Supporting information for

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1 Supporting information for M 2 B 10 O 14 F 6 (M=Ca, Sr): Two Noncentrosymmetric Alkaline-Earth Fluorooxoborates as the Promising Next-Generation Deep-Ultraviolet Nonlinear Optical Materials Min Luo, Fei Liang,, Yunxia Song, Dan Zhao ƾ, Feng Xu, Ning Ye*, and Zheshuai Lin Key Laboratory of Optoelectronic Materials Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian , China Beijing Center for Crystal R&D, Key Lab of Functional Crystals and Laser Technology of Chinese Academy of Sciences, Technical University of Chinese Academy of Sciences, Beijing , China ƾ College of Chemistry and Chemical Engineering, Henan Polytechnic University, Jiaozuo, Henan , China nye@fjirsm.ac.cn S1

2 Table of contents Sections Titles pages Section S1. Materials and Methods (Synthesis, Instrumentation, and Computational S3 S7 Details) Table S1. Crystal Data and Structure Refinement for Ca 2 B 10 O 14 F 6 and Sr 2 B 10 O 14 F 6. S8 Table S2-S3. Atomic coordinates and equivalent isotropic displacement parameters S9 for CBOF and SBOF, respectively. Table S4-S5. Selected Bond Distances (Å) for CBOF and SBOF, respectively. S10 Table S6 Bulk modulus and Young modulus of some DUV NLO materials. S11 Table S7 The Birefringence of CBOF and SBOF at the wavelength of nm. S11 Table S8 Contribution of Different Geometrical Factors (g) to Structure Factors (C) S11 Table S9 Calculated Sellmeier equations of the refractive index for CBOF and S11 SBOF. Figure S1-S2 Photograph of CBOF and SBOF for the measurement of birefringence S12 Figure S3. X-ray powder diffraction patterns of (a) CBOF and (b) SBOF. Black line is S13 crystal sample and red line is simulation results Figure S4 Energy dispersive X-ray spectroscopy (EDX) of (a) CBOF and (b) SBOF. S14 Figure S5 TGA and DTA curves of CBOF and SBOF S15 Figure S6 UV-Vis-NIR diffuse-reflectance spectroscopy of (a) CBOF and (b) SBOF. S16 Figure S7 The arrangement of BO 3 groups in CBOF. S16 Figure S8 Macroscopic coordinates(y-z) of the crystal and the microscopic S17 coordinates (x -y ) of the [BO 3 ] groups. Figure S9 Calculated electronic band structures for a) CBOF and b) SBOF based on S17 GGA Figure S10 Calculated electronic band structures for a) CBOF and b) SBOF based on S17 PBE0 Figure S11 SHG-density of the (a) virtual-electron and (b) virtual-hole process of S18 CBOF. Figure S12 SHG-density of the (a) virtual-electron and (b) virtual-hole process of S18 SBOF. Figure S13 Calculated the refractive index for (a) CBOF and (b) SBOF. S18 Figure S14 Phase-matching conditions of (a) CBOF and (b) SBOF. S19 References S19 S2

3 Section S1. Materials and Methods Synthesis. All of the chemicals were of analytical grade from commercial sources and used without further purification. CaF 2 (99.8%), SrF 2 (99.8%), ethylamine-borontrifluoride (99.8%), H 3 BO 3 (99.0%), B 2 O 3 and Ca(BF 4 ) 2 2H 2 O were purchased from Adamas. Single crystals of MB 5 O 7 F 3 (M=Ca, Sr) were grown by an unconventional method. A mixture of H 3 BO 3 (24.8 g, 4 0mmol), CaF 2 (7.8g, 10 mmol) and ethylamine-borontrifluoride (22.3g, 20 mmol) were sealed in an autoclave equipped with a gold liner (250 ml). The autoclave was heated at 300 C for three days and cooled to room temperature at a rate of 5 C /h. The reaction product was washed with hot water and colorless brick-shaped CBOF crystals were thus obtained. The single crystals of SBOF can be obtained in the same way. Polycrystalline samples of CBOF and SBOF can be obtained by low temperature solid-state reaction based on the following reactions: 6MF 2 (M=Ca, Sr)+2BF 3 (C 2 H 7 N)+7B 2 O 3 =3M 2 B 10 O 14 F 6 (M=Ca, Sr)+2(C 2 H 7 N); 2MF 2 (M=Ca, Sr)+2BF 3 (C 2 H 7 N)+8H 3 BO 3 = M 2 B 10 O 14 F 6 (M=Ca, Sr)+12H 2 O+2(C 2 H 7 N); 2Ca(BF 4 ) 2 +6H 3 BO 3 = Ca 2 B 10 O 7 F HF+4H 2 O Single-Crystal X-ray Diffraction. Single crystal X-ray diffraction data were collected at room temperature on a Bruker Smart APEX II CCD area detector with graphite-monochromatic Mo K α radiation (λ = Å). A colorless brick-shaped crystal was mounted on a glass fiber with epoxy for structure determination. The intensity data sets were corrected with the ω -scan technique. The data were integrated with the CrystalClear program. The intensities were corrected for Lorentz polarization, air absorption, and absorption attributable to the variation in the path length through the detector faceplate. Absorption corrections were also applied based on the Multiscan technique. The structure was solved with direct methods, refined with difference Fourier maps and full-matrix least-squares fitting on F 2 with SHELXL Moreover, all nonhydrogen atoms were refined with anisotropic thermal parameters. The structure was verified using the ADDSYM algorithm from the program PLATON 2, and no higher symmetries were found. The details of the crystallographic data and structure refinement information for CBOF and SBOF are listed in Table S1. Atomic coordinates, isotropic displacement coefficients and the results of Bond valence calculations are listed in Table S2-S3, and bond lengths are listed in Table S4-S5. Powder X-ray Diffraction. X-ray diffraction patterns of polycrystalline materials were obtained on a Rigaku Dmax2500 powder X-ray diffractometer by using Cu Kα radiation (λ= Å) at room temperature in the angular range of 2θ = 5-75 with a scan step width of 0.05 and a fixed time of 0.2s. S3

4 Energy-dispersive X-ray Spectroscopy Analysis Microprobe elemental analyses were performed on a field emission scanning electron microscope (FESEM, SU-8010) equipped with an energy dispersive X-ray spectroscope (EDS). Thermal Analysis. Thermogravimetric analyses (TGA) and differential scanning calorimetry (DSC) were measured on a NETZCH STA 449F3. Reference (Al 2 O 3 ) and crystal samples (3-10 mg) were enclosed in Al 2 O 3 crucibles and heated from room temperature to 1000 C at a rate of 10 C/min under a constant flow of nitrogen gas. Diffuse reflectance and transmittance spectroscopy UV-vis-NIR spectrophotometer of the powder sample was measured at room temperature in the range of nm with BaSO 4 as the standard of 100% reflectance. The reflectance spectrum was transformed into the absorbance spectrum using the Kubelka Munk function 3,4. Birefringence. The Birefringence of CBOF and SBOF crystals were measured on a Nikon ECLIPSE LV100 POL polarizing microscope. The wavelength of the light source was nm. The x-y plane of an oriented crystal (Figure S1a-S2a) was used for the measurement. The thickness of CBOF and SBOF were 6.3 and 17.5 μm (Figure S1b-2b). The formula of calculated Birefringence can be expressed as follows: R (Retardation) = n T In this formula, R denotes optical path difference, n represent birefringence, T denotes the thickness of crystal. The measured Retardation and the calculated birefringence ( n= n x -n y ) were presented in Table S7. Second-Harmonic Generation. Polycrystalline second-harmonic generation (SHG) signals were measured using the method source by Kurtz and Perry 5. Since SHG efficiencies are known to depend strongly on particle size, The measurements were performed with a Q-switched Nd:YAG laser at 1064 nm and a frequency doubling at 532 nm, for visible and UV SHG, respectively. To make relevant comparisons with known NLO materials, crystalline KDP and BBO were also ground and sieved into the same particle size ranges and used as the references for visible and UV SHG, respectively. The samples were pressed between glass microscope cover slides and secured with tape in 1-mm thick aluminum holders containing an 8-mm diameter hole. They were then placed in a light-tight box and irradiated with a pulsed laser. A cutoff filter was used to limit background flash-lamp light on the sample, and an interference filter was used to select the second harmonic for detection with a photomultiplier tube attached to a RIGOL DS1052E 50-MHz oscilloscope. This procedure was then repeated using the standard nonlinear optical materials KDP and BBO, and the ratio of the S4

5 second-harmonic intensity outputs was calculated. No index-matching fluid was used in any of the experiments. Computational Descriptions. First-Principles Calculations. The first-principles calculations are performed by the psuedopotential 6 methods implemented in the CASTEP package 7 based on the density functional theory (DFT). 8 A kinetic energy cutoff of 900 ev is chosen with Monkhorst-Pack k-point meshes (3 3 3) spanning less than 0.04/Å 3 in the Brillouin zone. 9 The cell parameters and the atomic positions in the unit cells of all crystals are fully optimized using BFGS method. 10 The convergence thresholds between optimization cycles for energy change, maximum force, maximum stress, and maximum displacement are set as ev/atom, 0.01 ev/å, 0.02 GPa, and Å, respectively. The optimization terminates when all of these criteria are satisfied. The optimized norm-conserving pseudopotentials 11 (Ca 4s 2, Sr 5s 2, B 2s 2 2p 1, O 2s 2 2p 4, F 2s 2 2p 5 ) are used to simulate ion-electron interactions for all constituent elements. Based on the optimized geometry structure, the imaginary part of the dielectric function is calculated and the real part of the dielectric function is determined using the Kramers Kronig transform, 12 and then the refractive indices n and the birefringence n are obtained. The shortest SHG output wavelength λ PM is calculated based on the dispersion curves of refractive index (e.g., n max and n min ), satisfying the condition of n max (2λ PM ) = n min (λ PM ). The second order susceptibility χ (2) and SHG coefficient d ij (d ij = 1/2 χ (2) ) is calculated using an expression originally proposed by Rashkeev et al 13 and developed by Lin et al: 14 χ ijk = χ ijk (VE) + χ ijk (VH) + χ ijk (twobands) (1) where χ ijk (VE), χ ijk (VH) and χ ijk (two bands) denote the contributions from virtual-electron processes, virtual-hole processes and two band processes, respectively. Furthermore, it should be emphasized that the generalized gradient approximation (GGA) method with PBE functional 15 usually heavily underestimates the energy bandgap E g. Generally, the error between hybrid PBE0 (HSE06) bandgap and experimental bandgap of DUV transparent materials is less than 5%, so PBE0 (HSE06) functional is accurate enough for bandgap prediction Herein, the scissors-corrected 15 GGA method is employed to calculate the optical properties, where the scissors operator is set as the difference between the PBE0 and GGA bandgaps. This self-consistent ab initio approach has been proven to be an efficient way for the investigation of linear and NLO properties in many types of NLO materials without introducing any experimental parameter. 21 The Elastic coefficients, Young's modulus of CBOF and SBOF are calculated, while KBBF, NH 4 B 4 O 6 F, CsB 4 O 6 F and CsKB 8 O 12 F are also listed as comparison. In addition, the binding energy between layers is calculated to value the growth tendencies of mentioned above S5

6 compounds compared with that of KBBF. The binding energy is defined as the difference between the total energy of unit cell and those of the anionic layers and isolated alkali metal/ alkali-earth metal cations. The Anionic Group Theory Calculation According to the anionic group theory, the macroscopic SHG coefficients for CBOF and SBOF originate from a geometrical addition of the microscopic second-order susceptibility of the planar [BO 3 ] group. The macroscopic second-order susceptibility χ (2) could be expressed by Eq. 2 according to the anionic group theory. x F (2) (2) ijk ii' jj' kk' V p i'j'k' i'j'k' (P) (2) where F is the correction factor of the localized field, V is the volume of the unit cell,α ii, α jj, and α kk are the direction cosines between the macroscopic coordinates axes of the crystal and the microscopic coordinates axes of [BO 3 ] groups, and β i j k is the microscopic second-order susceptibility tensors of an individual group, which can be calculated with quantum chemistry method. Because [BO 3 ] is a planar group in point group D 3h, in the Kleinman approximation, there are only two (2) (2) nonvanishing second-order susceptibility β 111 = β122..the geometrical factor, g, could be derived from Eq. (1). and Eq. (2) could be simplified according to the deduction process 44 : x F = g (3) V (2) (2) ijk ijk 111 g=max(g ijk ); (i,j,k=1,2,3) (4) In case of unspontaneous polarization, the structural criterion C is defined as: C g n (5) where n is the number of anionic groups in a unit cell. We assume that the title compounds have similar refractive indices, which results in the approximate localized field (F). Hence, according to Eqs. (3) and (5), the NLO coefficient is proportional to density of the [BO 3 ] group (n/v) and the structural criterion(c). In the structure, we already know that two adjacent BO 3 groups in the same layer present different orientation, forming an angle θ. To further elucidate the relationship between the NLO properties and structure, the relationship between the structural criterion C and the rotational angle θ have been investigated. The space group of CBOF and SBOF belong to class mm2, only three independent tensors of second-order susceptibility, namely 2 ( ), 311 restriction of Kleinman s symmetry. 2 ( ) and ( ), should be take into account under the S6

7 With 2 ( ) as an example, the following equation can be obtained according to Eq g (2) (2) F. g. ([B O ]); V n 2 2 [ (31) (11) 2 (11) (12) (32) (12) (31)] p Where α(11) and α(12) denote the direction cosines between the macroscopic coordinate X axis of the crystal and the microscopic coordinate x and y axis of [BO 3 ] groups, respectively. Analogously, α(31) and α(32) denote the direction cosines between the macroscopic coordinate Z axis of the crystal and the microscopic coordinate x and y axis of [BO 3 ] groups, respectively. As shown in Figure S7, the θ presents the angle between two [BO 3 ] groups pointing in different direction; θ 1 and θ 2 were defined as the angle between the microscopic coordinate x and the macroscopic coordinate Y and Z axis, respectively. Since two different orientation [BO 3 ] groups are equivalent in the crystallographic sites, OA should be equal to OB. Therefore, the relationship between θ, θ 1 and θ 2 can be derived according to their geometrical relationships, namely, θ1 = θ 2 and θ 2=90 - θ. In order to simplify the calculation, we assume that macroscopic coordinate 2 X is completely parallel to microscopic coordinate y. Combining with above-mentioned geometrical relationships, we can calculate that, α(11) = 0, α(12) = 1, α(31) = sin θ 2, α(32) = 0. Consequently, g 311 can be expressed as the following, g 311 = -sin θ 2 Similarly, g 322 g333 = -cos 2 sin ; sin 2 In case of unspontaneous polarization, the structural criterion C is defined as the following, c g n 8 g sin The calculated g ijk values were listed in Table S8 S7

8 Table S1 Crystal Data and Structure Refinement for Ca 2 B 10 O 14 F 6 and Sr 2 B 10 O 14 F 6. Formula Ca 2 B 10 O 14 F 6 Sr 2 B 10 O 14 F 6 Formula Mass (amu) Crystal System Orthorhombic Orthorhombic Space Group Cmc21 Cmc21 a (Å) 9.911(4) (14) b (Å) 8.402(3) (13) c (Å) 7.966(3) (14) V(Å 3 ) 663.4(5) (19) Z 2 2 ρ(calcd) (g/cm 3 ) Temperature (K) 296(2) 293(2) λ(å) F(000) μ (mm -1 ) R/wR (I>2σ (I)) / / R/wR (all data) / / GOF on F Absolute Parameter Structure 0.03(5) 0.01(2) R(F) = Σ F o F c /Σ F o. wr(f o 2 ) = [Σw(F o 2 F c 2 ) 2 /Σw(F o 2 ) 2 ] 1 S8

9 Table S2 Atomic coordinates and equivalent isotropic displacement parameters for Ca 2 B 10 O 14 F 6. atom x y z U eq (Å 2 ) BVS Ca(1) (1) 6175(1) 10(1) 2.00 F(1) 8697(1) 10283(2) 5285(2) 20(1) 0.96 F(2) (2) 6398(3) 21(1) 1.05 O(1) (2) 6162(4) 8(1) 1.99 O(2) 7552(2) 8149(2) 6455(2) 12(1) 2.04 O(3) 8843(2) 6749(2) 8477(2) 12(1) 2.10 O(4) 8555(2) 7931(2) 3729(2) 14(1) 2.04 B(1) 8660(2) 8607(3) 5392(3) 9(1) 3.07 B(2) 7646(3) 7316(3) 7918(3) 11(1) 3.06 B(3) (5) 7376(5) 9(1) 3.05 Table S3 Atomic coordinates and equivalent isotropic displacement parameters for Sr 2 B 10 O 14 F 6 atom x y z U eq (Å 2 ) BVS Sr(1) (1) 3803(3) 12(1) 2.39 F(1) 1310(3) -180(4) 4734(6) 22(1) 0.94 F(2) (5) 3626(9) 26(1) 1.12 O(1) (5) 3862(12) 10(1) 1.89 O(2) 2426(3) 1873(5) 3547(6) 15(1) 2.13 O(3) 1146(4) 3229(5) 1598(5) 15(1) 2.16 O(4) 1478(4) 2109(5) 6233(5) 14(1) 2.11 B(1) 1362(7) 1469(8) 4610(9) 12(2) 3.07 B(2) 2340(8) 2640(8) 2064(10) 14(2) 3.00 B(3) (11) 2658(12) 8(2) 3.11 S9

10 Table S4. Bond lengths (Å) for Ca 2 B 10 O 14 F 6. Ca(1)-F(2)# (2) F(2)-Ca(1)# (2) Ca(1)-F(1)# (18) O(1)-B(3) 1.517(5) Ca(1)-F(1)# (18) O(1)-B(1)# (3) Ca(1)-O(3)# (2) O(1)-B(1) 1.524(3) Ca(1)-O(3)# (2) O(2)-B(2) 1.363(3) Ca(1)-O(4)# (19) O(2)-B(1) 1.439(3) Ca(1)-O(4)# (19) O(3)-B(2) 1.353(3) Ca(1)-O(2) (18) O(3)-B(3) 1.444(3) Ca(1)-O(2)# (18) O(3)-Ca(1)# (2) Ca(1)-B(2) 2.977(3) O(4)-B(2)# (3) Ca(1)-B(2)# (3) O(4)-B(1) 1.445(3) Ca(1)-B(3)# (4) O(4)-Ca(1)# (19) F(1)-B(1) 1.411(3) B(2)-O(4)# (3) F(1)-Ca(1)# (18) B(3)-O(3)# (3) F(2)-B(3) 1.420(4) B(3)-Ca(1)# (4) Table S5. Bond lengths (Å) for Sr 2 B 10 O 14 F 6. Sr(1)-F(2)# (4) F(2)-Sr(1)# (4) Sr(1)-F(1)# (4) O(1)-B(3) 1.536(12) Sr(1)-F(1)# (4) O(1)-B(1)# (8) Sr(1)-O(4)# (5) O(1)-B(1) 1.544(8) Sr(1)-O(4)# (5) O(2)-B(2) 1.376(10) Sr(1)-O(3)# (5) O(2)-B(1) 1.414(8) Sr(1)-O(3)# (5) O(3)-B(2) 1.354(8) Sr(1)-O(2) 2.630(4) O(3)-B(3) 1.435(7) Sr(1)-O(2)# (4) O(3)-Sr(1)# (5) Sr(1)-B(2) 3.020(8) O(4)-B(2)# (8) Sr(1)-B(2)# (8) O(4)-B(1) 1.432(8) Sr(1)-B(3)# (10) O(4)-Sr(1)# (5) F(1)-B(1) 1.434(8) B(2)-O(4)# (8) F(1)-Sr(1)# (4) B(3)-O(3)# (7) F(2)-B(3) 1.397(11) B(3)-Sr(1)# (10) S10

11 Table S6 Bulk modulus and Young modulus of some DUV NLO materials. Crystals Bulk Modulus Young Modulus (GPa) X (GPa) Y (GPa) Z (GPa) KBBF NH 4 B 4 O 6 F CsB 4 O 6 F CsKB 8 O 12 F SBOF CBOF Table S7 The Birefringence of CBOF and SBOF at the wavelength of nm Crystals Retardation R (nm) Thickness T (μm) Birefringence ( n) CBOF SBOF Table S8 Contribution of Different Geometrical Factors (g) to Structure Factors (C) Crystals (n) g 311 /n g 322 /n g 333 /n CBOF (n=4) SBOF (n=4) Table S9. Calculated Sellmeier equations of the refractive index for CBOF and SBOF. CBOF n 2 x = /(λ ) λ 2 n 2 y = /(λ ) λ 2 n 2 z = /(λ ) λ 2 SBOF n 2 x = /(λ ) λ 2 n 2 y = /(λ ) λ 2 n 2 z = /(λ ) λ 2 S11

12 Figure S1 Photograph of crystal CBOF for the measurement of birefringence Figure S2 Photograph of crystal SBOF for the measurement of birefringence S12

13 (a) (b) Figure S3 X-ray powder diffraction patterns of (a) CBOF and (b) SBOF. Black line is crystal sample and red line is simulation results S13

14 (a) (b) Figure S4 Energy dispersive X-ray spectroscopy (EDX) of (a) CBOF and (b) SBOF. S14

15 (a) (b) Figure S5 TGA and DSC curves of (a) CBOF and (b) SBOF. S15

16 (a) (b) Figure S6 UV-vis-NIR diffuse-reflectance spectroscopy of (a) CBOF and (b) SBOF. Figure S7 the arrangement of BO 3 groups in CBOF. S16

17 Figure S8 Macroscopic coordinates(y-z) of the crystal and the microscopic coordinates (x -y ) of the [BO 3 ] groups. Figure S9 Calculated electronic band structures for a) CBOF and b) SBOF based on GGA. Figure S10 Calculated electronic band structures for a) CBOF and b) SBOF based on PBE0. S17

18 Figure S11 SHG-density of the (a) virtual-electron and (b) virtual-hole process of CBOF. Figure S12 SHG-density of the (a) virtual-electron and (b) virtual-hole process of SBOF. Figure S13 Calculated the refractive index for (a) CBOF and (b) SBOF. S18

19 References Figure S14. Phase-matching conditions of (a) CBOF and (b) SBOF. (1) G. M. Sheldrick, Acta Crystallogr. Sect. A 2008, 64, (2) A. L. Spek, J. Appl. Crystallogr. 2003, 36, (3) P. Kubelka, F. Z. Munk, Tech. Phys. 1931, 12, (4) J. Tauc, Mater. Res. Bull. 1970, 5, (5) S. K. Kurtz, T. T. Perry, J Appl Phys 1968, 39, (6) Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T. A.; Joannopoulos, J. D. Rev. Mod. Phys. 1992, 64, (7) Clark, S. J.; Segall, M. D.; Pickard, C. J.; Hasnip, P. J.; Probert, M. J.; Refson, K.; Payne, M. C. Z. Kristallogr. 2005, 220, 567. (8) Kohn, W. Rev. Mod. Phys. 1999, 71, (9) Monkhorst, H. J.; Pack, J. D. Phys. Rev. B 1976, 13, (10) Pfrommer, B. G.; Cote, M.; Louie, S. G.; Cohen, M. L. J. Comput. Phys. 1997, 131, 233. (11) Rappe, A. M.; Rabe, K. M.; Kaxiras, E.; Joannopoulos, J. D. Phys. Rev. B 1990, 41, (12) Kang, L.; Ramo, D. M.; Lin, Z.; Bristowe, P. D.; Qin, J.; Chen, C. J. Mater. Chem. C 2013, 1, (13) Rashkeev, S. N.; Lambrecht, W. R. L.; Segall, B. Phys. Rev. B 1998, 57, (14) Lin, J.; Lee, M. H.; Liu, Z. P.; Chen, C. T.; Pickard, C. J. Phys. Rev. B 1999, 60, (15) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, (16) Kang, L.; Luo, S.; Huang, H.; Zheng, T.; Lin, Z. S.; Chen, C. T. J. Phys-Condens. Mat. 2012, 24, (17) Wang, X.; Wang, Y.; Zhang, B.; Zhang, F.; Yang, Z.; Pan, S. Angew. Chem. Int. Ed. 2017, 56, (18) Zhang, B.; Shi, G.; Yang, Z.; Zhang, F.; Pan, S. Angew. Chem. Int. Ed. 2017, 56, (19) Shi, G.; Wang, Y.; Zhang, F.; Zhang, B.; Yang, Z.; Hou, X.; Pan, S.; Poeppelmeier, K. R. J. Am. Chem. Soc. 2017, 139, (20) Wang, C. S.; Klein, B. M. Phys. Rev. B 1981, 24, (21) Lin, Z. S.; Jiang, X. X.; Kang, L.; Gong, P. F.; Luo, S. Y.; Lee, M. H. J. Phys. D Appl. Phys. 2014, 47, S19