Phase Transitions in Low-Dimensional Layered Double Perovskites: The Role of the Organic Moieties

Halide double perovskites are an interesting alternative to Pb-containing counterparts as active materials in optoelectronic devices. Low-dimensional double perovskites are fabricated by introducing large organic cations, resulting in organic/inorganic architectures with one or more inorganic octahedra layers separated by organic cations. Here, we synthesized layered double perovskites based on 3D Cs2AgBiBr6, consisting of double (2L) or single (1L) inorganic octahedra layers, using ammonium cations of different sizes and chemical structures. Temperature-dependent Raman spectroscopy revealed phase transition signatures in both inorganic lattice and organic moieties by detecting variations in their vibrational modes. Changes in the conformational arrangement of the organic cations to an ordered state coincided with a phase transition in the 1L systems with the shortest ammonium moieties. Significant changes of photoluminescence intensity observed around the transition temperature suggest that optical properties may be affected by the octahedral tilts emerging at the phase transition.


Experimental Methods
Synthesis of the materials. The 3D Cs2AgBiBr6 crystals were prepared following the recipe from Slavney et al. 1 Briefly, BiBr3 (112.25 mg) and CsBr (106.5 mg) were mixed and dissolved in 2.5 mL of HBr (48% vol.) at 110°C under stirring during 30 min. Then, AgBr (47 mg) was added and under stirring dissolved for 2 h, yielding an orange solution. The slow cooling of this solution to room temperature led to the formation of orange-red crystals, which were isolated by filtration on a Büchner funnel with a fritted glass disc by vacuum suction while washing with acetone. We checked the purity of the crystals by Raman spectroscopy by analyzing the frequency of the A1g mode. 2 The layered materials were synthesized adapting the recipe from Connor et al. 3 The (R-

S3
Optical characterization. The temperature-dependent absorbance spectroscopy was carried out in a Bruker Vertex 80V FT-spectrometer equipped with an Oxford Optistat liquid N2-cryostat.
Absorbance spectra at room temperature were collected using a Varian Cary 5000 UV-Vis-NIR spectrophotometer (Agilent Technologies) and Jasco V730 UV-Vis spectrophotometer. Thin films of the materials were deposited on cleaned quartz substrates (SPI ® supplies) by spin coating (3000 rpm for 40s and then 5000 rpm for 20s) solutions prepared by dissolving the crystals (~300 mg/mL in DMSO for 3D and 2L and in DMF for 1L) followed by an annealing step at 285°C (5 min) 4 , 135°C (7 min) 3 and 100°C (4 min) 3 for the 3D, 2L and 1L perovskites, respectively. Prior to the spin coating step, the glass substrates were cleaned in an ultrasonic bath subsequently with acetone and isopropanol (8 min each step), dried under a N2 flow followed by a final O2 plasma treatment (120s, 100W).
Photoluminescence spectra were collected with a Horiba i-hr320 spectrometer equipped with a Si CCD, with excitation at 325 nm (power on sample ~0.1 mW), and using a Cassegrain objective (15×, 0.28 NA). All data has been corrected by the spectral response of the system. Temperaturedependent measurements were carried out using a liquid nitrogen cryostat from Linkam ® , with a quartz window for the optical access and emission collection in backscattering configuration.
Raman spectroscopy characterization. Room-temperature Raman measurements were carried out in a Renishaw ® inVia equipped with a 50× (0.75 N.A.) objective with an excitation wavelength of 532 nm using a laser power < 0.1 mW, to avoid the damage of the samples during the measurement.
The temperature-dependent Raman spectroscopy study was performed using a liquid nitrogen cryostat from Linkam ® mounted in a Renishaw ® inVia microscope equipped with a long working distance objective (50×, 0.50 NA).

S4
X-ray diffraction characterization. The XRD analysis was carried out using a PANalytical Empyrean X-ray diffractometer, equipped with a 1.8 kW CuKα ceramic X-ray tube and a PIXcel3D 2x2 area detector, operating at 45 kV and 40 mA at room temperature. The crystals were deposited onto a quartz zero-diffraction single crystal substrate for the XRD measurements. The diffraction patterns were collected under ambient conditions using parallel beam geometry and symmetric reflection mode. XRD data analysis was carried out using the HighScore 4.   Evaluation of the structure. The X-Ray diffraction patterns of all the samples involved in this study are shown in Figure S2. The XRD spectra of the 3D sample ( Figure S2a) matches with the patterns described in the reference card (ICSD 291597) for a cubic crystal system (Fm-3m space group) corresponding to the work of McClure et al. 5 When incorporating the organic moieties to form the 2L and 1L systems, this cubic structure evolves to monoclinic (see Table   S1), 3,6,7 and some diffraction peaks arising from specific reflections along the (h 0 0) direction start to appear in the 1L systems. From the periodicity of these diffraction peaks one can estimate the interlayer distance between the octahedral layers (d) displayed in Figure 1h (see main text and Table S2) between the (AgBr6) 5--(BiBr6) 3octahedral layers by applying the Bragg's law [nλ = 2d sinθ], in which n = 1 and λ(Cu) = 1.54 Å. 8,9 The d values determined by our XRD measurements agree well with the values estimated from the crystal structures built using Vesta ® software 10 from the crystallographic data available in literature 3,6 (using ammonium alkyl chain moieties) concretely for 1L-PA, 1L-BA and 1L-OcA. The corresponding crystal structures show a crossover or entanglement of the alkyl chains when increasing the alkyl chain length (see Figure S3a). To visualize the possible arrangement of the organic moieties in 1L-DA and 1L-DoA, we sketched their crystal structures based on the 1L-OcA structure considering the d value obtained from XRD, 23 Å and 20 Å, respectively. As can be observed in Figure S3b, in the case of 1L-DoA a clear crossover of the dodecylammonium moieties should occur, that would explain the shorter d value in comparison with 1L-DA sample. This change in the trend of the interlayer distance is different from the monotonical increasing observed in 2D lead halide perovskites, concretely (C4-C18)2PbI4, in which the crystal structure and space group is kept for the whole family of compounds. [11][12][13] However, in the double (C3-C8)4AgBiBr8 perovskites studied the space group changes when the alkyl chain length varies, thus, it is possible to have a different rearrangement of the moieties leading to differences in the interlayer distance trend. Figure S2. Representative XRD spectra of the synthesized perovskite single crystals: 3D, 2L (a) and 1L (b). The reference pattern (card ICSD 291597) for the 3D sample is also shown.  From the crystallographic data available in the literature for 3D, 14 2L-/1L-PA, 6 2L-/1L-BA 3 and 1L-OcA 6 (see Table S1), we quantified the lattice distortion induced by the presence of the corresponding organic molecules by the mean octahedral quadratic elongation parameter (λoct), 16 following the equation Eq. S1: [Eq. S1] in which ℓ0 and ℓi are the center (Ag + or Bi 3+ )-to-vertex (Br -) distance in the octahedron, respectively. The center-to-vertex distances have been determined using Vesta ® software 10 and the crystallographic data reported in refs. 3,6,7 . In this way, we evaluate the changes in the Ag-Br and Bi-Br bond lengths with respect to the symmetric octahedron in the 3D crystal (see Table S3).
Evaluating the λoct for both Ag and Br-containing octahedra, (AgBr6) 5 Figure S4 (prepared using Vesta ® software 10 ), in which the angles between the successive octahedra (AgBr6) 5-/(BiBr6) 3-/(AgBr6) 5in the same layer defined by the Bi-Br-Ag bonds vary from 186º to 163º when passing from 100 K to 298 K.  Figure S4. Structure of the 1L-BA crystal at T = 100K and T = 298K visualized with VESTA 3 software 10 based on the crystallographic data from ref. 3 .

Additional absorbance and photoluminescence spectroscopy characterization
As in the graphs shown in the main text for 3D and 2L/1L-PA (Figure 4a), in the absorbance spectra of the films prepared from the 2L/1L-BA and 2L/1L-PEA systems, only a slight absorption peak broadening with increasing temperature is observed, see Figure S12.  Figure S14, to determine if the linear fits converge to a single point corresponding to (E0, α0) that allows to estimate the optical bandgap (see Table S4 for the values, when crossing, namely at high temperatures). 3,19,20 We obtain similar results for the optical bandgap from this analysis of the temperature-dependent absorption coefficient and directly from the peak position in the absorption.  Complementary PL data: Representative temperature dependent PL spectra for 2L/1L-BA and 2L/1L-PEA samples is shown in Figures S15-S16.

Computational details
First-principles calculations have been carried out using SIESTA 21  to make sure that the optimization of the alkyl chain conformation does not affect the octahedral S20 tilt pattern in the inorganic layers. All the simulations have been carried out using the SIESTA code, 21 and including spin-orbit coupling. Reference calculations with a plane-wave code (Quantum Espresso 22 ) were performed to validate the basis set and convergence parameters used in SIESTA. Inclusion of spin-orbit coupling (SOC) is of utmost importance to reproduce the band structure, due to the presence of Bi 3+ ions, whose contribution dominates the lowest conduction bands. If spin-orbit coupling is neglected, the 1 eV splitting of the lowest conduction bands is not captured (Figure S17a,b).  The band structure computed using 2L-BA room temperature structure (with one particular molecular conformation chosen out of multiple atomic positions given in ref. 3 ) without geometry relaxation shows a flat band originating from carbon 2p-orbitals intersecting the top valence band.
Geometry optimization moves this flat band to lower energies, suggesting this band to be an artefact due to the molecular geometry taken arbitrarily from multiple average positions in the room temperature XRD, being far from the equilibrium conformation of the chain itself ( Figure   S18c). Figure S18d shows the band structure and the density of states (DOS) computed for а fictitious structure with octahedral tilts removed: band degeneracies appear at the Brillouin zone boundary in line with the higher symmetry, but the bands across the gap are largely similar to the ones computed using experimental structures. The symmetry of this structure is Cmmm (#65 in International Tables 26 ). The flatness of the conduction band can lead to very interesting phenomena: for example, applying a ferroelectric mode, such as Γ2 + , with amplitude as small as 1:10 of that of Γ3 + , the one already present at room temperature that causes the out-of-plane tilting of the octahedra, produces a shift in the position of the minimum of the conduction band, thus making the bandgap indirect ( Figure S19b). Figure S19. (a) Density of the Bi-centered Wannier function for the lowest conduction band of 1L-BA at low-temperature that does not hybridize with high energy Ag orbitals, resulting in a wavefunction localization on Bi and Br atoms and a flat conduction band. (b) Band structure and projected density of states of the 1L-PA structure at room temperature with a small ferroelectric Γ2 + mode applied. The red asterisk marks the minimum of the conduction band.