Strong Kleinman Forbidden Second Harmonic Generation in ...

Supporting Information

S1

Strong Kleinman Forbidden Second Harmonic

Generation in Chiral Sulfide: La4InSbS9

Hua-Jun Zhao, Yong-Fan Zhang, Ling Chen*

Synthesis. The elements were used as purchased and stored in a nitrogen-filled

glovebox (moisture and oxygen level is less than 0.1 ppm), and all manipulations

were performed inside the glovebox. La (99.99%), Pr (99.5%), and Nd (99.5%) were

purchased from Huhhot Jinrui Rare Earth Co., Ltd. S (99.999%) was purchased from

Alfa Aesar China (Tianjin) Co., Ltd. Sb (99.99%) and In (99.999%) were purchased

from Sinopharm Chemical Reagent Co., Ltd. All reactants in evacuated fused-silica

tubes were placed in resistance furnaces with controlled temperature.

The stoichiometric mixture of Ln, In, Sb, S were weighed accordingly with an

overall loading of about 300 mg and loaded into a silica tube, which was evacuated

and sealed. The sample were heated to 950 °C in 24 h and kept at that temperature for

4 days, subsequently cooled at 2.5 °C/h to 200°C before the furnace was turned off.

The yellow block crystals were picked for single crystal diffraction studies, which

yielded a formula of Ln4InSbS9. The EDX results on such crystals confirmed the

presence of Ln, In, Sb, and S with a molar ratio around 3.2(1):1.1(1):1.1(1):10.7(5).

No other element, such as Si from the reaction container, was found (Figure S1). The

homogeneity of the samples was confirmed by XRD analyses (Figure S2–4). No

corrosion on the silica tubing in any case was observed and all compounds were stable

in air for about one year.


S2

Figure S1. The EDX spectrum of Pr4InSbS9

Point-1 Point-2

Point-3 Point-4

Element Weight% Atomic% Formula

S K 32.77 66.65 10.43

In L 13.03 7.40 1.16

Sb L 11.93 6.39 1.00

Pr L 42.27 19.57 3.06

Totals 100.00

Average formula: Pr3.2(1)In1.1 (1)Sb1.1(1)S10.7(5)


S K 33.49 67.49 11.23

In L 10.68 6.01 1.00

Sb L 12.62 6.70 1.11

Pr L 43.20 19.81 3.30

Totals 100.00


S K 33.98 67.94 11.04

In L 11.44 6.39 1.04

Sb L 11.68 6.15 1.00

Pr L 42.90 19.52 3.17

Totals 100.00


S K 31.59 65.53 10.22

In L 11.06 6.41 1.00

Sb L 13.17 7.20 1.12

Pr L 44.18 20.86 3.25

Totals 100.00


S3

Figure S2. The experimental and simulated X-ray powder diffraction patterns of La4InSbS9.

Figure S3. The experimental and simulated X-ray powder diffraction patterns of Pr4InSbS9.

Figure S4. The experimental and simulated X-ray powder diffraction patterns of Nd4InSbS9.


S4

Crystal Structure Determinations. Data collections were performed on either a

Rigaku Saturn70 CCD or a Rigaku Mercury CCD equipped with

graphite-monochromated Mo Kα radiation (λ = 0.71073 Å) at 293 K. The data were

corrected for Lorentz and polarization factors. Absorption corrections were performed

by the multiscan method.1 All structure were solved by the direct methods and refined

by full-matrix least-squares fitting on F2 by SHELX-97.2 All atoms were refined with

anisotropic thermal parameters. All positions were fully occupied. Crystallographic

data and structural refinement details are summarized in Table S1 (the structure of

La4InSbS9 was solved in the P41212 group, and the others in P43212 group, but this

did not preclude the existence of the enantiomorph in one sample). The positional

coordinates and isotropic equivalent thermal parameters are given in Table S2, and

important bond distances are listed in Table S3.


S5

Table S1. Crystallographic Data and Refinement Details for Ln4InSbS9 (Ln = La, Pr, Nd).

Formula La4InSbS9 Pr4InSbS9 Nd4InSbS9

Fw 1080.75 1088.85 1102.17

Crystal system tetragonal tetragonal tetragonal

Crystal color yellow yellow yellow

Z 8 8 8

Space group P41212 (No. 92) P43212 (No. 96) P43212 (No. 96)

a (Å) 10.2728(2) 10.105(2) 10.0722(1)

c (Å) 28.313(1) 27.907(6) 27.830(1)

V (Å3) 2987.9(2) 2849.1(9) 2823.2(1)

F(000) 3776 3840 3872

Dc (g cm–3) 4.805 5.076 5.343

µ (mm-1) 15.701 18.149 19.857

2θmax (deg.) 54.96 54.96 54.94

GOOF on F2 1.192 0.988 1.119

R1, wR2 (I > 2σ(I)) a 0.0211, 0.0347 0.0178, 0.0336 0.0371, 0.0631

R1, wR2 (all data) 0.0218, 0.0349 0.0187, 0.0349 0.0419, 0.0651

Flack parameter 0.03(2) 0.05(1) -0.02(3)

diff peak, hole (e. Å-3) 0.722, -0.932 0.827, -0.803 1.498, -1.476

a R1 = Σ||Fo| - |Fc||/Σ|Fo|, wR2 = [Σw(Fo2 - Fc

2)2/Σw(Fo2)2]1/2


S6

Table S2. Atomic coordinates and equivalent isotropic displacement parameters of Ln4InSbS9 (Ln = La, Pr, Nd).

atom symmetry x y z U(eq)

La4InSbS9

La1 8b 0.22412(3) 0.44032(3) 0.08836(1) 0.01084(7)

La2 8b 0.48962(4) 0.14819(3) 0.05238(1) 0.01122(7)

La3 8b 0.49702(4) 0.26817(3) 0.19911(1) 0.01219(7)

La4 8b 0.05579(3) 0.27104(3) 0.34180(1) 0.01057(7)

In1 8b 0.01288(4) 0.20343(4) 0.20281(1) 0.01333(9)

Sb1 8b 0.36137(4) 0.49277(5) 0.30584(2) 0.0233(1)

S1 8b 0.3238(1) 0.4926(2) 0.21166(5) 0.0155(3)

S2 8b 0.0170(2) 0.1857(1) 0.44991(5) 0.0135(3)

S3 8b 0.0054(1) 0.0141(1) 0.14780(4) 0.0149(3)

S4 8b 0.0021(2) 0.3942(1) 0.15127(4) 0.0116(3)

S5 4a 0.6893(2) 0.6893(2) 0.0000 0.0336(7)

S6 8b 0.2056(2) 0.1941(2) 0.25351(5) 0.0166(4)

S7 8b 0.0037(1) 0.4969(1) 0.28184(4) 0.0110(2)

S8 8b 0.2975(2) 0.1757(2) 0.37639(5) 0.0118(3)

S9 8b 0.3105(2) 0.2013(2) 0.12748(5) 0.0116(3)

S10 4a 0.3166(2) 0.3166(2) 0.0000 0.0153(5)

Pr4InSbS9

Pr1 8b 0.43971(3) 0.22393(3) 0.08825(1) 0.00660(7)

Pr2 8b 0.48941(3) 0.14961(3) –0.052697(9) 0.00701(6)

Pr3 8b 0.76724(3) 0.00218(3) 0.050635(9) 0.00795(6)

Pr4 8b 0.44370(3) –0.22829(3) 0.09229(1) 0.00696(7)

In1 8b 0.20339(4) 0.01347(4) 0.20316(1) 0.00797(8)

Sb1 8b 0.64079(4) 0.50859(4) 0.19454(1) 0.01157(8)

S1 8b 0.6770(1) 0.5094(2) 0.28825(4) 0.0090(3)

S2 8b 0.4805(1) –0.3124(1) 0.20009(4) 0.0082(3)

S3 8b 0.5104(1) 0.4945(1) 0.10178(4) 0.0085(2)

S4 8b 0.3970(1) 0.0031(2) 0.15097(4) 0.0069(2)

S5 4a 0.1926(2) –0.1926(2) 0.2500 0.0266(6)

S6 8b 0.2936(2) –0.3028(2) 0.00549(5) 0.0096(3)

S7 8b 0.4964(1) –0.0016(1) 0.03151(4) 0.0071(2)

S8 8b 0.2018(2) –0.3241(1) 0.12667(4) 0.0077(3)

S9 8b 0.2013(2) 0.3104(1) 0.12804(4) 0.0070(3)

S10 4a 0.3166(2) 0.3166(2) 0.0000 0.0096(4)

Nd4InSbS9

Nd1 8b 0.55967(7) 0.77561(6) 0.08828(2) 0.0126(1)

Nd2 8b 0.51027(7) 0.84942(6) –0.05276(2) 0.0134(1)

Nd3 8b 0.23302(6) 0.99840(7) 0.05068(2) 0.0143(1)

Nd4 8b 0.55620(7) 1.22772(6) 0.09243(2) 0.0129(1)


S7

In1 8b 0.79569(8) 0.98705(9) 0.20315(3) 0.0152(2)

Sb1 8b –0.14136(8) 1.0093(1) 0.05544(3) 0.0215(2)

S1 8b 0.0099(3) 0.8229(3) 0.0388(1) 0.0167(6)

S2 8b 0.5200(3) 1.3120(3) 0.2004(1) 0.0134(6)

S3 8b 0.4904(3) 0.5047(3) 0.10105(9) 0.0166(5)

S4 8b 0.6021(2) 0.9964(3) 0.1510(1) 0.0123(5)

S5 4a 0.8070(4) 1.1930(4) 0.2500 0.042(2)

S6 8b 0.7066(3) 1.3025(3) 0.0058(1) 0.0167(7)

S7 8b 0.5033(3) 1.0010(3) 0.03145(9) 0.0126(5)

S8 8b 0.7985(3) 1.3234(3) 0.1265(1) 0.0125(6)

S9 8b 0.7981(3) 0.6899(3) 0.1280(1) 0.0120(6)

S10 4a 0.6835(3) 0.6835(3) 0.0000 0.0153(9)

S7, S8, S9, and S10 are the discrete atoms.

Table S3. Selected bond lengths (Å) of Ln4InSbS9 (Ln = La, Pr, Nd)

La4InSbS9 Pr4InSbS9 Nd4InSbS9

La1–S9 2.838(2) 2.794(2) 2.780(3)

La1–S9 2.872(2) 2.827(2) 2.819(3)

La1–S7 2.889(1) 2.834(1) 2.824(3)

La1–S3 2.908(2) 2.850(1) 2.839(3)

La1–S4 2.934(2) 2.869(2) 2.859(3)

La1–S10 2.9624(4) 2.9136(6) 2.9073(7)

La2–S7 2.848(1) 2.804(1) 2.798(3)

La2–S9 2.865(2) 2.823(1) 2.814(3)

La2–S10 2.8898(3) 2.8387(5) 2.8271(7)

La2–S8 2.891(2) 2.845(1) 2.829(3)

La2–S4 2.923(1) 2.863(1) 2.853(3)

La2–S6 2.930(2) 2.875(2) 2.857(3)

La3–S8 2.840(2) 2.792(1) 2.788(3)

La3–S7 2.845(1) 2.789(1) 2.775(3)

La3–S9 2.874(2) 2.828(1) 2.823(3)

La3–S2 2.906(1) 2.852(1) 2.839(3)

La3–S1 2.934(2) 2.888(2) 2.879(3)

La3–S2 2.939(2) 2.885(2) 2.872(3)

La4–S8 2.843(2) 2.799(2) 2.785(3)

La4–S8 2.857(2) 2.799(2) 2.789(3)

La4–S7 2.925(1) 2.900(1) 2.895(3)

La4–S3 2.943(2) 2.894(2) 2.877(3)


S8

La4–S4 2.955(2) 2.894(2) 2.880(3)

La4–S6 3.040(2) 2.956(2) 2.947(3)

La4–S2 3.210(1) 3.149(1) 3.141(3)

In1–S4 2.446(1) 2.438(2) 2.433(3)

In1–S6 2.447(2) 2.441(1) 2.439(3)

In1–S5 2.474(2) 2.461(2) 2.453(3)

In1–S3 2.494(1) 2.483(1) 2.476(3)

Sb1–S2 2.438(2) 2.434(2) 2.431(3)

Sb1–S1 2.461(2) 2.460(2) 2.461(3)

Sb1–S1 2.695(1) 2.641(1) 2.646(3)

Sb1–S3 2.905(1) 2.909(1) 2.924(3)

X-ray Powder Diffraction. XRD pattern were collected on a Rigaku DMAX

2500 diffractometer. The measured XRD patterns are in good agreement with the ones

simulated from crystal structure data (Figure S2–4).

Elemental analysis. The elemental analyses of Ln, In, Sb, S have been examined

with the aid of a fieldemission scanning electron microscope (FESEM, JSM6700F)

equipped with an energy dispersive X-ray spectroscope (EDX, Oxford INCA).

Magnetic Susceptibility. The dc magnetic susceptibility measurements were

performed on a Quantum Design PPMS-9T magnetometer in the temperature range of

2–300K. The X-ray pure polycrystalline samples were ground to a fine power to

minimize possible anisotropic effects and loaded into a gelatin capsule. The data were

corrected for the susceptibility of container and for the diamagnetic contribution from

the ion core. The susceptibility data in the temperature range 60–300 K were fit by a

least-squares method to the Curie–Weiss equation χM = C/(T – θ),where χM is the

magnetic susceptibility, C is the Curie constant and θ is the Weiss constant. The

effective magnetic moment (µeff) was calculated from the equation µeff = (7.997C)1/2


S9

µB.3

UV/Vis/NIR Diffuse Reflectance Spectroscopy. The optical diffuse reflectance

spectrum of powdered samples were measured at room temperature using a

Perkin-Elmer Lambda 900 UV-vis spectrophotometer equipped with an integrating

sphere attachment and BaSO4 as a reference. The absorption spectrum was calculated

from the reflection spectrum via the Kubelka-Munk function: α/S = (1 – R)2/2R, in

which α is the absorption coefficient, S is the scattering coefficient, and R is the

reflectance.4

Infrared Spectroscopy. IR spectra was recorded by using a Magna 750 FTIR

spectrometer with samples as KBr pellets in the range of 4000–400 cm-1.

SHG Measurements. Powder Second harmonic generation (SHG) was measured

by using the Kurtz and Perry method with a 2.05 µm Q-switch laser.5 The samples

were carefully ground and sieved into five distinct particle size ranges (30–46, 46–74,

74–106, 106–150, and 150–210 µm). The SHG effects of compounds sieved with

70–100 meshes (≈150–210 µm) were measured with the same graded powdery

AgGaS2 as a reference.

The thermogravimetric analysis. Thermogravimetric analyses (TGA) were

carried out with a NETZSCH STA 449C unit at a heating rate of 10 °C/min under a

nitrogen atmosphere. In order to check the thermal stability in details, we loaded the

sample of La4InSbS9 into silica tube, which was evacuated and sealed. The sample

was heated to 750, 800, and 900 °C, respectively, and kept at that temperature for 10

hrs. Serious XRD analyses indicated the sample heated at 750 °C was still single


S10

phased La4InSbS9; that heated at 800 °C contained minor binary La2S3 as impurity,

and that at 900 °C, contained considerable binary La2S3 impurity (about 50 %).

(Figure S11). These data were consistent with the TG analysis.

Calculations of electronic structures and static SHG coefficients.

First-principles calculations based on density functional theory (DFT) were carried

out utilizing the Vienna ab initio simulation package (VASP) and the projected

augmented wave (PAW) method.6–8 The generalized gradient approximation

Perdew-Burke-Ernzerh of (PBE)9 exchange-correlation functional was employed. The

kinetic cutoff energy for the plane-wave expansion was set to 280 eV, and more than

1000 empty energy bands were involved in the calculations. Tests for the

Monkhorst-Pack k-point mesh were carried out, and the results indicated that a (3 × 3

× 3) sampling k mesh was enough to ensure the convergence of the second harmonic

generation (SHG) coefficients of La4InSbS9 crystal. Ab initio molecular dynamic

(MD) simulations using the Nosé algorithm10 were performed to obtain possible

structures of La4InSbS9, considering the effects of nuclei vibrations. The MD

simulation was carried out with a low-energy cutoff (194 eV) and one k point (namely,

Γ point); the simulation length was 10 ps with time step of 1 fs at the temperature of

300 K. After simulation time was longer than 7 ps, eleven typical configurations were

chosen to study the variation of SHG coefficients.

In this work, the SHG coefficients were determined by using the so-called

length-gauge formalism derived by Aversa and Sipe.11, 12 At a zero-frequency limit,

the second-order nonlinear susceptibility ),,2( ωωωχ −abc can be expressed as:


S11

+++=− ∑ ][}{1

),,2( ln, ln

lnnmlmmln

knml mlnm

cb

ml

a

nmabcfff

rrr

Vωωω

ωωωωωωχ

∑ +++++knm

b

amn

a

bmn

c

nm

c

amn

a

cmn

b

nm

c

bmn

b

cmn

a

nm

mn

nm rrrrrrrrrf

V

i

,;;;;;;2

)]()()([4 ω

in which r is the position operator, mnnm ωωω hhh −= is the energy difference

between bands m and n, mnnm fff −= is the difference of the Fermi distribution

functions, V is the unit cell volume, and b

amnr ; is the so-called generalized derivative

of the coordinate operator in k space.

∑ −+∆+∆

=l

a

lm

b

nlnl

b

lm

a

nllm

nmnm

a

mn

b

nm

b

mn

a

nmb

amn rrrrirr

r )(; ωωωω

Figure S5. (a) The helical chain of [In2Sb2S1110–]∞ in La4InSbS9 (b) NCS chain of

[Ga2Sb2S1110–]∞ in Sm4GaSbS9. Pink, In; sky blue, Ga; Orange, Sb; Yellow, S.


S12

Table S4. The calculated second-order nonlinear optical susceptibilities (pm/V) based on the 11 typical ab initio molecular dynamic simulated configurations of La4InSbS9 at 300 K.

Figure S6. Inverse magnetic susceptibility plotted against temperature for Pr4InSbS9 and Nd4InSbS9.

Eg d11 d12/

d26

d13/

d35

d14/

d25/

d36

d15/

d31

d16/

d21 d22

d23/

d34

d24/

d32 d33

1 2.0500 –2.61 –0.63 0.29 1.29 1.77 –1.29 –14.95 –6.73 –1.46 –7.81

2 2.0460 –13.47 –1.64 –5.58 1.48 2.68 0.91 –8.36 –0.18 –4.15 18.94

3 2.0343 –1.30 0.58 2.00 –0.04 2.48 2.55 0.20 2.47 –1.57 9.30

4 1.8769 –21.17 –3.11 –12.90 –2.38 4.56 4.32 –14.80 –3.34 –0.01 14.27

5 2.0291 –9.00 –3.94 –5.05 0.37 –1.10 4.02 –8.05 –4.42 5.26 17.31

6 1.9891 10.12 10.00 –3.50 2.31 –2.38 –2.12 –0.96 –4.53 –13.98 –3.51

7 1.9107 –6.96 1.01 –2.52 –4.56 –1.94 –1.49 1.49 –1.27 3.39 –20.47

8 1.7041 12.11 3.82 16.06 0.87 8.51 0.70 0.26 –1.12 8.35 –18.85

9 1.6605 –3.45 –6.25 –3.45 3.35 1.09 3.79 4.56 –7.42 7.45 –2.64

10 1.7926 11.53 6.31 9.23 0.30 3.28 –11.17 –0.19 4.82 –4.76 7.80

11 1.7608 13.29 5.01 –0.78 –1.27 –6.37 –4.09 20.73 6.89 –10.78 24.37


S13

Figure S7. UV/Vis/NIR diffuse reflectance of (a) Pr4InSbS9, (b) Nd4InSbS9.

Figure S8. Transmittance curves of the powder AgGaS2 in the IR region and UV/Vis/NIR reflection spectrum (inset panel).


S14

Figure S9. The band structure of La4InSbS9.

Figure S10. Total and partial densities of states of La4InSbS9.


S15

Figure S11. The X-ray powder diffraction patterns of sample of La4InSbS9 heated at various temperatures and the simulated one. Arrows indicate the decomposed product.


S16

Reference.

1. CrystalClear, version 1.3.5; Rigaku Corp.: The Woodlands, TX, 1999.

2. Sheldrick, G. M. SHELXTL, version 5.1; Bruker-AXS: Madison, WI, 1998.

3. O’Connor, C. J. Prog. Inorg. Chem. 1982, 29, 203.

4. Kortüm, G. Reflectance Spectroscopy; Springer-Verlag: New York, 1969.

5. Kurtz, S. K.; Perry, T. T. Appl. Phys. 1968, 39, 3798.

6. Blöchl, O. E. Phys. Rev. B 1994, 50, 17953.

7. Kresse, G.; Furthmuller, J. J. Phys. Rev. B 1996, 54, 11169.

8. Kresse, G.; Furthmuller, J. Comput. Mater. Sci. 1996, 6, 15.

9. Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.;

Singh, D. J.; Fiolhais, C. Phys. Rev. B 1992, 46, 6671.

10. Nosé, S. J. Chem. Phys. 1984, 81, 511.

11. Rashkeev, S. N.; Lambrecht, W. R. L.; Segall, B. Phys. Rev. B 1998, 57,

3905.

12. Aversa, C.; Sipe, J. E. Phys. Rev. B 1995, 52, 14636.

Strong Kleinman Forbidden Second Harmonic Generation in ...

Documents

Transcript of Strong Kleinman Forbidden Second Harmonic Generation in ...