Nonlinear optical (NLO) crystals are the essential components of high-power lasers for generating ultraviolet (UV) light, especially the UV-C range, defined as 200-280 nm [1]. It has a variety of technological applications such as lithography, [2,3] micromachining, [4] and spectroscopy [5]. The wavelengths of interest are obtained using frequency conversion through nonlinear optical phenomena such as second harmonic generation (SHG) and sum frequency generation (SFG). Generally, a good UV NLO crystal should satisfy the following requirements: large second-order nonlinearity (large SHG tensor coefficients), broad UV transparency window, phase matchability, high laser damage threshold (LDT) values, and easy synthesis. It is well-known that bandgaps and nonlinear susceptibility generally scale inversely; hence, crystals with large bandgaps (and therefore DUV transparency) usually have low nonlinear susceptibility. As a result, ultraviolet NLO crystals typically have lower SHG coefficients as compared to visible and infrared NLO crystals. Since it is difficult to find a material that satisfies all the requirements, researchers are actively looking for new UV crystals and many borate-based NLO materials such as β-BaB 2 O 4 (BBO), [6] LiB 3 O 5 (LBO), [7] CsB 3 O 5 (CBO) [8] and KBe 2 BO 3 F 2 (KBBF) [5] have been discovered and utilized in UV NLO applications. Among these materials, KBBF is the only crystal with efficient frequency conversion below the DUV barrier of 200 nm. Clearly, the rapid development of UV laser applications demands the continuous exploration of new UV NLO crystals.
Borate is considered to be one of the best crystal systems for exploring good UV NLO crystals [6,7]. Because of the significant electronegativity difference in boron and oxygen, the B-O bonds have strong ionic characteristics, giving rise to large bandgaps and low short-cutoff wavelengths. The typical groups formed are planar [BO 3 ] triangles and [BO 4 ] tetrahedra. In particular, the planar [BO 3 ] units contain π-conjugated bonds in which the electrons are delocalized and easily polarized when an electric field is applied, thus giving rise to the strong SHG response. In addition, its planar nature increases the anisotropy and leads to more significant birefringence; thus they are more likely to be phase-matchable. In particular, rare earth borates are a promising crystal system to explore for new UV NLO crystals. Incorporating rare earth metals has several advantages. They have closed-shell or half-filled 4f orbitals; therefore, the d-d and f-f electronic transitions are impeded, which is beneficial for broadening the transparency window [8,9]. Also, because of the complex electronic configuration and the large ionic radius, the rare earth elements will bond with the oxygen ions to form distorted polyhedra, enhancing the overall SHG performance [9]. EuBa 3 (B 3 O 6 ) 3 (EBBO) is an example of rare earth borate-based crystals with planar [BO 3 ] triangles, which can be a new UV NLO crystal. In EBBO, three [BO 3 ] triangles form a planar [B 3 O 6 ] ring. This compound was previously synthesized in the polycrystalline form and reported to crystallize in the non-polar space group P6 3 /m [10]. First principles phonon computations identified that this family of materials of formula XA 3 (B 3 O 6 ) 3 (with X = In, Sc, . . . X = Ba, Sr, . . . which includes EBBO) present dynamic instabilities and that they should form in a noncentrosymmetric space group. In agreement with the theoretical prediction, we show that EBBO forms indeed in an acentric space group and exhibits an SHG response. We further explore EBBO as a candidate for UV nonlinear photonic applications. We report the first synthesis as well as the linear and nonlinear optical properties of single crystal EBBO and find that EBBO is both Type I and Type II phase-matchable. These findings further confirm that rare earth borate-based crystals are promising for NLO applications and that first principles phonon databases can be used to identify noncentrosymmetric materials with applications in NLO.
The polycrystalline EBBO powder was prepared using a solid-state reaction method. We used BaCO 3 (Alfa Asar, 99.5%), Eu 2 O 3 (Alfa Asar, 99.9%), and H 3 BO 3 (EMD chemicals, 99.4%) as source materials for the polycrystalline synthesis. Powders of BaCO 3 , Eu 2 O 3 , and H 3 BO 3 were mixed in a stoichiometric ratio and thoroughly ground in an agate mortar to ensure homogenous mixing. The mixed source material was placed in an Al 2 O 3 crucible, heated to 400°C, and held at this temperature for 1 hour to decompose BaCO 3 and H 3 BO 3 . Then the furnace was further heated to 850°C at the rate of 200°C/hour and held at this temperature for 72 hours, followed by turning off the furnace to cool down the material. Powder X-ray diffraction (XRD) analyses showed that the polycrystalline powder synthesized following the above procedures contains a pure EBBO phase.
The EBBO single crystals were grown using a floating-zone technique using a commercial image furnace equipped with double-elliptical mirrors (Quantum Design Model: IRF01-001-05). This method consists of melting the bottom end of a feed rod suspended from above and connecting the molten zone to a seed material held from below. The single crystal is continuously grown from the molten solution by lowering both the seed and feed rods.
We used polycrystalline EBBO powder to make feed and seed rods for growing the single crystals. We first ground it into a fine powder in an agate mortar for 30 minutes. An appropriate amount of the powder (10 g) was placed into a clean cylinder-shaped rubber balloon. The balloon loaded with powder was inserted into a quartz tube with a diameter of 11 mm and a length of about 110 mm and compressed in water under a pressure of 60 MPa. After compression, the rubber balloon was carefully cut with scissors. The rod was then sintered at 800 °C for 48 hours in air and cooled to room temperature in the furnace. The seed rod (3 cm in length) was prepared with a similar procedure. In the preparation of the feed and seed rods, we always placed a layer of EBBO powder between the EBBO rod and the Al 2 O 3 boat to prevent Al contamination.
To perform the floating-zone crystal growth, the feed rod was suspended from the upper shaft, and the seed rod was mounted on the bottom shaft. Both rods were well aligned along the central axis of the growth chamber (i.e., along the shaft direction). After completing the alignment, we closed the growth chamber and moved the bottom end of the feed rod and the top end of the seed rod to the melting zone with a small gap (∼1.5 mm) left between them. Then we flushed the growth chamber by flowing oxygen for 15 minutes and increased the oxygen pressure in the growth chamber up to 4 atm. After the pressure reached 4 atm, we started to ramp up the voltage of the halogen lamps and set the upper and lower shafts to rotate at 14 rpm (The rotation direction is opposite between the upper and lower shafts). The bottom end of the feed rod started to melt at 49 V. When the voltage was increased to 50 V, the bottom end of the feed rod had sufficiently melted. Then we connected the feed rod with the seed rod by slightly moving the bottom shaft upward. After the seed and feed rods were connected, we started the growth, with the growth speed set at 7 mm/h and the feed speed at 30 mm/h. As the growth continued, we adjusted the voltage in the 49-55 V range in terms of the shape of the melt in the melting zone. The best shape is "T"-like for growth. We obtained the "T"-shape melting-zone mostly at 50 V. The growth lasted 5 hours; the crystal rod we obtained at the end was about 30 mm and contained multiple domains. Single domains were obtained by cleaving the crystal rod using a razor blade.
The short-cutoff wavelength was determined by ultraviolet-visible (UV-Vis) spectroscopy (Perkin-Elmer Lambda 950 UV-Vis-NIR Spectrophotometer) and spectroscopic ellipsometry (Woollam M-2000F) at room temperature. The UV-Vis transmittance spectrum was collected on a single crystal EBBO of thickness ∼500 µm sample in the range of 250-850 nm with unpolarized light. The ellipsometry data was collected on a polycrystalline pallet from 0.200 µm to 1 µm.
The complex linear optical constants ñ = n + ik were determined using spectroscopic ellipsometry (Woollam M-2000F). The ellipsometry spectra were collected from 0.200µm to 1µm and fitted to the Cauchy equation
The extinction coefficient (describing the absorption) is represented by the Urbach absorption equation k = k 0 e (E-E o )/E u , where k 0 and E 0 are the characteristic parameters of the material and E u is the Urbach energy related to the temperature. The absorption coefficient α can be found from k to extract the bandgap of the crystal by the Tauc analysis (αhν) 1/n = A(hν -E g ) [11]. Here, ν is the frequency of the photons and n is 0.5 for direct, and 2 for indirect bandgaps. By plotting (αhν) 1/n vs. E, one can identify the correct transition and the bandgap by extrapolating the curve to (αhν) 1/n = 0.
The SHG measurement was performed in reflection geometry at normal incidence (i.e. incident laser beam along the surface normal). The 800 nm fundamental laser beam was generated by Spectra-Physics Ti:sapphire (80 fs, 80 MHz) and its polarization was rotated by an angle of ψ using a halfwave plate. Then after passing through an analyzer, the p-polarized (|) and s-polarized (⊥) SHG light was detected by a photomultiplier tube. The typical peak power used was around 700 W (pulse energy ∼0.056 nJ). The beam diameter was roughly 600 nm. A wedged z-cut LiNbO 3 crystal (MTI Corporation) was used as a reference.
The structural optimizations and subsequent self-consistent field calculations were carried out using the Vienna ab initio simulation package (VASP) [13][14][15][16]. The Perdew-Burke-Ernzerhof generalized-gradient approximation (GGA-PBE) [17] was employed to model the exchangecorrelation energy. The projector augmented wave (PAW) method [18] was used, and the wavefunctions were expanded on a plane-wave basis set with a kinetic energy cutoff of 520 eV. Preliminary results showed that explicitly considering the 4-f electrons in the valence leads to a metal. Indeed, these electrons were located around the Fermi level, although a wide bandgap should be present. To address this issue, we tested the Eu_3 VASP pseudopotential with 9 valence electrons (5p 6 5d 1 6s 2 ), resulting in an indirect gap of ∼ 5 eV, and a direct gap of ∼5.3 eV. This pseudopotential was therefore adopted. A 3 × 3 × 1 Monkhorst-Pack k-point mesh [19,20] was initially employed to sample the Brillouin zone, and the electronic self-consistent loops were converged to 1 × 10 -6 eV of the total energy. The ionic relaxation was considered converged when the force on each atom was below 2 meV/Å. Further calculations with k-points grid of 5 × 5 × 1, energy and forces convergence thresholds of 1 × 10 -9 eV and 0.5 meV/Å, respectively, were subsequently performed to obtain a better estimation of the energy differences between the competing phases. Phonons were computed using the density functional perturbation theory (DFPT) as implemented in ABINIT [21,22] and following the procedure used by Petretto et al. [23]. The calculations were performed with GGA-PBE functional (considering the f electrons as frozen for the Eu) and a q-point grid of 2 × 2 × 2.
Starting from a phonon database [12,13] of materials present in the Materials Project [14] and previously synthesized as reported in the Inorganic Crystal Structure Database (ICSD), [15] a family of compounds with general chemical formula XBa 3 B 9 O 18 (X = Sc, In,Y, Lu) [10,[16][17][18] and with the centrosymmetric crystal structure (P6 3 /m) was identified as presenting polar imaginary phonon modes. This is a signature of polar structural instability, which has been used, for instance, to identify a new class of ferroelectric materials [19,20]. Further computations with higher accuracy parameters and using phonons obtained with DFPT confirmed the dynamical instabilities. Among this family, we focus here on EBBO and report its phonon band structure in Fig. 1(a). The centrosymmetric structure is shown in Fig. 1(b) (superposed to a distortion). Dynamical instabilities across the Brillouin zone are present in the phonon band structure, indicating a series of competing distortions (available in Supplement 1), some belonging to polar point groups (Fig. 1(a)). We distorted the structure following all unstable phonons (limiting our distortions to a 2 × 2 × 2 supercell) and subsequently relaxed. Table 1 reports all the distorted structures following this procedure and their energy compared to the centrosymmetric phase. Our preliminary conclusion from theory was that the structural ground state of EBBO is either P3 or P6 3 (see Fig. 1(c) and (d)). Both structures exhibit very similar patterns of atomic displacements and very close energy. Further calculations with more accurate relaxation criteria were performed to distinguish the true ground state but they led to even smaller energy differences. In the P3 or P6 3 , the atomic displacement breaking centrosymmetry is due to barium moving in an oxygen environment along the c axis (Fig. 1(c) and (d)). Interestingly, in the P 1 structure, which is only marginally higher in energy than the P3 and P6 3 phases, the barium displacement pattern is antipolar (Fig. 1(e)). The presence of several phases very close in energy is the signature of a flat potential energy landscape. In all phases, the Eu and the metaborate B 3 O 6 group do not move significantly. The noncentrosymmetric stable ground state indicates that this material could present a second harmonic generation response and potentially ferroelectric. Table 1. Energy difference (meV/atom) between the centrosymmetric structure (P6 3 /m) and the different distorted structures obtained from the phonon band structure of EuBa 3 B 9 O 18 . P6 3 P 1 Pm P2 1 /c P2 1 /m P3 -2.97 -2.33 2.98 -1.52 0.18 -3.19
Motivated by the computational results, we synthesized the polycrystalline EBBO with high purity using the solid-state reaction. The phase and phase purity were confirmed by the PXRD patterns shown in Fig. 2(a). Then the pure polycrystalline EBBO was used to synthesize the single crystals shown in Fig. 2(b) using the floating zone technique. The as-grown EBBO single crystals are transparent and stable in an ambient atmosphere for at least six months. It is also stable in various solvents such as water, alcohol, and acetone. EBBO consists of planar metaborate [B 3 O 6 ] rings with π-conjugated bonds, aligning parallel to each other along the [0001] direction. It also comprises EuO 6 octahedra and irregular BaO 6 and BaO 9 polyhedra, similar to the reported YBa 3 B 9 O 18 structure [21]. Because of its planar nature, single crystal EBBO can be easily cleaved along the (0001) plane, verified by XRD (Fig. 2(c)).
As shown later, we clearly observed the SHG response from the EBBO crystal, in agreement with the computational results suggesting the symmetry lowering from the centric P6 3 /m structure. To identify the detailed atomic structure experimentally, single-crystal XRD measurements were perfomed for the grown EBBO crystals on a Rigaku MicroMax 007 rotating anode (Cu) x-ray generator equipped with Osmic Varimax VHF monochromator, a universal four-circle kappa goniometer and a HyPix-Arc150 area detector. The collected diffraction dataset was refined using a structural model with P6 3 , P3, and P 6, which are noncentrosymmetric subgroups of P6 3 /m. The P6 3 /m, P6 3 , and P 6 have the same unit-cell size, whereas the unit cell of the P3 structure is doubled along the c axis, i.e., a × b × 2c cell metric, where a, b, and c are the lattice vectors of the P6 3 /m structure. The reflection conditions of the four space groups are listed in Table 2.
Table 2. Reflection conditions of the space groups P6 3 /m, P6 3 , P3, and P 6. hhil h h0l hh2hl 000l P6 3 /m and P6 3 None None None l = 2n P3 None None None None P 6 None None None None
First, we looked for superlattice reflections representing an enlarged unit cell with respect to the a × b × c cell metric. No superlattice reflections were, however, observed, indicating the low possibility of the P3 structure with the doubled unit cell. Indeed, the P3 model resulted in a bad fit to the collected dataset (R int = 38.95%), and thus we excluded the space group P3. The dataset was then fitted with the structural model with P6 3 and P 6 symmetries. Although the P6 3 model led to the best fit (R 1 = 8.81%), this value is very similar to that obtained through the refinement with the P 6 model (R 1 = 8.85%). Thus, we cannot unambiguously determine the crystal structure of EBBO only via single-crystal XRD and the subsequent refinements. With the help of nonlinear optical measurements, we assigned the P 6 structure to EBBO (see Fig. 1(b)); the P 6 is the only one consistent with our SHG results (shown later), where a significant SHG signal was observed at normal incident geometry. Note that no SHG signal is expected from the P6 3 structure at this optical geometry. The structural parameters of the P 6 phase obtained from the refinement are summarized in Table S1. The refined crystal structure is depicted in Figure 1(b).
In this refinement, we applied the split-atom model for one of the Ba sites, and this treatment improved the fitting significantly. This is consistent with the symmetry-breaking shift of Ba atoms revealed by our FP calculations. Such displacive-type static disorder may cause the discrepancy in the space group symmetry between the computation and experiment. If the displacive disorder is ignored, as is often the case in FP calculations, the Ba atoms have no degree of freedom to shift under the P 6 symmetry, and thus the stability of the P 6 phase is probably underestimated. Despite such difficulties, analyzing unstable phonons is an effective means to search for hidden noncentrosymmetric materials as showcased in this research.
To understand the lower limit of the spectral range in which EBBO is applicable, we investigated its short-cutoff wavelength using both UV-Vis spectroscopy and ellipsometry. UV-Vis transmittance was collected on the (0001) plane of a single crystal EBBO with a thickness of ∼500 µm (Fig. 3(a)). In addition, the absorption coefficient α was extracted from ellipsometry data measured on a polycrystalline pellet as shown in the inset of Fig. 3(b). Both the UV-Vis transmittance and ellipsometry data yielded the same short-cutoff wavelength of ∼250 nm. The bandgap of the crystal was extracted by the Tauc analysis (αhν) 1/n = A(hν -E g ), in which n equals 0.5 and 2 for direct and indirect bandgap, respectively [11]. By plotting the Tauc plots for both direct and indirect bandgaps, we found that the better fit was the direct bandgap, which was 5.56 eV, as shown in Fig. 3(b).
To extract the complex ordinary and extraordinary refractive indices, we performed spectroscopic ellipsometry at room temperature on a single crystal in three crystal orientations: 3 and Table 4.
Table 3. The parameters of Cauchy equations for anisotropic refractive indices. n A B (µm 2 ) C (µm 4 ) n o 1.697 0.00506 1.6234 × 10 -4 n e 1.583 0.00467 1.1898 × 10 -4
Table 4. The parameters of Urbach absorption equations for imaginary refractive index. k k 0 E u (eV) E 0 (eV) k o 0.11911 2.825 4.96 k e 0.02883 3.472 4.96
Second harmonic generation (SHG) is a process combining two photons of frequency ω into one photon of frequency 2ω through a noncentrosymmetric material. For real applications, the SHG process should take place only from the ground state to the virtual states to ensure minimal absorption and a non-resonant process. In the case of EBBO, the bandgap is 5.56 eV (∼220 nm); therefore fundamental wavelength needs to be longer than 440 nm. The wavelength demonstrated here was 800 nm, and the wavelength of the SHG was 400 nm.
The SHG measurement was performed in normal reflection geometry with a nonlinear optical microscope, shown in Fig. 4(a). The fundamental laser beam was linearly polarized and rotated by an angle of ψ using a halfwave plate, and the SHG light was decomposed into p-polarized (∥) and s-polarized (⊥) SHG light and detected by a photomultiplier tube.
Since the crystal belongs to the hexagonal crystal system, its crystal physics coordinate (Z 1 , Z 2 , Z 3 ) is defined as Z 1 //[2 11 0], Z 2 //[01 10], Z 3 //[0001]. The crystal was oriented such that -Z 2 and Z 1 axes were parallel to the lab axes X and Y, respectively.
A significant SHG signal indicates the absence of the inversion symmetry, in consistent with our FP calculations result. The observation of SHG signal in normal incidence rules out the P6 3 space group since point group 6 should not show any SHG signal when the incidence beam is along the 6-fold axis. This fact combined with the x-ray analysis presented earlier points to the P 6 as the most likely space group for this crystal. To obtain the d ij coefficients ratios of EBBO, the polar plots were fitted to an analytical model based on its point group symmetry 6 and compared with that measured on a wedged z-cut LiNbO 3 reference under the same experimental conditions. The theoretical expressions for the SHG intensity at normal incidence can thus be expressed as
(1)
The two non-zero SHG coefficients, d 11 and d 22 , could both be probed using the chosen geometry. The ratio of the SHG coefficients d 11 with respect to d 22 was extracted by fitting the SHG polar plots to Eq. ( 2), as shown in Fig. 4(b). The theoretical fit yielded the result of d 11 /d 22 = 1.47 ± 0.04. By comparing the SHG intensity with that of a z-cut LiNbO 3 reference measured under the same experimental conditions (details are provided in the Supplement 1 and Code 1) [22], one can extract that |d 11 | = 0.52 ± 0.03 pm/V and |d 22 | = 0.35 ± 0.02 pm/V. In particular note that d 11 and d 22 share the same sign.
To ensure that the detected signal was from the second-order NLO effect, the SHG intensities were measured as a function of incident power, shown in Fig. 4(c). The solid red line is the quadratic fit, and the black dots are the experimental data. The SHG response demonstrates a clear quadratic dependence on the input power, confirming that the measured signal was generated by the second-order NLO effect.
To obtain efficient frequency conversion, phase-matching is one of the most important criteria. The phase-matching conditions can be calculated using the Cauchy equations. From the previous section, we know that EBBO is a negative uniaxial crystal (n o >n e ). Therefore, the Type I phase-matching condition is achieved when n o,ω = n e,2ω (θ m ) and n ω o + n ω e (θ m ) = 2n 2ω e (θ m ) for Type II. We found that EBBO can be both Type I and Type II phase-matched, as shown in Fig. 5(a) and (b). We introduce an angle φ as the azimuthal angle, as defined in Fig. 5(c). For fundamental light of 800 nm, the effective d coefficients, d eff , for both conditions can be expressed as (2) The value of d 31 can be estimated to be 0.45 pm/V using Miller's rule, assuming that the Miller's coefficient defined as δ = χ (2) ω χ (1) 2ω (χ (1) ω ) 2 is the same as d 11 . The maximal |d eff, I | is 0.77 pm/V at φ = 108.7°and |d eff, II | is 0.34 pm/V at φ = 8.3°(Fig. 5(d)). These are estimates assuming that Miller's rule applies; this assumption requires a more careful future testing.
We identify EBBO as a potential new noncentrosymmetric material by analyzing unstable phonons from first principles computations in the reported centrosymmetric (P6 3 /m) structure. The inversion symmetry breaking is confirmed experimentally through SHG measurement, which confirms that the previous reported structure was incorrect [10]. Combining theory and experiment, we identify EBBO's space group to be P 6. Moreover, we report the first successful single crystal synthesis of EBBO using the floating-zone method. The anisotropic linear and nonlinear optical properties have been systematically characterized. It is also Type I and Type II phase-matchable in a wide range of wavelengths. FP calculations are performed to determine the most stable structure. This work suggests that rare earth metal borates are a good material system for UV NLO crystal exploration. It also shows how crystal structure previously reported to be centrosymmetric can be identified to be in fact noncentrosymmetric in first principles high-throughput phonon databases. This approach is of interest for the identification of new materials with NLO or ferroelectric properties. The point group 6 is non-polar. Nonetheless, motivated by the theoretical calculations, attempts were made to measure the ferroelectric hysteresis loop, which were unsuccessful as expected.