Structural frustration, metastability and cascade of polar phases in a layered lead bromide perovskite

Abstract

Kinetically trapped perovskites offer a unique platform for controlling functional properties through non-equilibrium phase formation. Here, we report that a layered hybrid perovskite, CPA₂PbBr₄, exhibits an unusual kinetic trapping phenomenon where rapid cooling stabilizes a metastable polar phase (IV, Pna2₁) instead of the thermodynamic ground state. This compound displays a cascade of polar phases below 350 K: the room-temperature phase III (Cmc2₁), the metastable phase IV, and the low-temperature phase V (P2₁), all of which are noncentrosymmetric and polar. The polar order in each phase is characterized by distinct CPA⁺ cation orientations and PbBr₆ octahedral distortions, giving rise to switchable dielectric response and second-harmonic generation (SHG). SHG studies reveal that thermal cycling suppresses SHG intensity of phase III without structural changes, attributed to generation of strain that limits coherence length. The material exhibits efficient broadband photoluminescence (PL) with strong thermochromism, arising from self-trapped excitons in the distorted lattice. Pyroelectric measurements and P–E hysteresis loops confirm spontaneous polarization values of 1.2–2.2 µC cm⁻² across the polar phases. Our findings demonstrate that kinetic control of phase selection provides a powerful strategy for tuning polar order and multifunctional properties in hybrid perovskites, with implications for optoelectronic and photonic applications.

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1. Introduction

Hybrid lead halide perovskites are versatile semiconductors that underpin a broad range of optoelectronic technologies, including light-emitting and photovoltaic devices,^1–3 lasers,⁴ and sensors.⁵ Depending on the size and shape of the organic cation, lead halides may crystallize into three,- two,- one, or zero-dimensional architecture (3D, 2D, 1D, and 0D).^6–9 In addition, the metal halide octahedra can adopt different connection motifs, namely corner-sharing, edge-sharing, or face-sharing.^6,10,11 The dimensionality and connectivity of the octahedral framework exert a profound influence on the optoelectronic properties of hybrid halides, in particular on the band gap, exciton binding energy, and charge carrier transport.^6,10–13 For example, lowering the dimensionality and changing the connectivity from corner-sharing to edge or face-sharing typically leads to band gap widening and an increase in exciton binding energy.^10–13 As a result, 3D analogues are regarded as the most promising for solar cell applications,¹ whereas their lower dimensional counterparts have attracted intense interest for light-emitting devices.^12–14

A particularly important subgroup of lead halides comprises thin-layered (n = 1) 2D analogues with general formulae A′₂PbX₄ and A″PbX₄ (A′ = monovalent organic cations, A″ = divalent organic cations, X = halide), which consist of thin inorganic perovskite layers separated by organic spacers. The appeal of such n = 1 perovskites arises from several key features. First, the separation of the inorganic layers gives rise to natural quantum well structures with stable excitons at room temperature (RT).^1,11,14 Consequently, 2D perovskites often display efficient PL arising from radiative recombination of free excitons (FEs), which is highly desirable for fabrication of light emitting diodes.^1,11,14 Furthermore, 2D perovskites may exhibit broadband and strongly Stokes-shifted emission, which is usually observed in systems with pronounced octahedral distortions and enhanced electron–phonon coupling.^6,10,13–16 Compounds that show such broadband emission, particularly white-light emission, are of great interest as candidates for solid state lighting and display technologies.^15–17 The 2D nature of these perovskites is also advantageous for the preparation of thin films and flexible displays.^14,18 They generally exhibit greater chemical stability than their 3D analogues, and the use of hydrophobic amines further improves their resistance to moisture.^8,19

More recently, 2D lead halide perovskites have emerged as promising nonlinear optical (NLO) and ferroelectric materials.^12,20–24 Only a limited number of n = 1 NLO and/or ferroelectric bromides have been described,^20–26 yet these compounds already demonstrate substantial potential for applications such as piezoelectric sensors²⁵ and self-powered photodetectors.²⁶ Materials exhibiting efficient second-harmonic generation (SHG) have attracted considerable attention, particularly with respect to their switchable properties, which make them highly attractive for advanced optical technologies.^12,22,27 In view of the strong drive toward device miniaturization and control by external stimuli, it is highly desirable to discover compounds that combine several functional properties in a single phase. For example, the coexistence of ferroelectricity and PL is appealing for integrated photoelectronic devices. Among the known n = 1 hybrid lead bromide ferroelectrics, PL has been reported only for MHy₂PbBr₄ and BPA₂PbBr₄ (MHy⁺ = methylhydrazinium, BPA⁺ = 3-bromopropylammonium).^24,28 In the former, both FE and self-trapped exciton (STE) emission were observed, whereas the latter exhibits only broadband STE-related PL.^24,28

Most SHG-active hybrid organic–inorganic lead halide perovskites are known to exhibit a single noncentrosymmetric phase. Multiple noncentrosymmetric phases have been identified in only a few cases, including the thick-layered (n = 3) iBA₂MHy₂Pb₃Br₁₀ (iBA⁺ = isobutylammonium)²² and the thin-layered (n = 1) CPA₂PbCl₄ (CPA⁺ = 3chloropropylammonium),²² and BPA₂PbBr₄.²⁸ Numerous studies have highlighted the critical role of kinetics in the formation of perovskite phases. One of the most important examples is 3D FAPbI₃, which on slow cooling undergoes a phase transition (PT) from the photoactive black cubic phase to the photo inactive yellow hexagonal phase, while kinetic trapping of the cubic phase can be achieved by thermal quenching.²⁹ The cubic to hexagonal PT in this compound is characterized by a very large thermal hysteresis of about 60 K, indicating that the PT requires complex shifts and rotations of FA⁺, lead, and iodide ions.²⁹ The authors proposed that a potential barrier between the cubic and hexagonal structures arises from the entropy contribution to the Gibbs free energy associated with isotropic FA⁺ rotations in the cubic phase. Therefore, the PT is entropy-driven and, upon heating, the entropy term necessitates activation of the isotropic rotation of FA⁺ cations.²⁹ High-temperature (HT) phases can also be quenched in 2D perovskites. A notable example is [S-2-MeBA]₂PbI₄ (S-2-MeBA = (S)-(–)-2-methylbutylammonium), which undergoes a structural PT near 180 K upon slow cooling (<250 Kh⁻¹), whereas no PT is observed under rapid quenching.³⁰ In this way, the low-temperature (LT) phase can be locked into a metastable RT phase. Remarkably, this metastable phase exhibits more pronounced spin splitting than the RT phase, suggesting that kinetic control of PTs offers an efficient strategy for tuning physical phenomena.³⁰

Very recently, He et al. reported CPA₂PbBr₄ perovskite³¹ (in their work referred to as (Cl-PA)₂PbBr₄), demonstrating that halogen substitution on the non-ferroelectric propylammonium analogue PA₂PbBr₄ can be used to regulate the hydrogen-bonding (HB) and halogen⋯halogen interaction network and thereby induce a high-T_c molecular photoferroelectric phase. At RT they found a polar Cmc2₁ structure (point group mm2) with a large dipole moment of the organic cation, enhanced PbBr₆ octahedral distortion, a sizable spontaneous polarization, and an unusually large piezoelectric coefficient d₃₃ ≈ 36 pCN⁻¹, which together underpin strong bulk photovoltaic and piezoelectric responses. On this basis, He et al. established this as a hybrid molecular ferroelectric and demonstrated promising performance of this material as a passive X-ray photoconductor with a high mobility–lifetime product, large X-ray sensitivity and a very low detection limit under zero bias.³¹ However, that work primarily focused on the HT and RT ferroelectric behaviour driven by cooperative non-covalent interactions, while the rich LT polymorphism, kinetic aspects of the PTs, and the interplay between structural frustration, broadband self-trapped-exciton emission, dielectric switching and SHG response in this composition remained unexplored.

Herein, we report that CPA₂PbBr₄ is a very rare example of multifunctional lead halide perovskite exhibiting multiple polar phases, dielectric switching, ferroelectricity, broadband PL and pronounced thermochromism. We also show that depending on the cooling rate and thermal history of this compound, the lowest-temperature phase shows different crystal structures and different temperature-dependence of PL, SHG, dielectric and phonon properties. Thus, in contrast to lead halide perovskites reported in the literature, fast cooling does not lead to kinetic trapping of the RT phase but to stabilization of a new polymorph. Therefore, CPA₂PbBr₄ is an example of a 2D perovskite with a “sluggish” PT exhibiting very large thermal hysteresis, which can be used for kinetic control of its crystal structures and physicochemical properties.

2. Experimental section

2.1. Synthesis

All reagents (PbBr₂ 98%, 3-chloropropylamine hydrochloride 98%, HBr 48 wt% in H₂O) used for the synthesis were commercially purchased from Sigma-Aldrich and used without further purification. In order to grow single crystals of CPA₂PbBr₄, 4 mmol of PbBr₂ and 8 mmol of 3-chloropropylamine hydrochloride were dissolved in hydrobromic acid. The clear solution was obtained after stirring for 20 minutes and then left for crystallization at RT. Plate-like crystals, which grew overnight, were separated from the liquid and recrystallized from HBr. The comparison of their powder XRD pattern with the calculated one based on the single-crystal data attests the phase purity of the bulk sample (Fig. S1).

2.2. X-ray powder diffraction

Powder XRD patterns of pristine CPA₂PbBr₄ were obtained in the reflection mode on an X'Pert PRO X-ray diffraction system equipped with a PIXcel ultrafast line detector and Soller slits for Cu Kα1 radiation (λ = 1.54056 Å). PXRD patterns comparing the pristine CPA₂PbBr₄ sample and the sample after the SHG experiment were collected using a Proto AXRD benchtop powder diffractometer with a Cu Kα anode operating at 30 kV and 20 mA, equipped with a Dectris Mythen2 R 1D hybrid photon-counting detector and Soller slits. The powdered sample was placed on a background-free, 1 mm-thick (510) silicon wafer, which served as the sample holder for both PXRD and temperature-resolved SHG experiment.

2.3. Thermogravimetric analysis (TGA) and differential thermal analysis (DTA)

The TGA/DTA measurements were performed using a Setaram SETSYS 16/18 instrument in the temperature range of 298–1100 K, with a ramp rate of 10 K min⁻¹, under flowing nitrogen (flow rate: 1 dm³h⁻¹). All measurements were conducted in Al₂O₃ crucibles. The sample weight was 10.59 mg for the pristine CPA₂PbBr₄ and 10.64 mg for CPA₂PbBr₄ annealed at 380 K for 10 minutes.

2.4. Differential scanning calorimetry (DSC)

Calorimetry measurements were performed using a Mettler Toledo DSC-3 calorimeter in the temperature range of 120–380 K. Nitrogen was used as a cooling gas to maintain thermal stability during the measurements. The heating and cooling rates were 5 K min⁻¹, and the sample weight was 18.4 mg. Additionally, measurements were carried out at different heating/cooling rates (1, 3, and 10 K min⁻¹) to evaluate the kinetic effects on the PTs. The excess heat associated with the PTs was calculated by subtracting a baseline from the data, representing the system's response in the absence of PTs.

2.5. Single-crystal X-ray diffraction

Single-crystal X-ray diffraction (SCXRD) data were collected using a four-circle Xcalibur diffractometer (Oxford Diffraction) operating with an Atlas CCD camera and fine-focus sealed X-ray tube (Mo Kα, λ = 0.7107 Å). The non-ambient temperature was provided by Oxford Cryostream1000. Absorption was corrected via multi-scan methods using CrysAlis PRO 1.171.42.93a (Rigaku OD, 2023) and spherical harmonics, implemented in the SCALE3 ABSPACK scaling algorithm. The crystal structures were solved in five subsequent polymorphic phases numbered from I to V with decreasing temperature in Olex2 1.5 using SHELXT and refined with SHELXL programs.^32–34 In disordered HT phase I the hydrogen atoms were not included in the structure model whereas in phases II–V hydrogen atoms were placed at calculated positions and refined as riding atoms. Phase IV was stabilized after cooling from RT at a rate of ∼5 K min⁻¹. Phase V was recorded by slow cooling, ∼2.5 K min⁻¹ between the temperature points at which lattice-parameter-oriented data were collected for 30 min every 10 K. The crystal data, data collection and refinement results are listed in Table 1. HB geometry is presented in Table S1.

Table 1 Experimental and refinement details of CPA₂PbBr₄ (M_r = 715.95)

	I, 370 K	II, 350 K	III, 295 K	IV ^a, 100 K	V ^b, 100 K
a Fast-cooled from room temperature at a rate of 260 K h^−1.b Slow-cooled, slow cooling was preceded by heating to 370 K and a series of 30 min experiments down to 100 K for lattice-parameter-oriented data collection.
Crystal data
Crystal system, space group (s.g. No.)	Orthorhombic, Cmce, (64)	Orthorhombic, Pbca (61)	Orthorhombic, Cmc21 (36)	Orthorhombic, Pna21 (33)	Monoclinic, P21 ^a (4)
Temperature (K)	370	350	295	100	100
a, b, c (Å)	27.554 (7), 8.280 (3), 8.283 (3)	26.849 (7), 8.335 (3), 8.203 (3)	26.852 (7), 8.325 (3), 8.160 (3)	16.781 (5), 26.750 (7), 7.907 (3)	13.823 (4), 7.785 (3), 8.504 (3)
α, β, γ (°)	90, 90, 90	90, 90, 90	90, 90, 90	90, 90, 90	90, 106.48 (3), 90
V (Å^3)	1889.7 (11)	1835.8 (11)	1824.0 (11)	3549.4 (19)	877.6 (5)
Z (Z primitive)	4 (2)	4 (4)	4 (2)	8 (8)	2 (2)
µ (mm^−1)	17.65	18.17	18.28	18.79	19.00
Data collection
No. of measured, independent and observed [I > 2σ(I)] reflections	4561, 992, 579	9895, 1875, 1080	36 026, 1908, 1754	30 729, 6725, 5285	5479, 5479, 4342
Rint	0.055	0.049	0.048	0.057	—
Refinement
R[F^2 > 2σ(F^2)], wR(F^2), S	0.045, 0.126, 1.00	0.060, 0.137, 1.11	0.028, 0.068, 1.13	0.040, 0.079, 1.06	0.060, 0.186, 1.11
No. of reflections	992	1875	1908	6725	5479
No. of parameters	57	71	74	257	91
No. of restraints	30	20	22	1	19
Δρmax, Δρmin (eÅ^−3)	0.045, 0.126, 1.00	0.060, 0.137, 1.11	0.028, 0.068, 1.13	0.040, 0.079, 1.06	0.060, 0.186, 1.11
Absolute structural parameter	—	—	—	−0.016 (6)	−0.014 (7)

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2.6. Raman measurements

Temperature-dependent Raman spectra in the 3500–50 cm⁻¹ range were measured using a Renishaw inVia Raman spectrometer equipped with a confocal DM2500 Leica optical microscope, a CCD detector and an argon laser (λ_ex = 488 nm). To obtain information on the modes below 50 cm⁻¹, the second experiment was performed in the 400–10 cm⁻¹ range using the same spectrometer, an Eclipse filter and a diode laser (λ_ex = 830 nm). The temperature of the sample was controlled using a Linkam THMS600 cryostat cell. The spectral resolution in both experiments was 2 cm⁻¹.

2.7. Dielectric studies

Dielectric measurements were carried out using a Broadband Impedance Novocontrol Alpha-A analyser. A sinusoidal voltage with an amplitude of 1 V and a frequency range of 1 Hz to 1 MHz was applied across the sample. Measurements were performed on single crystal samples with dimensions of 1.5 mm 2 × 0.25 mm and 1.3 mm 2 × 0.3 mm along the a and c crystallographic directions, respectively. To ensure proper electrical contact, silver paste was applied to the parallel surfaces of the samples. The temperature was controlled using the Novocontrol Quattro system using a nitrogen gas cryostat. The measurements were conducted in the temperature range of 130–380 K, with a stability better than 0.1 K and a temperature step of 2 K. Pyroelectric current measurements were performed on single crystals along the c polar direction with silver electrical contacts. The crystals were cooled down to 160 K. During cooling, an electric poling field was applied. At 150 K, the sample electrodes were shorted for about 10 minutes. Current measurements were performed using a Keithley 6514 electrometer during the heating at a rate of 1 K min⁻¹. Polarization–electric field (P–E) measurements were carried out using a Precision Premier II Ferroelectric Tester. Electrodes made of conductive silver paste were applied to a single crystal with an area of 0.0012 cm² and a thickness of 100 µm. Before the measurements, the samples were heated for 10 minutes at a temperature of 350 K. The measurements were performed at room temperature. A maximum voltage of 500 V and various frequencies were applied along the polar axis, and the data were recorded using Vision software.

2.8. Absorption and photoluminescence (PL) studies

RT diffuse reflectance spectra of powdered CPA₂PbBr₄ were measured using a Varian Cary 5E UV-vis-NIR spectrophotometer. Temperature-dependent PL spectra of the sample were recorded using an FLS1000 PL spectrophotometer (Edinburgh Instruments, Livingston, Scotland) equipped with a 450 W xenon lamp. The temperature was controlled with a Linkam THMS 600 heating/freezing stage (The McCrone Group, Westmont, IL USA).

2.9. Second harmonic generation (SHG)

SHG measurements were performed using a laser system comprising a Coherent Astrella Ti: Sapphire regenerative amplifier (800 nm, 75 fs, 1 kHz) pumping a TOPAS Prime optical parametric amplifier (OPA). The OPA output was tuned to 1400 nm and was used unattenuated and unfocused, delivering a fluence of 0.25 mJ cm⁻² at the sample. For experiments on powders, single crystals of CPA₂PbBr₄ were mechanically crushed, and sieved using an Aldrich micro-sieve set, yielding a particle size fraction of 88–125 µm. The graded powder was packed uniformly between microscope glass slides, sealed, and mounted on a horizontal sample holder. For measurements of single crystal samples, the population ca. 6 single crystals were placed on a microscopic glass and measured without crushing. Identical excitation parameters and geometric configurations were maintained for both samples. Signal collection was performed in the reflection mode. Specifically, the 1400 nm laser beam was directed onto the sample at a 45° incident angle. Signal collection optics consisting of a Ø 25.0 mm plano-convex lens (f = 25.4 mm) coupled to a 400 µm, 0.22 NA optical fibre, was aligned normal to the sample surface with a 30 mm working distance. SHG spectra were acquired using an Ocean Optics Flame-T CCD spectrograph (200 µm entrance slit), with residual pump light attenuated by a Thorlabs FESH0750 short-pass filter. Temperature control is achieved using a Linkam LTS420 with 0.1 K accuracy.

2.10. Domain structure

The domain structure was observed using a Zeiss Primotech polarizing microscope in transmitted-light mode, combined with a Linkam THMS600 heating–cooling stage. The crystal was examined under crossed polarizers, with the incident light polarized at −45° with respect to the longest edge of the crystal and the analyser set at 45°. Video 1 shows merged images of a crystal in the 100–300 K range subjected to fast cooling to 100 K with a rate ∼20 K min⁻¹ and subsequent heating with a rate of ∼10 K min⁻¹. Video 2 shows a crystal in the 220–250 K range that was cooled to 170 K with a rate ∼20 K min⁻¹ and then heated with a rate of ∼10 K min⁻¹. A full wave retardation plate λ was inserted into the optical path during all measurements.

3. Results and discussion

3.1. TGA, DTA and DSC

The TGA curves show a very small weight loss of approximately 0.5% up to 480 K, followed by a further weight loss of ∼47.8% in the 480–670 K range (Fig. S2). The minor loss may most likely be attributed to the evaporation of adsorbed water, whereas the major loss corresponds to the release of CPA bromide; the calculated value is 48.7%. Upon further heating, PbBr₂ starts to sublime near 790 K and this process is completed near 900 K (Fig. S2). The DTA curve shows two endothermic events with peaks at 348.6 and 365.0 K (Fig. S2), which are not associated with any weight loss. These peaks indicate the presence of two PTs. The origin of the third, very broad endothermic peak in the 450–520 K range, which is not associated with any significant weight loss, remains unclear. However, we suppose that it may be related either to partial decomposition without evaporation of the organic component or to a chemical reaction between CEA⁺ and Br⁻ leading to substitution of Cl in CEA by Br from the inorganic part. Above 540 K, several endothermic and exothermic events occur that correspond to pronounced decomposition of the sample and sublimation of PbBr₂. Repeated measurement on the sample annealed at 380 K for 10 minutes shows the same behaviour, confirming that the pristine and annealed samples have the same chemical composition, i.e., annealing does not lead to loss of any compound.

The DSC measurement during the first cooling from RT to 120 K with a rate of 5 K min⁻¹ shows very weak and broad anomaly near 210 K (Fig. 1a and S3). This feature is characterized by a low-amplitude change in heat capacity and a smooth, continuous change in entropy, without a well-defined latent heat. Such behavior is indicative of a gradual structural rearrangement rather than a discontinuous first-order PT. The associated change in enthalpy ΔH and entropy ΔS is estimated to be ∼0.76 kJ mol⁻¹ and ∼4.1 J mol⁻¹ K⁻¹, respectively. For an order–disorder transition, ΔS = Rln(N), where R is the gas constant and N is the ratio of the number of configurations in the disordered and ordered phase. The estimated N is 1.67. The relatively small value of N suggests that the PT involves subtle orientational or positional rearrangements within the crystal structure. During the first heating run, four distinct anomalies are observed. The first anomaly appearing at T₄ = 171 K (Fig. 1a and S3) is broad and exothermic, which is atypical for a conventional structural PT that usually exhibits endothermic signatures upon heating. Exothermic peaks may appear due to cold crystallization, observed for instance for the glassy state of 1-MeHa₂PbI₄ (1-MeHa = 1-methyl-hexylammonium).³⁵ Another possibility is a PT from a metastable disordered phase to an ordered phase.³⁶ Based on X-ray diffraction and Raman data (see next paragraphs), the presence of the unusual exothermic peak for CPA₂PbBr₄ can be attributed to a PT from the metastable phase exhibiting some disorder to a well-ordered thermodynamically stable phase. Importantly, to verify the reproducibility of this feature, DSC measurements were repeated at different heating/cooling rates (1, 3, and 10 K min⁻¹), with each first heating run performed on a pristine sample. These measurements consistently reveal that on cooling with a rate of 10 or 3 K min⁻¹, the anomaly near 210 K is hardly visible but on heating, the same low-temperature exothermic peak appears near 175 K although with some variability in the shape and intensity (Fig. S3b). This behavior is characteristic of metastable phases, for which the extent of transformation and degree of ordering may depend sensitively on the kinetics. When the cooling rate decreases to 1 K min⁻¹, a much narrower and stronger peak appears around 195 K and the exothermic peak is no longer present on subsequent heating (Fig. S3b). This behavior suggests that at this very slow cooling rate, metastable phase IV is no longer reached but the transition occurs to a new phase V. The remaining anomalies, which occur at T₃ = 232 K, T₂ = 344 K, and T₁ = 352 K, are endothermic and well-defined. In the second cooling cycle, corresponding exothermic peaks are observed at T₃ = 210 K, T₂ = 341 K, and T₁ = 365 K. In the subsequent heating run, the transition temperatures closely match those observed during the first heating cycle, demonstrating good reversibility and repeatability of these PTs (Fig. 1 and S3). As shown in Fig. 1b, the intensity of the two HT DSC peaks, and consequently the associated entropy changes ΔS, are nearly identical across different cooling/heating loops. In the case of the PT at T₃, the anomaly becomes more pronounced in the second cycle and remains comparable during both cooling and heating (Fig. 1 and S3). The associated change in enthalpy ΔH (ΔS) is ∼5.46 kJ mol⁻¹ (∼15.0 J mol⁻¹ K⁻¹), ∼2.65 kJ mol⁻¹ (∼7.0 J mol⁻¹ K⁻¹) and ∼6.22 kJ mol⁻¹ (∼29 J mol⁻¹ K⁻¹) for the PT at T₁, T₂ and T₃, respectively (average values, second loop). The strongly symmetric shape of DSC anomalies, their sharp ΔS changes, and the presence of significant thermal hysteresis all point to the first-order character of the PTs. The estimated N values of approximately 6, 2 and 33 for the PT at T₁, T₂ and T₃, respectively, indicate discrete entropy lowering steps associated with progressive ordering of the CPA₂PbBr₄ structure. Notably, the transition at T₃ is characterized by the largest ΔS, N and thermal hysteresis (∼23 K), indicating the sluggish character of this PT and suggesting that it is associated with large structural changes and substantial reduction in orientational and/or conformational disorder. The thermal behaviour thus reflects a cascade of distinct structural PTs in CPA₂PbBr₄, involving both gradual and abrupt ordering processes.

Fig. 1 Temperature dependences of (a) the heat capacity change ΔC_p and (b) the entropy change ΔS associated with the sequence of PTs in CPA₂PbBr₄. The measurements were performed during four consecutive thermal processes: first cooling from 288 K to 120 K (loop I, blue), first heating from 120 K to 380 K (loop I, red), second cooling from 380 K to 120 K (loop II, blue), and second heating from 120 K to 380 K (loop II, red).

3.2. Single-crystal X-ray diffraction

The CPA₂PbBr₄ crystals exhibit rich temperature-controlled polymorphism, undergoing five distinct phases with varying symmetry and crystal packing. Starting from the orthorhombic Cmce phase I, which is isostructural to the HT phase of CPA₂PbCl₄,22 the symmetry decreases successively through orthorhombic Pbca (phase II), polar orthorhombic Cmc2₁ (phase III), a second polar orthorhombic phase, Pna2₁ (phase IV) and finally a third polar monoclinic P2₁ (phase V). The stabilization of LT phases following the I → II → III sequence depends on the cooling/heating rate. Phase IV was observed at 100 K after quenching from RT (cooling rate ∼5 K min⁻¹), whereas gradual, slow cooling from RT to 100 K led to the stabilization of monoclinic phase V. Furthermore, slow, gradual heating induced IV → V transformation. The temperature dependence of the unit cell volume during cooling/heating cycles at different temperature rates showing this complex phase behaviour is given in Fig. S4.

Phases II and III are maximal non-isomorphic subgroups of phase I. Considering the volume of the primitive cells (see Table 1), phase II is a k-type subgroup, while phase III is a t-type subgroup. Phase IV is the maximal non-isomorphic k-type subgroup of III, and phase V is the maximal non-isomorphic t-type subgroup of III. The diagram presented in Fig. 2 illustrates the group–subgroup relationships in CPA₂PbBr₄.

Fig. 2 Group–subgroup relationship scheme for PTs in CPA₂PbBr₄.

This complex phase sequence highlights the intricate non-covalent interactions between the inorganic and molecular components, further influenced by changes in CPA⁺ conformation, which become active as the temperature decreases. He et al. recently reported the phase behavior in the HT region, resolving the RT structure with Cmc2₁₁ symmetry and identifying an HT phase described by the Pbca space group.³¹ Here, we expand on their findings by establishing the presence of the HT Cmce parent phase, refining the phase sequence, and providing a comprehensive characterization of newly identified LT polymorphs.

As previously reported,³¹ The crystal structure of CPA₂PbBr₄ consists of [100] perovskite layers formed by corner-sharing PbBr₆ octahedra, with CPA⁺ molecular counterions positioned between them. The prototype phase I exhibits significant dynamic structural disorder, with CPA⁺ cations split between two symmetry-related positions. Note that, despite employing a two-state model for CPA⁺, in which the cation is disordered over two equivalent positions with 0.5 occupancy to represent diffuse electron density between the inorganic slabs, the large entropy associated with the PTs indicates substantially more pronounced disorder. The same behavior was reported for CPA₂PbCl₄.²² This discrepancy suggests that CPA⁺ may undergo nearly free rotation about its molecular axes and conformational changes, and that Br⁻ ions may also contribute to the PT entropy, in agreement with the large atomic displacement parameters observed for both the organic and inorganic components. Note that the model reported by He et al. also assumed twofold disorder in the high-temperature phase.³¹

The first PT, primarily of an order–disorder character, occurs as the CPA⁺ rotations become restricted in phase II. The molecules are anchored in the structure by Cl⋯Br halogen interactions between the chlorinated CPA⁺ and Br⁻ ligands in the perovskite layers. The Cl⋯Br distances decrease significantly from 4.10 Å (phase I, 370 K) to 3.74 Å (phase II, 350 K), leading to a contraction of the a lattice parameter from 27.554 (7) Å to 26.849 (7) Å. The relatively large atomic displacement parameters in phase II suggest a considerable degree of residual freedom, particularly in the CPA⁺ chains.

The transition to phase III involves a reorganization of CPA⁺ cations through shifts and rotations, resulting in the loss of the inversion centre. These changes also lead to an increase of the octahedral distortion, as evidenced by the increase of the angle variance (σ² [deg.2]), bond length distortion (Δ [Å]), in-plane distortion (D_in [°]) and out-of-plane distortion (D_out [°]) from 6, 3.3 × 10⁻³ Å, 26.1° and 3.1° at 350 K to 18, 9.8 × 10⁻³ Å, 34.5° and 0° at 295 K (Table S2). Fig. 3 illustrates the key structural motifs in CPA₂PbBr₄ that undergo transformation during the PTs. CPA⁺ reorientations induce a spontaneous dipole moment along the orthorhombic c axis, parallel to the perovskite layers. Phase III is isostructural to phase II of CPA₂PbCl₄,²² with nearly identical maximal in-plane distortions of the octahedral layers (D_in = 34.5° and 36.0° for the bromide and chloride, respectively) and lack of out-of-plane distortions (D_out). Notably, unlike in the chlorine analogue, which exhibits an order–disorder PT and very large ΔS (∼42.2 J mol⁻¹ K⁻¹),²² in CPA₂PbBr₄ the PT to the polar phase occurs via reorientations of CPA⁺ cations. Nevertheless, the relatively large ΔS value for the bromide (∼7.0 J mol⁻¹ K⁻¹) indicates that a contribution from some dynamic ordering processes, undetectable at the level of the average crystal structure, cannot be excluded, i.e., the PT has mixed displacive and order–disorder character. This behaviour together with much larger displacement parameters for the bromine analogue indicate that in contrast to the chlorine analogue, phase III of CPA₂PbBr₄ still exhibits a considerable degree of residual disorder.

Fig. 3 Crystal structure of CPA₂PbBr₄ in (a) prototype disordered phase I, 375 K (b) ordered, centrosymmetric phase II, 350 K; and (c) polar RT phase III, 295 K. The arrows illustrate the direction of molecular dipoles in the structure. The displacement parameters are drawn at 50% probability level.

Phase IV of CPA₂PbBr₄ is isostructural to phase III of CPA₂PbCl₄.²² Similarly to the II–III PT in CPA₂PbCl₄, the III–IV PT in CPA₂PbBr₄ involves a change in the conformation of half of the CPA⁺ chains from anti to gauche (Fig. S5) This change activates N–H⋯Br HBs, which induces out-of-plane distortions of the octahedral layers (max D_out = 9.6°) and increase in-plane distortions to max D_in = 41.4° (Table S2). In phase IV, the number of symmetry-independent CPA⁺ cations increases from one to four (two adopt anti conformation and two convert to gauche) while the inorganic content of the asymmetric unit increases from one Pb and three Br atoms to two Pb and eight Br atoms. Fig. 4 depicts the LT structure of CPA₂PbBr₄, including the distortions of the octahedral layers across the phases. Fig. S5 shows possible CPA⁺ conformers in phases III–V as well as the packing along the polar direction in phase V.

Fig. 4 (a and b) LT polymorphs of CPA₂PbBr₄, T = 100 K. The change in the spatial arrangement of CPA⁺ cations (resulting from the conversion of all CPA⁺ to gauche) in the monoclinic polymorph V leads to the reduction of resultant dipole moment in this phase.

The LT phase V is well-ordered and characterized by the largest out-of-plane distortions in the octahedral layers, which, nearly inactive during phases I–III, increase to a max. D_out of 9.6° in phase IV and further to max. 20.2° in phase V at 100 K. Meanwhile, the in-plane rotations in phase V (max D_in = 29.6°) are comparable to those in phase III (D_in = 34.5°) and significantly lower than those in phase IV (max. D_in = 41.4°). The mean octahedral distortion parameters, Δ and σ², are also significantly smaller for the monoclinic phase V, i.e., they decrease from 34 deg.2 and 16.2 × 10⁻³ Å for phase IV to 15 deg.² and 6.9 × 10⁻³ Å for phase V.

Interestingly, despite having the lowest monoclinic symmetry, the translational symmetry of phase V directly corresponds to that of the prototype HT phase I. The volume of phase V is the smallest in the sequence of PTs and correlates with the volume of the primitive cell of phase I. This results in halving of the number of atoms and molecules in the asymmetric unit compared to phase IV, with two CPA⁺ molecules, one Pb atom, and four independent Br sites. Consequently, the number of possible independent interactions is reduced. In phase V, there are two, almost equal Cl⋯Br halogen bonds (of 3.53 Å and 3.55 Å), compared to four Cl⋯Br bonds in phase IV, ranging from 3.38 Å to 3.76 Å. The same applies to the HB interactions, with the number of independent bonds reduced by half in phase V compared to phase IV. Additionally, the interlayer distance in phase V is shorter than in phase IV, measuring 13.25 Å and 13.38 Å, respectively. The geometrical parameters point to a higher degree of stability of phase V compared to phase IV.

3.3. Temperature-dependent Raman study

To determine the mechanism of the PTs and molecular dynamics in CPA₂PbBr₄, we performed Raman spectroscopy in the 80–390 K range, see Fig. 5 for representative spectra of each discussed crystal phase and Fig. S6 for all spectra recorded during heating and cooling runs. The observed modes and their assignments, based on the isostructural CPA₂PbCl₄ analogue,²² are listed in Table S3.

Fig. 5 Raman spectra of CPA₂PbBr₄ during heating (a) and cooling (b) runs for selected temperatures shown in 3300–2820 cm⁻¹, 1670–225 cm⁻¹ and 220–10 cm⁻¹ ranges.

During the heating run of the sample cooled to 80 K with a rate of ∼20 K min⁻¹, spectra measured between 80 and 170 K correspond to the metastable phase IV. Although SCXRD indicates an ordered structure for this phase, the large full width at half maximum (FWHM) of the τ(NH₃⁺) band near 289 cm⁻¹ (28.9 cm⁻¹ at 80 K) reveals significant residual disorder even at low temperatures, i.e., so-called persistent disorder.³⁷ As temperature increases, the FWHM of the τ(NH₃) mode 286 cm⁻¹ nearly doubles from 29.7 cm⁻¹ at 80 K to 58.1 cm⁻¹ at 170 K. The broadening of vibrational modes with increasing temperature is related to increased phonon–phonon anharmonic interactions. In systems exhibiting order–disorder PTs, an additional contribution arises from the increasing number of accessible vibrational degrees of freedom. In the low-temperature range, the first contribution is usually small, typically only a few cm⁻¹ and this behavior is clearly observed for the τ(NH₃) mode of the well-ordered phase V (see the 307 cm⁻¹ band in Fig. S6e). The second contribution is usually much larger. Therefore, the very large increase in the FWHM of the τ(NH₃) mode in phase IV suggests that the disorder is dynamic rather than static.

Heating from 170 to 180 K triggers significant spectral changes, which are finished at 190 K, indicative of a strongly first-order PT to phase V (Fig. 5a and S6), consistent with diffraction data. This transition is characterized by a narrowing of many bands (Fig. 5a, S6 and S7), implying a transition to a highly ordered state. In particular, the FWHM of the τ(NH₃) mode drops precipitously from 58.1 cm⁻¹ at 170 K to 17.2 cm⁻¹ at 190 K, indicating restricted CPA⁺ dynamics in phase V. Simultaneously, modes involving the NH₃⁺ group undergo large shifts; the τ(NH₃) and ν_s (NH₃) modes shift from 289 and 3033 cm⁻¹ (170 K) to 307 and 3079 cm⁻¹ (190 K). These shifts reflect a pronounced reorganization of the HB network, driven by cation reorientation and conformational changes. Lattice modes also exhibit significant sharpening (e.g., the 36 cm⁻¹ band narrows to 2.7 cm⁻¹), confirming that the PT from the metastable phase IV to the stable phase V involves a transition from a dynamically disordered state to a rigid, well-ordered structure. This anomalous increase in order upon heating explains the unusual exothermic anomaly observed in DSC measurements (vide supra). Note that phase IV shows a larger number of lattice modes than phase V (Fig. 5a, S6c and Table S3). This behaviour is consistent with doubling of the formula units and crystallographically independent Pb²⁺ and Br⁻ ions in phase IV compared to phase V.

Upon further heating, the transition from phase V to the Cmc2₁ phase III occurs between 230 and 240 K. This transformation is marked by a decrease in the number of observed bands, substantial broadening, and intensity changes, see Fig. 5, S6 and S7 and Table S3. The re-emergence of broad bands (Fig. S7), such as the τ(NH₃) mode broadening to 71.8 cm⁻¹ at 250 K, indicates return to a disordered state similar to, but more pronounced, than in phase IV (FWHM of 58.1 cm⁻¹ at 170 K). Notably, spectral features absent in phase V, such as the band near 425 cm⁻¹, reappear in phase III, suggesting that the cation orientation and interlayer environment in phase III bear structural similarities to the metastable phase IV, consistent with their comparable interlayer distances (Fig. S4). Further details on Raman features of the HT phase III and the LT metastable phase IV are provided in Supplementary discussion in the SI.

Above 240 K, molecular dynamics intensify, evidenced by further broadening of N–H stretching bands (3200–3000 cm⁻¹) and the τ(NH₃) mode (Fig. 5). The subsequent PT to phase II near 350 K shows minimal change in internal modes, implying that the internal structure of CPA⁺ remains largely conserved. However, the lattice region changes significantly: the number of modes decreases from 9 to 6, and low-frequency modes shift (e.g., 38 cm⁻¹ at 340 K to 33 cm⁻¹ at 350 K), reflecting decreased octahedral distortion and tilting. The final transition to phase I is purely order–disorder in nature, evidenced by increased bandwidths without distinct shifts or intensity changes, aligning with X-ray studies showing negligible changes in bond distortion.

Crucially, during cooling from 380 K and isothermal hold of the sample for about 10 min at each temperature point for collecting the spectra (every 10 K), phase III remains stable down to 190 K. At 180 K, the spectra abruptly transform into a pattern matching phase V observed during heating (190–230 K). This confirms that phase IV is strictly a metastable state accessible only via rapid quenching (rate of ∼20 K min⁻¹ in the Raman experiment), whereas the III → V transition represents the thermodynamic equilibrium path.

3.4. Dielectric studies

Broadband dielectric spectroscopy (BDS) measurements were carried out to analyze the dielectric properties and characterize the mechanisms associated with the PTs. The temperature dependence of the dielectric permittivity (ε′) for CPA₂PbBr₄ measured along the a and c crystallographic axes is shown in Fig. 6a, b and S8, respectively. A pronounced change in ε′ was observed during the first cooling near the structural PT from phase III to phase IV (Fig. 6b and S8a). During the first heating cycle, ε′ increases reaching maximum (minimum) near the structural PT from phase IV to phase V (from phase V to phase III), i.e., dielectric anomalies coincide with the DSC results, confirming the thermal signatures of the PTs. In subsequent cycles, discontinuous changes in ε′ are reproducibly detected, consistent with the first-order PT from phase III to phase V, and a marked temperature hysteresis emerges between the second heating and cooling runs. These variations can be ascribed to dielectric switching phenomena with change in ε′ of ∼4 (Fig. 6a).^38–41 At higher temperatures, a significant frequency dispersion of ε′ is observed (Fig. 6a), which is attributed to enhanced ionic conductivity. This effect leads to an increase in dielectric losses (ε″; Fig. S8b–d) and partially masks the intrinsic dielectric anomalies associated with the PTs between phases III and II and between phases II and I. As a result, these transitions are manifested as relatively subtle features in ε′ despite their clear signatures in the calorimetric and structural data. The dielectric response along the polar c axis shows qualitatively similar behavior (Fig. S8), confirming the consistency of the observed phase-transition sequence. However, under the same experimental conditions, the anomalies are less pronounced, likely owing to the combined effects of conductivity and dielectric losses. The relatively high permittivity values observed along a and c crystallographic directions are attributed to a combination of intrinsic contributions from the polar lattice and extrinsic effects, such as interfacial polarization and charge transport, which are commonly encountered in hybrid perovskites. Importantly, the absence of a pronounced Curie–Weiss-type dielectric anomaly is observed for measurements performed along the polar c axis (Fig. S8a). This behavior is attributed to the combined effects of strong frequency dispersion, conductivity-related contributions, and the first-order character of the PT. As a result, the dielectric response deviates from that of classical proper ferroelectrics and should be interpreted in conjunction with structural, P–E and pyroelectric data, which independently confirm the ferroelectric nature of the material. Note that the absence of a pronounced Curie–Weiss-type dielectric anomaly at the ferroelectric has been previously reported for this compound,³¹ related BPA₂PbBr₄,²⁸ and many other 2D lead halide ferroelectrics.^42–44

Fig. 6 Temperature dependence of the real (a and b) part of dielectric permittivity measured in single crystals along the a axis. (c) Changes of the pyroelectric current of a single crystal in the direction of the polar axis after positive (E₊) poling in a DC electric field. (d) Relative change of spontaneous polarization as a function of temperature determined by the integration of the pyroelectric current.

Since SHG (vide infra) and X-ray diffraction measurements confirmed polar structures and spontaneous polarization of phases III, IV and V, the pyroelectric effect was investigated to obtain direct evidence of ferroelectricity. The pyroelectric current measured along the polar axis increases sharply on heating through the IV → V and V → III PTs (Fig. 6c and S9a). Reversal of the current polarity upon opposite electrical poling confirms its ferroelectric origin. Integration of the pyroelectric current yields the change in polarization (ΔP_s) values of the Pna2₁ phase IV ∼2.2 and 2.0 µC cm⁻² for positive and negative poling, respectively (Fig. 6d and S9b). A similar value was reported for isostructural Cmc2₁ phases of ferroelectric CPA₂PbCl₄ (∼2.1–2.2 µC cm⁻²).²² Ferroelectricity in the Cmc2₁ phase III was further corroborated by P–E hysteresis loops (inset in Fig. S9b), revealing a spontaneous polarization of ∼1.2 µC cm⁻² and a maximum polarization of 1.6–2.0 µC cm⁻². The hysteresis loop shows a characteristic ferroelectric shape but is broadened, which is consistent with conductivity-related effects indicated by BDS measurements and may influence the apparent coercive field. These values are consistent with previously reported data, which indicated a polarization of approximately 1.3 µC cm⁻² in phase III.³¹ This value is smaller than that reported for ferroelectric BPA₂PbBr₄ (2.71 µC cm⁻²).²⁸

3.5. Linear optical properties

The RT diffuse reflectance spectrum of CPA₂PbBr₄ reveals a sharp excitonic absorption feature at 401 nm (3.09 eV, Fig. 7a) and a bandgap energy E_g of 3.15 eV (inset in Fig. 7a), determined via the Kubelka–Munk function with Tauc modification.^45,46 These values are characteristic of 2D lead bromides but exhibit a notable blue shift compared to analogues with less distorted inorganic layers, such as MHy₂PbBr₄ (exciton at 423 nm, E_g = 3.02 eV).²⁴ This shift correlates with the significant in-plane octahedral distortion in CPA₂PbBr₄ (D_in ≈ 35) versus the straighter Pb–Br–Pb angles in MHy₂PbBr₄ (D_in ≈ 4.7° and 13°), consistent with established trends linking distortion to bandgap widening.^24,46

Fig. 7 (a) Diffuse reflectance spectrum of CPA₂PbBr₄. Inset shows the energy band gap determined using the Tauc plot. (b) PL spectra of CPA₂PbBr₄ during heating from 85 to 300 K. (c) Temperature dependence of the integrated intensity of STE and NBE emission bands of CPA₂PbBr₄ during heating. (d) CIE coordinates of CPA₂PbBr₄ during the heating run.

To elucidate the impact of the complex phase behaviour on optoelectronic properties, we performed temperature-dependent PL measurements. The metastable phase IV, stabilized by quenching to 85 K (cooling rate ∼20 K min⁻¹), exhibits a rich emission profile comprising both near-bandgap emission (NBE) and broad, Stokes-shifted PL (Fig. 7b, S10a and S11a). At 85 K, the NBE is dominated by two distinct peaks at 388.7 nm (band B2) and 397.6 nm (band B3), see Fig. S11a and S12a, which we attribute to bound excitons (BEs) localized at shallow defects. Simultaneously, a prominent broad emission band (B4) centred at roughly 580 nm displays a large full width at half maximum (FWHM) of 130 nm and a significant Stokes shift of ∼195 nm (Fig. 7b, S11a and S13b). These characteristics are fingerprints of radiative recombination of self-trapped excitons (STEs), arising from strong electron–phonon coupling in the highly distorted lattice of phase IV.^{14–16,47,48}

Upon heating phase IV, the excitonic features evolve dynamically. At 115 K, a new high-energy peak (band B1) emerges at 386.1 nm, which we assign to free exciton (FE) recombination thermally activated from trap states. As the temperature rises toward the IV → V transition, this FE band exhibits a significant red shift, reaching 390.9 nm at 180 K. In 2D perovskites, thermal expansion of Pb–Br bonds typically induces a blue shift, whereas a reduction in octahedral distortion leads to a red shift.^49–52 The observed red shift confirms that the relaxation of the highly distorted framework of phase IV dominates the bandgap evolution. Concurrently, the BE bands B2 and B3 merge near 160 K (Fig. S11a and S12a), while the STE band (B4) undergoes a pronounced continuous blue shift to 531 nm at 180 K (Fig. 7b, S10a and S12b). This blue shift, coupled with a decrease in the STE/NBE intensity ratio (Fig. S12c), indicates a progressive reduction in the lattice distortion and electron–phonon coupling strength as the metastable phase IV relaxes toward the stable phase V. Quite unusual is the observation that the integrated intensity of the NBE increases markedly between 85 and 230 K (Fig. 7b and c). This anti-thermal quenching behaviour implies an efficient thermally activated detrapping mechanism, where carriers are transferred from the STE state or shallow traps back to the FE manifold. An activation energy of 50 meV was derived for the partial quenching of the STE band in phase IV, suggesting a relatively low barrier for this transfer.

The transition from the intermediate phase V to the HT polar phase III at 240 K is marked by an abrupt discontinuity in the PL spectral features. The B1 FE band intensity drops suddenly, and a new emission peak (B2 of phase III) appears at 400.4 nm. Simultaneously, the STE band shifts to 496 nm (235 K). In phase III, normal thermal quenching behaviour resumes; the NBE intensity decreases above 235 K with a fitted activation energy (E_a) of 274 meV (Fig. S13), while the STE emission is quenched with an E_a of 206 meV (Fig. S14). The chromaticity of the emission evolves along a specific trajectory in the CIE 1931 colour space. During the heating run (Fig. 7d), the emission colour shifts from greenish-yellow (x = 0.38, y = 0.52) at 85 K, through yellow-green, to varying shades of white as the temperature exceeds 150 K. The white light emission is particularly robust in phase III, obtained by the balanced contribution of the blue NBE and the broad yellow-orange STE band.

During slow cooling from 300 K and isothermal hold of the sample for about 5 min at each temperature point for collecting the spectra (every 5 K), the path is retraced with a hysteresis (Fig. S10b, S11b, S12 and S15a). The distinct spectral signatures of phase IV (e.g., the specific B2/B3 splitting and weaker, red-shifted STE position) are notably absent during slow cooling. Furthermore, only one anomaly in the integrated intensities is observed near 190 K (Fig. S15b). These features further validate the metastable nature of the quenched state. Analysis of the integral intensity gives E_a of 225 meV for quenching of the NBE emission in phase III (Fig. S16). The corresponding values for the STE quenching are 173 and 51 meV for phase III and V, respectively (Fig. S17). CIE coordinates show that the white emission persists down to 170 K before shifting back to yellow-green (Fig. S18).

3.6. Second harmonic generation studies

SHG studies display a very nuanced picture of PT behaviour related to structural frustration. First, using 1400 nm femtosecond pumping we performed the TR-SHG study of powdered CPA₂PbBr_4. This measurement was performed from 123 K to 375 K for three cycles using a 10 K min⁻¹ ramp between the temperature points and 1 K sampling interval (Fig. 8a). Experimental spectra are provided in Fig. S19. There is no SHG activity for phases I and II, in line with their centrosymmetric structures. The SHG results show no abrupt change in the SHG intensity upon the first cooling of the powdered CPA₂PbBr₄ sample near the III → IV PT. However, the signal gradually increases below 200 K. The insensitivity of SHG to the PT arises from the fact that the organic cations adopt a similar orientation in phases IV and III (compare Fig. 3c and 4a). Also, as noted in preceding sections, Raman spectroscopy reveals a gradual evolution in the splitting of several vibrational bands, indicating progressive structural distortion and reorientation of the CPA⁺ cations. Consequently, the SHG intensity continuously increases with decreasing temperature below 200 K.

Fig. 8 Plots of integral intensities of SHG signal (700 nm) plotted versus temperature for three consecutive heating–cooling cycles in which (a) the initial cooling from 293 K to 123 K was performed with 10 K min⁻¹ rate and 1 K sampling interval; (b) the initial cooling from 293 K to 80 K was performed with 30 K min⁻¹ rate and 1 K sampling interval.

During the first heating cycle, the SHG signal traces the same path as during cooling. By contrast, when the sample crosses HT PTs and reaches 380 K and is subsequently cooled, a pronounced jump in SHG intensity appears at around 190 K. This discontinuity corresponds to the III → V PT: diffraction measurements confirm that this transformation involves reorientation of a fraction of CPA⁺ cations, leading to substantial dipole compensation. This explains the sharp decrease in SHG intensity.

A particularly intriguing feature, observed during the subsequent heating cycles (second and third heating), is that near 230 K the stepwise increase in SHG intensity is significantly smaller than during cooling. Note that dielectric measurements do not display such anomalies. The reduced SHG persists up to approximately 340 K, where the III → II PT occurs. This transformation, from a noncentrosymmetric into a centrosymmetric phase, results in complete suppression of the SHG response. In the next thermal cycle, the behaviour is fully reproducible: during the third cooling, the SHG response of phase III resets, recovering the same SHG intensity as in the second cooling run. Further cooling induces the transition into the thermodynamically stable phase V at 190 K, where, in a similar manner to the second heating run, the SHG intensity during the third heating run remains present but suppressed compared to the first heating run.

Our initial assumption was that, during the second and subsequent heating cycles, a new crystal phase distinct from phase III was formed. However, there is strong evidence that, during these heating cycles, the material remains in phase III, despite the reduced SHG intensity. First, when the SHG intensity is monitored isothermally at 293 K immediately after three heating–cooling cycles, the integrated SHG intensity spontaneously increases over time (Fig. S20). Second, DSC, BDS, and Raman spectroscopy all indicate that the III → II and V → III PTs are reversible upon repeated heating–cooling cycles. This rules out the formation of an additional crystal phase, which would otherwise be clearly detectable by these techniques. Third, PXRD patterns of the pristine powdered sample and of the same sample measured immediately after SHG cycling match each other well and agree with the calculated pattern for phase III (Fig. S21). This is direct crystallographic evidence for phase III preservation. Taken together, these observations demonstrate that the crystal structure per se is not altered and instead points to a phenomenon that suppresses the SHG response without involving a conventional molecular-scale structural change.

It is well established that the SHG intensity depends on the coherence length determined by the phase-matching condition, and in polycrystalline or multidomain samples the effective interaction length is often limited by crystallite or domain dimensions that are comparable to this coherence length.^53,54 The transition between phase V and phase III involves a change of crystal symmetry from monoclinic to orthorhombic and a change in strain. Such structural transformations are typically accompanied by the appearance/disappearance of ferroelastic domains. In a separate experiment using a polarized-light microscope, we observe that a CPA₂PbBr₄ crystal cooled to 100 K at a rate of 20 K min⁻¹ shows no domain structure, in agreement with stabilization of the metastable orthorhombic phase IV (see SI Video 1). Upon heating, ferroelastic domains appear at 185 K, proving the emergence of the monoclinic phase V. On further heating, the ferroelastic domains disappear above 240 K, indicating transition into orthorhombic phase III; however, the crystal cracks during this process (SI Videos 1 and 2). Appearance of these cracks due to V → III PT may generate heterogeneous strain fields, which can limit the effective coherence length and, consequently the SHG intensity. This leads us to the notion that, as discussed above, complete restoration of SHG intensity upon crossing the high-temperature PT III → II and spontaneous increase of SHG for the post-cycled sample (Fig. S20) both indicate that strain is directly related to observed low SHG response and its release generally leads to the regeneration of SHG.

A separate measurement was performed on a single-crystal sample that was additionally subjected to rapid cooling (ca. 30 K min⁻¹ from 293 K to 80 K, Fig. 8b and S22). All subsequent heating and cooling runs were performed at a 10 K min⁻¹ rate. As expected, the first heating cycle differs significantly from that of the powder sample. The dip in the SHG curve during heating corresponds to phase V; thus, the IV → V transition occurs around 170–180 K, followed by the onset of the V → III transition at approximately 230 K, which completes near 260 K. During the first cooling run from 375 K, a clear transition from phase III to phase V is observed at 180 K (Fig. 8b); however, we cannot exclude the possible presence of residual phase IV, as the SHG signal remains substantial at 120 K. During the second heating cycle, the SHG intensity is again reduced, albeit to a lesser extent. In the second cooling and third heating cycles, the behaviour becomes typical of the powder sample, with no dip and no evidence of phase IV persisting; phase V is present only below 180 K during cooling and extends up to approximately 240 K during heating. This measurement confirms that phase IV is metastable, as evidenced by the absence of a dip in the powder-sample experiment, where phase IV is transformed directly into phase III upon heating.

4. Conclusions

It is well established that under rapid cooling, LT PTs in hybrid compounds can be suppressed, locking the structure in a metastable RT or HT phase. This behaviour has been demonstrated for compounds exhibiting sluggish PTs with very large thermal hysteresis. Using a combination of experimental methods, we demonstrate that CPA₂PbBr₄ is another example of such a compound, exhibiting an LT PT with very large thermal hysteresis resulting from substantial structural differences between phases V and III. This compound can be trapped in a metastable phase IV upon cooling the pristine sample from 300 K even with a rate as small as 3 K min⁻¹ but it is not observed when the cooling rate of the pristine sample decreases to 1 K min⁻¹. The kinetically trapped phase (phase IV) has a different structure than its stable RT polymorph. Interestingly, this metastable phase, which retains some residual disorder, is transformed upon heating into a thermodynamically stable, well-ordered LT monoclinic phase V. This anomalous PT on heating produces an unusual exothermic peak in thermal measurements. Upon further heating/cooling cycles (heating from 80 K up to 300 K or 380 K followed by cooling or heating the pristine sample to 380 K followed by cooling), the metastable phase does not reappear.

Our study also demonstrates that all phases observed below 350 K are polar. CPA₂PbBr₄ exhibits efficient emission with strong thermochromism, as well as switchable dielectric and NLO properties. Photoluminescence, NLO, and electrical properties differ between the lowest-temperature phases (stable phase V and metastable phase IV). Notably, SHG studies reveal that thermal cycling induces suppression of SHG intensity without altering the crystal structure. This phenomenon is attributed to the appearance of cracks in phase III during the monoclinic-to-orthorhombic (V → III) transition, which generate strain and limit the coherence length. Thus, strain appears responsible for the reduced SHG response, as evidenced by complete restoration of SHG intensity upon crossing the HT III → II transition and the spontaneous recovery of SHG in post-cycled samples at room temperature.

Overall, we report the discovery of a new hybrid perovskite exhibiting coexistence of multiple functional properties. Our studies highlight the importance of kinetics in controlling structural order/disorder and distortion, and thus the physicochemical properties of hybrid perovskites. This is particularly significant because kinetic trapping was observed under relatively moderate cooling rates (3–30 K min⁻¹), commonly employed for monitoring LT structures or in temperature-dependent PL measurements. These findings underscore the critical importance of carefully controlling the cooling rate in such studies, especially when a perovskite undergoes an LT PT associated with very large thermal hysteresis.

Author contributions

Conceptualization: M. M. Data curation: M. P., K.F.-P., A. G., D. S., D. D. and J. K. Z. Formal analysis: M. P., K. F.-P., A. G., D. D., D. S., J. K. Z. and A. S. Investigation: M. P., K. F.-P., A. G., D. D., D. S. and J. K. Z. Methodology: all authors. Project administration: M. M. Resources: M. M. Supervision: M. M. Validation: M. M., J. K. Z., D. S. and A. S. Writing – original draft: all authors. Writing – review and editing: all authors. All the authors have given their approval to the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Data availability

CCDC 2336098–2336102 contain the supplementary crystallographic data for this paper.^55a–e

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: Tables S1–S3: hydrogen-bond, structural and optical parameters, Raman wavenumbers. Fig. S1–S22: powder XRD patterns, TG, DTA and DSC plots, the unit cell volume changes with temperature, CPA⁺ conformations, Raman, dielectric and SHG spectra, pyroelectric current and P–E hysteresis loop. Videos 1 and 2: optical images under a polarized light microscope on heating the quenched sample to 100 and 170 K. See DOI: https://doi.org/10.1039/d5sc09693f.

Acknowledgements

The work was financially supported by the statutory funds of the Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Wroclaw. J. K. Z. acknowledges support from Academia Iuvenum, Wroclaw University of Science and Technology.

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