Photophysical Ion Dynamics in Hybrid Perovskite MAPbX3 (X=Br, Cl) Single Crystals

Hybrid organic–inorganic perovskites (HOIPs) are promising candidates for next‐generation photovoltaic materials. However, there is a debate regarding the impact of interactions between the organic center and the surrounding inorganic cage on the solar cell's high diffusion lengths. It remains unclear whether the diffusion mechanism is consistent across various halide perovskite families and how light illumination affects carrier lifetimes. The focus is on ion kinetics of (CH3NH3)PbX3 (X = Br, Cl) perovskite halide single crystals. Muon spectroscopy (μ+SR)is employed to investigate the fluctuations and diffusion of ions via the relaxation of muon spins in local nuclear field environments. Within a temperature range of 30–340 K, ion kinetics are studied with and without white‐light illumination. The results show a temperature shift of the tetragonal‐orthorhombic phase transition on the illuminated samples, as an effect of increased organic molecule fluctuations. This relation is supported by density functional theory (DFT) calculations along the reduction of the nuclear field distribution width between the phase transitions. The analysis shows that, depending on the halide ion, the motional narrowing from H and N nuclear moments represents the molecular fluctuations. The results demonstrate the importance of the halide ion and the effect of illumination on the compound's structural stability and electronic properties.


Introduction
In the pursuit of global environmental restoration, extensive endeavors have been undertaken to harness the sun's energy, since the first practical silicon solar cell was introduced in 1954. [1]Presently, most investigations are primarily centered on the enhancement of solar cell efficiencies, with the concurrent objective of utilizing materials that are abundant on our planet.In this regard, HOIPs have been found to effectively fulfill most objectives. [2]The power conversion efficiency of hybrid perovskite solar cells has been shown to reach 26.1%, rivalling crystalline silicon cells. [3,4]Given the prerequisite that they are produced in an environmentally friendly manner, and that the assembly of a functional perovskite cell is as straightforward as positioning the perovskite absorber between an electron transport layer and a hole transport layer, perovskite solar cells appear to possess considerable promise for fostering sustainable growth. [2,5]The HOIP crystals in question are a form of the ABX 3 single perovskite structure. [6]They are composed of a methylammonium (MA) organic cation (CH 3 NH 3 ) + at the A-site, a Pb 2 + cation at the B-site, and a halogen anion, Br − or Cl − , at the Xsite, as illustrated in Figure 1a.The MA molecule sits in the center of a framework with edge-sharing PbX 6 octahedra.Both MAPbBr 3 and MAPbCl 3 crystallize in the cubic Pm3m system at room temperature. [7]The Br crystal undergoes two structural transitions, one at ≈230 K from cubic to tetragonal and one at ≈144 K from tetragonal to orthorhombic (see Table S2.1,Supporting Information).10] For the Cl crystal the same structural transitions occur at ≈175 and ≈169 K (see Table S2.1,Supporting Information), respectively. [11]he halogen anions are highly electro-negative, enhancing the ionicity of the perovskite.The semiconducting properties arise from the inorganic structure and by exchanging or mixing the halogen ions, one can tune the bandgap energy to tailor the material for specific applications. [12]The reported bandgap values for MAPbBr 3 and MAPbCl 3 are 2.39 and 3.16 eV respectively, making them sensitive to visible and ultraviolet light. [13,14]Their carrier lifetimes, as determined by photoluminescence and transient absorption spectroscopy, [15][16][17][18][19] cover the nano-to microsecond time scale, revealing fast, and slow carrier dynamics.The rotating organic cations play a crucial role in determining the structure and the stability of the crystal.These organic molecules form permanent dipoles that can be frozen in space or possess rotational degrees of freedom, which can be observed on the picosecond time scale, with or without intersite correlations. [20]These molecular fluctuations may drive the formation of polarons that create a dynamic screening to the charge carriers.This is the most likely scenario put forward to explain the long carrier lifetimes in MAPbX 3 . [21,22] + SR is a well established microscopic technique in the study of ion kinetics. [23,24]A recent  + SR study reported the ion diffusion in the archetypal halide perovskite MAPbI 3 . [25]Although their results demonstrate a relation between the rotation of the Following each muon decay, the emitted positrons with momentum direction statistically along the muon spins reach the surrounding detectors.The evolution of muon spin precession can be studied from the ensemble of detected positrons.b) Pictures of the sample holders used for the dark and light on/off experiments.In the light on/off experiment, the sample holder is bent to 45°for the sample to be subjected to both light and the muon beam.
electric dipoles of MA molecules and the charge carrier lifetime in MAPbI 3 , it remains ambiguous if a similar mechanism can be extended to other halide perovskite solar cell compounds.Furthermore, their study has been conducted on MAPbI 3 powder sample, giving an average of the diffusion length among multiple directions and influenced by grain boundaries. [26]Finally, their measurement does not consider the effect of illumination, which can drastically influence the dynamics of ions.
Here, we employ  + SR with a pulsed muon source (Figure 2a) to study the ion dynamics in MAPbX 3 (X = Cl, Br) single crystals as a function of temperature, with and without white light illumination (see Experimental Section).Contrary to powder samples, single crystals present the advantage of studying the ion diffusion along specific directions [27] and present an ideal platform in the development of optoelectronic devices.Through our measurements we extract the evolution of the internal nuclear magnetic field distributions of the involved ions over a temperature range of 30 − 340 K.The fluctuation rate of the field distribution is a direct measure of the dynamics of the ionic species.Using muon as a local probe with well-defined implantation sites and a wide time window of 10 −5 -10 −11 s, gives spatially specific information on the muon-lattice dynamics.Both static and dynamic contributions to the muon spin depolarization are identified and evaluated.Our results show that, depending on the halide ion and the local conditions (e.g., with or without light), the motional narrowing from H and N nuclear moments has an impact on the structure stability and the charge carrier lifetimes.

Results
Zero field (ZF), longitudinal field (LF), and transverse field (TF)  + SR measurements were conducted in illuminated and dark environment (Figures 2 and 3) to characterize the local nuclear magnetic field distributions as a function of temperature. [24,28]During the illuminated measurements the depolarization in the consecutive light on/off periods (see Experimental Section) were identical (see Section S.3, Supporting Information), indicating that photoinduced ion dynamics were sustained through the light-off cycle.In contrast, the depolarization in the constant dark configuration, produced effectively different results.

(CH 3 NH 3 )PbBr 3
The ZF and LF time spectra for MAPbBr 3 , collected at T = 30 K in the dark condition or under illumination, are shown in Figure 3 with subtracted background asymmetries and normalized.A Gaussian Kubo-Toyabe (KT)-like relaxation [24,29] is observed together with a small offset.Therefore, the time spectra were fitted using dynamic Gaussian-KT together with a nonrelaxing component: where A 0 is the initial asymmetry whose values depend on the instrument, while P LF is the polarisation function under ZF and LF configurations.A KT and A BG are the asymmetry of each contribution to the muon depolarization and correspond to the volume fraction of the measured sample.The KT parameters, Δ KT and  KT , are the field distribution width and the field fluctuation rate. [29]Since weak LF is able to decouple the muon spin from the static intrinsic fields (Figure 3a), the randomly oriented internal field is expected to originate from I H = 1/2, I N = 1, I Pb = 1/2 and I Br = 3/2 nuclear moments.Weak LF is not expected to affect the spin-spin correlation times in the system and the KT parameters were fitted as common parameters across the different field configurations.Moreover, A BG was kept fixed across the temperature range, a value estimated at a low temperature measurement for which the internal magnetic field of the sample is shown to be static.The obtained KT fit parameters from Equation ( 1), under these conditions, are shown in Figure 4a,b as a function of temperature.At low temperatures, no significant difference is observed between light and dark measurements.Below 140 K, Δ KT poses a constant value of about ≈ 0.28 μs −1 .This value is consistent with the expected value considering a muon situated at fractional coordinates (0.22, 0.25, 0.25) in the orthorhombic cell, for which Δ ortho ≈ 0.298 μs −1 using the powder average expression in the Van Vleck formalism. [30,31]The sudden decrease around T Br C1 = 145 K is consistent with the incommensurate phase transition, [8,32,33] evidence of which were found in X-ray diffraction with the appearance of satellite peaks at various fraction positions around the unit cell sites, as well as an additional heat flow peak in DSC measurements (see Figure S1.1, Supporting Information).
The structural transitions change the nuclear coupling between lattice and muons and a new value of Δ KT ≈ 0.12 μs −1 is stabilised in the tetragonal phase.Another drop is observed around T Br C2 = 220 K, which subsequently infers a structural transition from tetragonal to cubic symmetry. [10,32]It is not unexpected that these structural transitions are present in both dark and light configurations as inferred from Figure 4b.It is evident that the nuclear coupling under new symmetry cannot solely explain the magnitude of the drop in Δ KT , since there is a large difference between the calculated (solid red lines) and experimental values.The drop can however be explained by introducing dynamics and is thereupon related to the local field fluctuation rate ( KT ).We present  KT as a function of temperature in Figure 4a.An exponential-like increase is observed from lower temperatures and up to about T Br C1 .This increase resembles an Arrhenius activation, and the calculated activation energies are tabulated in Table 2. Additionally, the corresponding fits are presented in the Figure S3.3 (Supporting Information).A second increase is observed approaching T Br C2 .The value and behavior of  KT is similar to what was observed for MAPbI 3 . [34]Past  + SR work on MAPbI 3 suggested this increase to stem from fluctuations caused by the rotations of the MA molecule. [25,34]Consequently, the decrease observed just above T Br C1 was explained as motional narrowing associated to the dynamics of H atoms, and further increase of  KT at higher temperatures was asserted to be due to I diffusion.Given the resemblance in behavior of MAPbBr 3 , it is naturally reasonable to assume that a similar mechanism is behind the obtained temperature dependence.However, the proposed scenario has not yet been validated.
In order to confirm the premise, we have calculated the expected internal field distribution widths Δ, at the muon sites, for their respective crystal symmetries.Table 1 summarizes the calculation results of the expected Δ, for each crystal symmetry, at the expected muon sites.The electrostatic potential minima  (Figure 1b) suggest two muon sites with fractional coordinates  1 : (0.22, 0.25, 0.25) and  2 : (0.0, 0.5, 0.5).
The results are shown as solid lines in Figure 4b.The agreement of the calculated values (Δ static Br ) with the measured values in the orthorhombic phase confirms the  1 muon site determined via our method.However, mismatches are observed in tetragonal and cubic phases.other words, the nuclear coupling under new symmetry cannot explain the total magnitude of the drop.In fact, the calculated value (calc.narrowed) sets a lower boundary to the measured value if H and N contributions are excluded from the calculation.This suggests that the field distributions associated to H and N nuclear moments are motionally narrowed [23,35] and is consistent with the scenario put forward in the past; [25,34] the drop in  KT at T Br C1 is caused by motional narrowing associated to the MA cage.This scenario is also endorsed by the endothermic minima of the MDSC non-reversible component (see Figure S1.1, Supporting Information).An analysis using quasi-elastic neutron scattering [21] and nuclear magnetic resonance studies, [36][37][38] where the rotational freedom of the MA cage increases in the tetragonal and cubic phases compared to the orthorhombic phase, also supports this proposed framework.Therefore, we conclude that mainly Br nuclear moments contribute to the increase of  KT at higher temperatures.Interestingly, there is a large difference between dark and light configurations in  KT at low temperatures, and is further discussed below.

(CH 3 NH 3 )PbCl 3
The ZF and LF time spectra collected for MAPbCl 3 at T = 50 K are shown in Figure 3b.Similar to the X = Br compound, a KT and an offset signal is manifested in the time spectra.In this case, the KT signal is the effect due to I H , I N , I Pb , and I Cl = 3/2 nuclear moments.Equation (1) was used in order to fit the time spectra as a function of temperature, under the same conditions as described above and is shown in Figure 4c,d.Δ KT shows a independent behavior at low temperatures.The value ≈ 0.23 μs −1 is in agreement with the expected local field value at the (0.22, 0.25, 0.25) muon site, in the orthorhombic phase.We should however note that the main result presented here is not dependent on the specific muon site.Regardless, Δ KT experiences a sudden drop around T Cl C1 = 172 K, which is consistent with a structural transition temperature. [11]Once again, this transition changes the nuclear coupling with the muons.Unlike the X = Br compound, Δ KT is not stabilized onto another value but a continuous decrease is observed in the tetragonal phase.The origin is discussed later on.A final structural transition is present around T Cl C2 = 190 K and results in a second drop of Δ KT , which stabilizes at a value Δ KT ≈ 0.1 μs −1 .These structural transitions are present in both light and dark configuration.
The local field fluctuations rate,  KT , is shown in Figure 4c.An exponential like increase is observed at lower temperature up to T Cl C1 .The Arrhenius fits are presented in the Figure S3.3 (Supporting Information) and the activation energies for both the light and dark environment are documented in Table 2.The E a values decrease with illumination, but increase with halide substitution depending on ionic size and hydrogen bonding strength, as reported in previous studies.As already mentioned, a similar increase in  was observed in MAPbI 3 [25,34] and was previously speculated to be due to fluctuations from the MA molecule, for which the sudden decrease was explained by motional narrowing from H moments. Similar to the X = Br sample, the increased dynamics are indicated by the DSC non-reversible heat flow component (see Figure S1.1, Supporting Information).We have calculated the local field arising from nuclear moments at the muon sites in their respective crystal symmetries, to support this assessment.
The results of our calculations for each crystal symmetry are presented in Table 1 and are shown as solid lines in Figure 4d.Once again, the calculated static value is comparable with the experimental values in the orthorhombic phase.However, in the (CH 3 NH 3 )PbCl 3 case the static calculations continue to produce a better fit for the tetragonal and cubic phases in contrast to excluding H and N contributions.47] Mostly Cl nuclear moments are expected to contribute to the increase of  at higher temperatures.The temperature dependence of  KT seems comparable between light and dark modes but differences are present at lower temperatures and the origin is discussed below.

Discussion
The analysis on muon depolarization spectra for MAPbBr 3 and MAPbCl 3 has confirmed the structural transitions [10,11] and given evidence of increasing MA + fluctuations and Br − ,Cl − diffusion [48] as the crystal structure evolves from orthorhombic to tetragonal, to cubic crystal symmetry with increasing temperature.The calculated local field values for both static and motionally narrowed MA + are presented together with the experimental results.A similar framework was considered previously in the same and sister compounds. [21,34,49,50]In the MAPbI 3 compound, the temperature dependence of the field distribution width was shown to coincide with photoluminescence carrier lifetimes as a function of temperature. [25]Furthermore, MA + has a permanent electric dipole moment, the fluctuations of which result to an abrupt increase of the complex permittivity components at T C1 . [7,51]It is thus of high interest to study complex permittivity measurements at frequencies near the charge carrier lifetimes of those compounds [52] and determine possible correlations between charge carriers and MA + .
The effect of illumination is indirectly observed but evident in the  KT and Δ KT evolution with temperature.For both samples, the effect of the flash lamp is most prominent below T C1 , where MA cage fluctuations are initiated.In fact, the peak feature of  KT is shifted to lower temperature under illumination.Coincidentally, the sharp drop of Δ KT seems to be occurring at lower temperature as well.This suggests that the structural transition taking place at T C1 is driven by MA motion, specifically C3 rotation.This assessment is in line with quasi-elastic neutron scattering measurements [21] in which the relaxation time of the rotational motion around the C3 axis seem to exhibit a plateau below T C1 .
A question remains however, why are the MA cage fluctuations affected by the illumination.From the presented data, it appears that illumination is enhancing the MA dynamics, as evidenced from the temperature shift of the lower peak and the increase of  KT in terms of absolute value.Recent studies proposed a relationship between carrier lifetime and MA fluctuations. [25,53,54]he long carrier life was ascribed to the dynamic motion of MA molecules, in which dynamic screening via formation of polarons protects the carriers.It is currently believed that the MA dynamics is driving the formation of polarons and thus increasing the lifetime of the carriers. [22,55]Our results suggest that these effects appear in symbioses.By exciting electrons and inducing electron carriers, the dynamics of the MA cage is enhanced and is likely resulting in the formation of polarons.
The high temperature behavior of  KT was ascribed to Br and Cl dynamics, respectively.For the X = Cl sample no significant difference is observed between dark and light configuration.Similarly, the X = Br sample does not show any large differences.While we cannot fully exclude the possibility of diffusing muons above 150 K, future negative  − SR measurements can experimentally determine the diffusing species. [56]ne may argue that the Br diffusion is lower in light configuration.However, the number of measurement points need to be increased in order to further comment on the origins or the validity of this effect.With that said, it has been suggested that electronic carrier diffusion can either enhance or suppress ionic diffusion through ambipolar transport. [57]Also, we should note that the efficiency of solar cells can be improved by restricting the diffusion of these ions.In fact, partial substitution of I with Br [49] showed that the activation energy of I diffusion increases.In other words, partial cation substitution may restrict the diffusive behavior and thus increase the overall solar cell performance.
The diagmagnetic sample fraction is estimated from the TF precesion amplitude (Figure 5).Its temperature dependence is observed in the initial TF asymmetry (A 0 ), in good agreement with previous dielectric studies. [7,51][60][61] A muonium quasi-atom is formed when a  + captures an e − .The capture cross section is inversely proportional to the dielectric constant, which can explain why the muonium formation is more prominent in MAPbCl 3 . [62]With this in mind, we would like to conclude with a last remark on the possibility of monitoring hydrogen kinematics through the study of muoniums.Recently, it was reported that highly diffusive H + impurities are present in MAPbI 3 , [63] hampering the solar cell's performance.This is a common issue with semiconducting materials, where  + SR has been successfully employed to further our understanding on the fundamental aspects of hydrogen kinematics. [64,65]

Conclusion
The current study presented  + SR measurements on single crystal, HOIPs MAPbX 3 (X = Br, Cl), in which the static and dynamic changes of internal, nuclear magnetic fields were measured as a function of temperature and magnetic field.At low temperatures, the onset of MA molecule fluctuations is found to drive the orthorhombic/tetragonal structural transition.The presented data suggest Cl − and Br − diffusion to take place at high temperatures.By illuminating the sample, the number of excited carriers can be increased.This has an effect on the lattice dynamics of these systems as the MA cage dynamics are enhanced when the number of carriers increases.The interaction between photogenerated carriers and MA ions supports the idea of screening via formation of polarons, facilitating the appearance of long carrier lifetimes in these compounds.The next step concerning  + SR would be a controlled, laser illumination with measurements in various crystallographic directions to access detailed diffusion information of all ionic species.Finally, muonium formation was observed that opens up the possibility to study hydrogen kinematics in the title compounds in future  + SR studies.

Experimental Section
Single crystals of MAPbBr 3 and MAPbCl 3 were grown according to Ref. [66].Differential scanning calorimetry (DSC) and temperaturemodulated DSC were performed on both crystals to macroscopically identify the structural transition and molecular fluctuation occurrences (see Figure S1.1, Supporting Information).
The  + SR measurements were conducted at the pulsed surface muon beam-line EMU at ISIS. [67] Rectangular single crystal pieces were aligned on Ag holders and mounted in the fly-pass configuration.The crystals were wrapped in Ag foil for measurements in the dark.For measurements in an illuminated environment a transparent, 10 μm Mylar film was used instead, and the sample was mounted at 45°(Figure 2b) making it possible to accommodate both light and muon pulses.The samples were measured in ZF, LF, and TF geometry, where transverse and longitudinal magnetic field refers to the applied field direction with respect to the initial muon spin polarization.][70] The flash lamp was operated with intensity 1.52 mJ∕pulse, but pulsed at 50 Hz in order to minimize the temperature increase caused by light irradiation.The relative intensity was stable at ≈ 20% between 750-370 nm and decreased below 370 nm.Spectra were recorded during two periods of 10 s, light on and off, with 500 muon pulses being recorded in each state.The 80 ns wide muon pulses, each containing a few hundred muons, were implanted in the sample at 50 Hz, synchronously with the light on and off cycle.Data acquisition alternated continuously between the two states for the duration of the run.The software package musrfit was used to analyze the data. [71]he electrostatic potential of the compounds was calculated with DFT, determined via a self consistent run using the pseudopotential-based plane-wave method as implemented in Quantum Espresso. [72]The pseudopotentials are based on [73, 74].This calculation was performed for all crystal symmetries the system exhibits between 100 -300 K; orthorhombic, tetragonal, and cubic structures.The electrostatic minimum asserted to be the muon site (Figure 1b).It was noted that local distortion due to the implanted muon was not considered.

Figure 1 .
Figure 1.Example of the orthorhombic crystal structure of MAPbX 3 (X = Cl, Br) and electrostatic potential calculation for determining the muon implantation sites.a) The orthorhombic crystal perovskite structure of MAPbCl 3 , including (b) the probable locations of implanted muons.These probable muon sites were determined from the minima of electrostatic potential calculations.Intersections of the charge density in the lattice planes (100) and (400) present the possible muon sites (pink color).

Figure 2 .
Figure 2. Illustration of the  + SR set-up featuring the mounting of the HOIP crystals MAPbX 3 (X = Cl, Br).a) Schematic of the  + SR experiment in EMU, ISIS.A spin polarized, pulsed muon beam hits the sample.The positive muons are implanted at electrostatically preferable lattice sites and their spin precesses as affected by surrounding local magnetic fields.Following each muon decay, the emitted positrons with momentum direction statistically along the muon spins reach the surrounding detectors.The evolution of muon spin precession can be studied from the ensemble of detected positrons.b) Pictures of the sample holders used for the dark and light on/off experiments.In the light on/off experiment, the sample holder is bent to 45°for the sample to be subjected to both light and the muon beam.

Figure 3 .
Figure 3. ZF and LF  + SR depolarization spectra of MAPbBr 3 and MAPbCl 3 in a dark and illuminated environment.The ZF and LF= 5, 10, 20 Oe time spectra are recorded at a) T = 30 K for MAPbBr 3 and b) T = 50 K for MAPbCl 3 , in the dark condition and under illumination.The solid lines are fits obtained from Equation (1).

Figure 4 .
Figure 4. Fitting parameters from the MAPbBr 3 and MAPbCl 3  + SR depolarization spectra.Temperature dependent a) field fluctuation rate ( KT ) and b) field distribution width (Δ) of MAPbBr 3 in dark and illuminated configuration, obtained using Equation (1).Temperature dependent c) field fluctuation rate ( KT ) and d) field distribution width (Δ) of MAPbCl 3 in dark and light configurations, obtained using Equation (1).The dashed lines mark the structural transition temperatures.The solid lines in (a,c) are a guide to the eye, while in (b,d) are the calculated values in the static and motionally narrowed case (see Table1).

Figure 5 .
Figure 5.The initial asymmetry of MAPbBr 3 and MAPbCl 3 with and without illumination.The initial asymmetry (A 0 ), estimated in TF configuration for a) MAPbBr 3 and b) MAPbCl 3 in the dark and light configurations.

Table 1 .
Calculated local field distribution widths.The local field distribution widths (Δ static Cl and Br) for the respective muon sites, for each crystal symmetry, calculated in the Van Vleck limit.The value in which the MA cage is motionally narrowed (Δ narrowed X, X =

Table 2 .
Calculated activation energies (E a ) for MAPbBr 3 and MAPbCl 3 , below T C1 , in the dark and light environment.The references include E a results in the same temperature range.