rotated with respect to the c* crystallo-physical axis of the crystal by ρ = 17°; that is, the c′ axis of the indicatrix is anticlockwise rotated by ρ ≈ 18.5° with respect to the c crystallographic axis, as the sample is viewed from the +b crystallographic axis. In biaxial crystals it is customary to label the principal axes of the indicatrix as ng, nm, and np, according to the magnitude of the refractive indices (g > m > p). Figure 8 shows the room temperature refractive indices of a 5 atom %Tm:0.5 atom % Ho:Li3Lu3Ba2(MoO4)8 crystal. The fit of these results by the Sellmeier dispersion law, n2 = A +

Bλ 2 − Dλ 2 λ − C2 2

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b-polarized light. Figure 9b shows the optical absorption changes at the wavelength of each maximum when the light polarization is

Figure 10. 10 K optical absorption of the 5I8 → 5I7 optical absorption of Ho3+ in several laser crystals.

Figure 11. Room temperature group velocity dispersion (GVD) for light polarized parallel to the principal axes of the dielectric permittivity tensor of a 5 atom % Tm:, 0.5 atom % Ho:Li3Lu3Ba2(MoO4)8 crystal.

Figure 9. (a) 5I8 → 5I7 room temperature absorption cross section (σABS) of Ho3+:Li3Lu3Ba2(MoO4)8 crystal along the three optical axes (//a′, //b, //c′). (b) Evolution of the 5I8 → 5I7 Ho3+ absorption intensity for selected peak wavelengths, λ = 1950.9 nm (■) and λ = 2050.5 nm (○), as a function of the angle between the crystallographic and optical absorption frames. The red arrows indicate the position of the (a′, c′) absorption frame with regard to the (a, c) crystallographic frame.

λ = 2.06 μm mode-locked laser pulses of 570 fs43 and 191 fs19 have been demonstrated, respectively. The intermediate value of the fwhm of Ho:Li3Lu3Ba2(MoO4)8 bands suggests that this crystal may support laser pulses with duration in between the above values. A more quantitative estimation of such laser potential is provided by the Fourier limit of the time-bandwidth product, Δν × Δt = 0.315 (assuming pulses with sech2 shape). In the case of Tm3+, tunable laser emission has been observed from λ ≈ 1850 to 2000 nm with a fwhm = 100 nm. On the other hand, the gain cross section of the 3F4 → 3H6 Tm3+ transition for a population inversion ratio β = 0.2 has a fwhm ≈ 80 nm for Tm:Li3Lu3Ba2(MoO4)8,18 so the Fourier limit of the Tm laser pulses at λ ≈ 1930 nm is Δt ≈ 40 fs. In the case of Ho:Li3Lu3Ba2(MoO4)8 crystal, laser action has not been demonstrated so far, but the gain cross sections have been calculated using the reciprocity principle44 and are given as Supporting Information (Figure SI3). Positive gain cross sections can only be obtained for relatively high inversion ratios, that is, β ≥ 0.3. Taking as reference the results for β ≥ 0.4 (fwhm = 30 nm), the Fourier limit of the Ho3+ laser pulses at λ ≈ 2053 nm is Δt ≈ 150 fs. This reflects the narrower nature of the Ho3+ bands with regard to those of Tm3+. Although the lowest laser pulse duration is determined by the Fourier limit of the time-bandwidth product, in practice this only can be achieved if the pulse chirping induced by the propagation along the laser gain media is properly compensated. Pulse chirping is determined by the group velocity dispersion (GVD)

rotated with respect to the (a, c) crystal axes. Maximum absorption was obtained for light polarized at ρ = 20° in the clockwise direction from the crystallographic c-axis as the sample is viewed from the +b crystal axis.

4. PROSPECTS FOR ULTRASHORT LASER PULSES APPLICATIONS As mentioned in the Introduction, the motivation for crystal growth of Li3Lu3Ba2(MoO4)8 is the potential application as ultrafast laser media. A qualitative comparison of such potential can be acquired from the fwhm of the optical absorption bands, particularly for the case of Ho3+ which exhibits narrower bands than Tm3+. Figure 10 shows selected parts of the 5I8 → 5I7 optical absorption of Ho3+ at 10 K. Low temperature measurements were used in order to avoid overlap between different contributions of the Stark sublevels of the 5I8 Ho3+ multiplet. It can be observed that in Ho:Li3Lu3Ba2(MoO4)8 crystal the fwhm is 7.4 cm−1, which is larger than that found in the ordered Ho:KLu(WO4)2 crystal (isostructural to the KY(WO4)2 laser crystal), fwhm = 2.6 cm−1, but smaller than in the also disordered Ho:NaBi(WO4)2 crystal (isostructural to the NaY(WO4)2 laser crystal), fwhm = 12.6 cm−1. In the two latter crystal classes at H



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of the crystal, which is related to the refractive index dispersion by45 GVD =

λ 3 ⎛ d 2n ⎞ ⎟ ⎜ 2πc 2 ⎝ dλ 2 ⎠

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ASSOCIATED CONTENT

S Supporting Information *

Crystallographic data for undoped, 10 atom % Tm-doped and 10 atom % Ho-doped Li3Lu3Ba2(MoO4)8 crystals, Tables SI1− SI9 and Figure SI1. Thermal expansion data of 5 atom % Tmdoped Li3Lu3Ba2(MoO4)8 crystals, Table SI10 and Figure SI2. Temperature dependence of the thermal conductivity of 10 atom % Tm- and 0.2 atom % Ho-codoped Li3Lu3Ba2(MoO4)8 crystal, Table SI11. Gain cross section of Ho3+ in Li3Lu3Ba2(MoO4)8 crystals, Figure SI3. This information is available free of charge via the Internet at http://pubs.acs.org/.

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Using the results of Figure 8, GVD values for the three principal axes of the dielectric permittivity have been calculated and are shown in Figure 11 for the spectral region of typical Nd3+, Yb3+, Er3+, Tm3+, and Ho3+ emissions. Low GVD values are desirable for the generation of fs laser pulses. The results in Figure 11 show lowest GVD for light polarized parallel to the c′ principal axis.

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5. CONCLUSIONS Li3Lu3Ba2(MoO4)8 compound decomposes upon melting at ≈1163 K; this is the lowest melting temperature of the Li3T3Ba2(MoO4)8 (T = Y, La, Gd, or Lu) series. Growth of single crystals of this compound was possible by using Li2MoO4 solvent and the top seeded solution growth (TSSG) method without pulling. Growth was carried out at the 1073−1033 K interval. Crystal morphology is determined by the development of specific crystal faces depending on the seed orientation. Li3Lu3Ba2(MoO4)8 is a monoclinic crystal, with C2/c (No. 15) space group. The crystals obtained are Li deficient and Li incorporates in two lattice sites, namely, 8f (Li1) and 4e (Li2). The Li occupancy factor of the 8f site is ≈0.2, and the rest of this site is occupied by Lu3+ cations. In doped crystals, Ho3+ and Tm3+ incorporate with segregation coefficients larger than 1 sharing the 8f crystal site with Li1 and Lu ions. As a consequence of the disordered cationic distribution around the optically active Ln3+ centers, the optical absorption and emission bands of the trivalent lanthanides are inhomogeneously broadened. The magnitude of this effect is intermediate between that found in crystals without disorder, like KLu(WO4)2, and crystals with disorder over two crystals sites, like the tetragonal double tungstate crystal family, that is, NaY(WO4)2-like. The crystallographic b axis and the principal b′ axis of physical properties are parallel, but the principal (a′, c′) frame of the physical properties is rotated around b′ with respect to the crystallo-physical (a, c*) frame. When viewed from the +b crystal axis, the rotation angle of the thermal expansion, optical indicatrix, λ ≈ 800 nm Tm3+ optical absorption and λ ≈ 2060 nm Ho3+ optical absorption are 6.72° in the clockwise direction, 17° in the anticlockwise direction, 20° in the anticlockwise direction, and 20° in the clockwise direction, respectively. From the perspective of applications as laser media, good properties of the studied materials are the low growth temperature, the large specific heat (Cp = 205.2 cal/mol × K at 300 K), the low thermal expansion anisotropy (

8. A Spectrally Broadened Disordered Crystal for ... - ACS Publications

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