Phase Transitions, Dielectric Response, and Nonlinear Optical Properties of Aziridinium Lead Halide Perovskites

Hybrid organic–inorganic lead halide perovskites are promising candidates for next-generation solar cells, light-emitting diodes, photodetectors, and lasers. The structural, dynamic, and phase-transition properties play a key role in the performance of these materials. In this work, we use a multitechnique experimental (thermal, X-ray diffraction, Raman scattering, dielectric, nonlinear optical) and theoretical (machine-learning force field) approach to map the phase diagrams and obtain information on molecular dynamics and mechanism of the structural phase transitions in novel 3D AZRPbX3 perovskites (AZR = aziridinium; X = Cl, Br, I). Our work reveals that all perovskites undergo order–disorder phase transitions at low temperatures, which significantly affect the structural, dielectric, phonon, and nonlinear optical properties of these compounds. The desirable cubic phases of AZRPbX3 remain stable at lower temperatures (132, 145, and 162 K for I, Br, and Cl) compared to the methylammonium and formamidinium analogues. Similar to other 3D-connected hybrid perovskites, the dielectric response reveals a rather high dielectric permittivity, an important feature for defect tolerance. We further show that AZRPbBr3 and AZRPbI3 exhibit strong nonlinear optical absorption. The high two-photon brightness of AZRPbI3 emission stands out among lead perovskites emitting in the near-infrared region.


Figure S4.
The results of the Rietveld refinement for powder diffraction data of AZRPbI 3 , T =20 K. Crystal system: orthorhombic, space group Pnma ., lattice parameters a = 8.878(1) Ȧ, b= 12.657 (1) Ȧ and c = 8.859(1) Ȧ, R all = 0.06; wR all = 0.10; GOF = 11.58;R p = 0.028, wR p = 0.037.The degree of orthorhombic distortion is small, thus, basing on the atomic positions the tetragonal phase is postulated by Platon (see the check cif report).However, due to the presence of Bragg peaks breaking the I cell cantering, the tetragonal I4/mcm model (LT phase of MAPbI 3 ) was excluded.Also the tetragonal P4/mmm model of the second LT phase of MAPbI 3 does not fit the X-ray data as the unit cell of this phase has reduced volume.

Dielectric properties
We analyzed the frequency domain dielectric data of AZRPbX 3 compounds using the Cole-Cole equation: Here, is the dielectric permittivity in the high-frequency limit, denotes the dielectric (∞) ∆ strength, τ is the mean relaxation time, and ω = 2πν is the angular measurement frequency.The relaxation width is described by the parameter 0 ≤ α < 1.For α = 0, the Cole-Cole process reduces to the Debye relaxation, which describes non-interacting electric dipoles.

Figure S5 .
Figure S5.Powder diffraction patterns of the cubic (180 K) and orthorhombic Pnma (70 K) phases of AZRPbI 3 .The reduction of symmetry manifests as a splitting of diffraction peaks and reduction of their intensity.The 210 and 212 peaks violating reflection conditions for the I-cantered lattice (h+k+l=2n) are highlighted in the inset.

Figure S7 .
Figure S7.Temperature dependent powder X-ray diffractograms showing the symmetry breaking at low temperatures of AZRPbBr 3 .The grey areas mark the 2 thresholds, where the peaks from the sample holder were recorded.

Figure S8 .
Figure S8.The powder X-ray diffractograms of AZRPbCl 3 show the substantial symmetry lowering at low temperature.The peaks at 200 K are indexed in the cubic unit cell of .3

Figure S9 .S14Figure S10 .
Figure S9.Relative energy of AZRPbBr 3 per formula unit with respect to the rotation angle of

Figures
Figures S14, S16 and S18 show the best fits to the experimental ε″ data using the Cole-Cole model, which allowed us to obtain the temperature dependences of the fit parameters.The temperature dependences of the determined values of τ are presented in Figures S15, S17 and S19 showing the Arrhenius behavior described by τ = τ 0 exp(E a /kT), where E a and τ 0 denote the activation energy and attempt time, respectively, and k is the Boltzmann constant.

Figure S14 .
Figure S14.Frequency dependence of ε″ of AZRPbBr 3 for selected temperatures.Solid curves are

Figure S15 .
Figure S15.Arrhenius plot of the mean relaxation time of the dipolar processes of AZRPbBr 3 .

Figure S16 .
Figure S16.Frequency dependence of ε″ of AZRPbCl 3 for selected temperatures.Solid curves are

Figure S17 .
Figure S17.Arrhenius plot of the mean relaxation time of the dipolar processes of AZRPbCl 3 .

Figure S18 .
Figure S18.Frequency dependence of ε″ of AZRPbl 3 for selected temperatures.Solid curves are

Figure S19 .
Figure S19.Arrhenius plot of the mean relaxation time of the dipolar processes of AZRPbI 3 .Lines

Figure S20 .
Figure S20.Overlay of experimental spectra obtained upon irradiation of AZRPbCl 3 with 800 nm

Figure S21 .
Figure S21.Overlay of experimental spectra obtained upon irradiation of AZRPbCl 3 with 800 nm

Figure S22 .
Figure S22.Overlay of experimental spectra obtained upon irradiation of AZRPbCl 3 with 1300

Figure S23 .
Figure S23.Overlay of experimental spectra obtained upon irradiation of AZRPbCl 3 with 1300

Figure S24 .
Figure S24.Overlay of experimental spectra obtained upon irradiation of AZRPbBr 3 with 1300

Figure S25 .
Figure S25.Overlay of experimental spectra obtained upon irradiation of AZRPbBr 3 with 1300

Figure S26 .
Figure S26.Overlay of experimental spectra obtained upon irradiation of AZRPbI 3 with 1300 nm

Figure S27 .
Figure S27.Overlay of experimental spectra obtained upon irradiation of AZRPbI 3 with 1300 nm

Figure S28 .
Figure S28.Overlay of experimental spectra obtained during power-dependent irradiation of

Figure S29 .
Figure S29.Log−log plot of integral intensities plotted as the function of applied laser power (800

Figure S30 .
Figure S30.Overlay of experimental spectra obtained during power-dependent irradiation of

Figure S31 .
Figure S31.Log−log plot of integral intensities plotted as the function of applied laser power (800

Figure S32 .S37Figure S33 .
Figure S32.Overlay of experimental spectra obtained during power-dependent irradiation of

Figure S34 .
Figure S34.Overlay of experimental spectra obtained during power-dependent irradiation of

Figure S35 .
Figure S35.Log−log plot of integral intensities plotted as the function of applied laser power

Table S1 .
Crystal data and structure refinement for AZRPbBr 3 .