Photoinduced metastable cation disorder in metal halide double perovskites

Abstract

Lead-free perovskites have emerged as environmentally benign alternatives to lead halide counterparts for photovoltaic and optoelectronic applications. Among them, the double perovskite Cs₂AgInCl₆ family, with proper composition engineering, exhibits remarkable white-light emission characteristics enabled by strong electron-phonon coupling and the formation of self-trapped excitons (STEs). Despite these advantages, the fundamental photophysics and structural dynamics governing their excited-state behavior remain poorly understood. Here, we report a long-lived metastable phase in the Cs₂AgInCl₆ double perovskite family and unravel this process and the concomitant electronic and structural evolution using a suite of tools including transient optical spectroscopy, time-resolved x-ray diffraction (TR-XRD), time-resolved x-ray absorption spectroscopy (TR-XAS), and inelastic x-ray scattering (IXS). We show that the photoinduced, transient metastable phase is associated with B-site [silver (Ag)–indium (In)] disorder, which induces a markedly reduced optical bandgap. Supported by TR-XRD and first-principles calculations, the Ag-In disorder drives the formation of Ag-rich and In-rich domains with millisecond lifetimes, with lifetimes increasing at lower temperatures. TR-XAS further reveals that the photogenerated STEs oxidize Ag⁺ to Ag²⁺, which facilitates this highly temporally asymmetric order-disorder transition. Our findings demonstrate a previously unidentified mechanism, mediated by hole-localized STE formation, that enables prolongation of transient light-induced states to the multimillisecond regime in halide double perovskites, opening possibilities to harvesting the functional properties of metastable phases of these material systems.

A long-lived metastable state is observed in a metal halide double perovskite.

INTRODUCTION

Metal halide perovskites have attracted intense research interest over the past decade due to their outstanding optoelectronic properties, including tunable direct bandgaps, high optical absorption coefficients, long carrier lifetimes, and solution processability (1–4). These features enabled wide-ranging applications in photovoltaics (5, 6), light-emitting diodes (7, 8), and photodetectors (9, 10), to name a few. Lead-based perovskites exemplified by (MA/FA)PbI₃ and (MA/FA)PbBr₃ have led to record-holding power conversion efficiencies in perovskite solar cells and high external quantum efficiencies in perovskite light-emitting devices (11–13). Despite these successes, concerns about lead toxicity and long-term material instability under environmental stressors have motivated efforts to develop lead-free alternatives (14, 15). One promising class of materials is lead-free double perovskites, which adopt the A₂B⁺B³⁺X₆ structure by substituting pairs of Pb²⁺ ions with monovalent and trivalent cations (16–18). This heterovalent substitution not only retains the desirable three-dimensional (3D) perovskite framework but also enables a diverse selection of elements for tailored electronic and optical properties (19, 20). Among various double perovskites, Cs₂AgBiBr₆ attracted attention in the fields of solar cells and photodetectors, whereas Cs₂AgInCl₆ and its Na-doped analog Cs₂(Na/Ag)InCl₆ have recently gained increasing interest in light-emitting applications (21, 22).

RESULTS

Photoluminescence response with microsecond lifetimes

Similar to lead-based perovskites, double perovskites also exhibit the characteristic softness of their lattices (23, 24). As a prototypical double perovskite, Cs₂AgInCl₆ exhibits exceptionally strong electron-phonon coupling, where photoexcited carriers rapidly induce a characteristic Jahn-Teller distortion of the [AgCl₆] octahedra and the formation of self-trapped excitons (STEs) within a few hundred femtoseconds (Fig. 1A) (25, 26). This strong coupling leads to a broad, strongly Stokes-shifted photoluminescence (PL) emission spectrum spanning the entire visible range (400 to 800 nm; Fig. 1B) with microsecond PL lifetimes (Fig. 1C) (21). STE-dominated carrier dynamics can be effectively described using a configurational coordinate diagram (Fig. 1D), where STEs are intrinsic, transient structural distortions associated with the excited state of trapped charge carriers stabilized in the soft lattice. Previously, time-resolved PL and picosecond-to-nanosecond transient absorption (ps-ns TA) spectroscopy have been used to investigate the excited-state dynamics of STEs. The broadband PL and sub-bandgap photoinduced absorption (PIA) are considered characteristic signatures of STEs (27–29).

Fig. 1. Illustration of STE-related dynamics and B-site cation disorder.

(A) Crystal structure of Cs₂AgInCl₆ (CAIC) and a schematic illustration of the Jahn-Teller distortion of Ag-centered octahedra formed upon photoexcitation. (B) PL spectrum of Na-doped Cs₂AgInCl₆ (CNAIC) measured at room temperature. a.u., arbitrary units. (C) Time-resolved and wavelength-resolved PL of CNAIC measured at room temperature. (D) Configurational coordinate diagram showing the electronic processes after pulsed photoexcitation. FC, free carrier; FE, free exciton; STE, self-trapped exciton; GS, ground state; PL, photoluminescence; PIA, photoinduced absorption. (E) Schematic illustration of the B-site cation disorder in double perovskites. (F) Bandgap reduction associated with B-site disorder. CB, conduction band; VB, valence band.

On the other hand, bandgap reduction induced by B-site cation disorder, as illustrated in Fig. 1 (E and F), has been observed in double perovskites such as Cs₂AgBiBr₆ and was typically thermally activated. The spectroscopic dynamics of STEs and B-site cation disorder have generally been regarded as independent processes as the photothermal effect associated with optical excitation is insufficient to induce substantial thermal disorder. In this work, we observe that, owing to the strong electron-phonon coupling and soft lattice characteristics of double perovskites, B-site cation disorder in the Cs₂AgInCl₆ family can be triggered by photoexcitation or, more specifically, by photogenerated carriers.

Both STEs and photoinduced B-site disorder, if present, manifest spectroscopically as broadband sub-bandgap PIA. To distinguish between these contributions, we first compared the PIA dynamics with the intrinsic STE dynamics over an extended delay time window. This analysis reveals an additional, previously unreported process with a millisecond-scale recovery time that is distinct from STEs. By combining time-resolved x-ray diffraction (TR-XRD), we demonstrate that this long-lived PIA originates from disorder induced by Ag-In octahedral translocation. Unlike thermally induced disorder, the photoinduced disorder exhibits strongly asymmetric temporal behavior: It forms on a subnanosecond timescale but recovers over milliseconds. Furthermore, time-resolved x-ray absorption spectroscopy (TR-XAS) confirms that Ag⁺ is transiently oxidized to Ag²⁺ during photoexcitation. We propose that this STE-associated valence change is the key factor underlying the observed temporal asymmetry. The photoinduced cation swapping, which is expected to show even longer lifetimes at liquid helium temperatures, marks an alternative mechanism to the stabilization of metastable phases for the exploitation of their functional properties (30–33).

Photoinduced broadband absorption with extended lifetimes

Compared with ABX₃-type perovskites, the A₂B⁺B³⁺X₆-type double perovskites exhibit higher compositional complexity (22, 34). In the Cs₂AgInCl₆-based system, both Ag⁺ and its substitutional Na⁺ dopant occupy the B⁺ site, whereas In³⁺ with a trace amount of Bi³⁺ dopants take the B³⁺ sites. A previous study showed that Na⁺ primarily modifies the band structure and the spatial distribution of electronic wave functions, altering charge-carrier and STE properties including the bandgap and exciton binding energy (21). In contrast, trace Bi³⁺ passivates defects and enhances the emission efficiency of STEs (21). In this work, we primarily investigate the properties of both pristine double perovskite Cs₂AgInCl₆ (abbreviated as CAIC; photoluminescence quantum yield or PLQY < 1%) and the highly emissive Cs₂Ag_0.6Na_0.4InCl₆ with 0.5% Bi doping (abbreviated as CNAIC; PLQY ∼ 90%). Their static optical and structural properties are summarized in Supplementary Note 1.

We first examined the charge carrier dynamics in the more emissive CNAIC with in-house transient optical spectroscopy. As presented in Fig. 1C, time-resolved and wavelength-resolved PL measurement reveals that the broadband PL emission associated with STEs decays over several microseconds. The PL lifetime exhibits negligible wavelength dependence (Fig. 2A), indicating that the broad PL emission arises from a single STE species rather than multiple emissive STE states (35). Temperature-dependent PL data shown in Fig. 2B reveal modestly enhanced PL lifetimes achieved at lower temperatures, although still in the microsecond range. This behavior is expected as the high PLQY of CNAIC suggests that radiative recombination is the dominant carrier relaxation pathway, whereas temperature, which primarily influences nonradiative channels, does not strongly influence the radiative rates and hence the PL lifetimes.

Fig. 2. Kinetics discrepancy between PL and TA responses.

(A) Wavelength-dependent PL kinetics of CNAIC at room temperature. (B) Temperature-dependent PL kinetics of CNAIC. (C) Transient $\mathrm{\Delta }T/T$ spectral map of CNAIC at room temperature in the delay time window of 0∼40 μs. (D) Transient $\mathrm{\Delta }T/T$ spectra of CNAIC at room temperature at selected delay times in the window of 0∼1400 μs. The neighboring curves are offset by 0.2 for clarity. (E and F) $\mathrm{\Delta }T/T$ kinetics of CNAIC in (E) and CAIC in (F), respectively, both at 295 and 78 K, spectrally integrated from 500 to 600 nm. In this figure, $T$ and $\mathrm{\Delta }T$ refer to optical transmittance rather than temperature.

Following time-resolved PL measurements, we then probed the carrier dynamics using TA spectroscopy measured in transmittance configuration. Generally, in light-emitting materials with large Stokes shifts, a transient enhanced transmission within the PL spectral regime is expected typically due to stimulated emission (36). However, previous studies on metal halide perovskite–based STE emitters have reported broadband PIA in the visible range upon photoexcitation (21, 25). The broad PIA was attributed to excited-state transitions of STEs to higher-lying energy levels in the conduction band. Nevertheless, those previous studies explored time windows up to a few nanoseconds using mechanical delay lines, leaving the microsecond-long decay dynamics of STE-related absorption unexplored. By extending the TA measurement window to several tens of microseconds using an electronically delayed probe, which, in principle, is sufficient to capture the complete recombination dynamics of STEs in correlation with time-resolved PL data, we found, unexpectedly, that the broadband PIA persists far longer than the STE PL lifetime.

As shown in Fig. 2C, microsecond transient absorption (μs-TA) spectroscopy data show a strong residual PIA signal persisting beyond 35 μs. In addition to the long-lived PIA, a nonzero signal is also observed before time zero (fig. S4), indicating that the PIA decay exceeds the pump pulse interval of 1 ms. To capture the full decay of this long-lived PIA component, we reduced the pump repetition rate from 1 kHz to 100 Hz and focused on delay times beyond the complete decay of STEs (i.e., several microseconds after the pump excitation). As revealed in Fig. 2D, the non-STE–related broadband PIA decays within several hundred microseconds, and its broadband spectral shape remains nearly unchanged throughout the decay process (fig. S5). The extended long-lived PIA indicates the presence of a previously unidentified state of matter—distinct from STEs—that may be activated upon photoexcitation. In addition, the invariance of the PIA spectral profile with delay time (fig. S5) implies that it is governed by a single, well-defined mechanism. Another notable observation is the clear spectral distinction between PL and PIA: The PL exhibits a Gaussian-like peak centered at ∼550 nm, whereas the PIA displays a relatively flat, broadband absorption profile. This difference further suggests that the PIA does not originate solely from photoexcited carriers. In general, if the TA response is purely carrier induced, a spectral correlation between the TA and PL signals would be expected.

Figure 2E presents the normalized, wavelength-integrated transient $∆T/T$ of CNAIC at room temperature and 78 K, revealing an elongated lifetime at lower temperature. Similar measurements performed on undoped CAIC likewise exhibit longer-lived PIA signals (Fig. 2F). Notably, the PIA in CAIC shows a stronger temperature dependence than that in CNAIC. As detailed in Supplementary Note 2, we further investigated the influence of compositional engineering on the PIA in CAIC-based double perovskites and found that the PIA is an intrinsic characteristic of the Cs₂AgInCl₆ family, irrespective of Na⁺ and/or Bi³⁺ incorporation, which only moderately modulates the PIA decay dynamics while having negligible impact on the spectral shape of the PIA. According to the Arrhenius relation, a weaker temperature dependence generally indicates a smaller energy barrier associated with the lattice reconfiguration process (Supplementary Note 2). This suggests that Na doping lowers the energy barrier for the recovery process.

Combining the PL and TA results, meanwhile considering the large difference in the STE emission efficiency of CAIC and CNAIC (∼90% in the latter), we hypothesize that the long-lived PIA originates from a mechanism distinct from the excited STE state. In general, when band structure modifications induced by electronic excitation can be excluded, a plausible origin of a long-lived TA signal is a photothermal effect (37–39). However, because both CNAIC and CAIC have bandgaps in the ultraviolet (UV) region (fig. S2) (21), the temperature-induced bandgap shift—i.e., changes in the imaginary part of the complex refractive index—should not result in substantial broadband absorption in the visible range. The potential contribution of the real component of the refractive index, which might alter the transmittance through changes in interfacial reflectance, was thoroughly examined and excluded in Supplementary Note 3.

We note that STEs and B-site cation disorder are not the only mechanisms that may give rise to bandgap reduction and PIA (24, 40). Other long-lived excited states, such as dark excitons or defect-trapped carriers, may also contribute to broadband PIA. Therefore, spectroscopic measurements alone cannot unambiguously identify B-site cation disorder as the underlying origin. The most direct approach is to probe the lattice dynamics associated with the long-lived PIA. It should be noted that, unlike spectroscopic probes, structural probes such as XRD simultaneously capture contributions from both the ground-state and photoexcited lattices. Therefore, a sufficiently high excited-state population is required to generate a measurable signal. Given that the intrinsic excitonic absorption of CAIC is substantially weaker than that of CNAIC, all subsequent TR-XRD measurements in this work were performed on CNAIC. However, this does not affect the validity of using the proposed Ag-In swapping model (vide infra) for our analysis as we have demonstrated that the observed PIA is an intrinsic property of the Ag-In double perovskite system regardless of doping.

The lattice dynamics correlated to STEs

Both the formation of STEs and the hypothesized metastable phase involve substantial lattice reorganization. Going beyond optical spectroscopic measurements of photoexcited charge-carrier dynamics, we performed TR-XRD at the Advanced Photon Source (APS) to directly probe transient lattice dynamics of CNAIC with x-ray pulses following pulsed photoexcitation at 360 nm (Fig. 3A; see Materials and Methods). The (222) plane, as the natural habit plane for solution-grown, multimillimeter-sized CNAIC and CAIC single crystals, can be readily accessed in a standard θ-2θ geometry in the TR-XRD experiments. The x-ray detector was electronically gated to selectively capture x-ray pulses synchronized with the pump laser pulses at the same repetition rate. The pump-probe delay time was continuously varied with a delay generator, and the time resolution of ∼150 ps was determined by the x-ray pulse width. Given the crystal orientation, the scans correspond naturally to rocking curves of the (222) plane. Rocking curves of other diffraction peaks were measured by varying the azimuthal orientation of the sample, as described in Supplementary Note 5.

Fig. 3. TR-XRD response during the first several microsecond delay time window (1-kHz laser pump rate).

(A) Schematic of the TR-XRD experiments. The incident x-ray beam is aligned horizontally, whereas the laser is directed vertically from above. The sample rotation axis is orthogonal to both the laser and the incident x-ray beam. (B) XRD beam profiles of the (222), (220), and (400) planes of CNAIC measured under laser-off conditions. The x and y directions here correspond to the x and y directions shown in (A). (C) Temporal evolution of the integrated diffraction intensity after photoexcitation, showing an instantaneous rise followed by microsecond-scale decay characteristics consistent with STE relaxation. (D) Temporal evolution of the peak center-of-mass positions after photoexcitation, showing lattice expansion induced by STEs. (E) (222) diffraction profiles collected on the x-ray detector under laser-on conditions at −3-ns, 6-ns, and 4500-ns delay times. A secondary peak appears on the high-Q side under illumination highlighted with red arrows, signifying a contracted, photoinduced metastable phase. (F) (220) diffraction profiles collected on the x-ray detector under laser-on conditions at −3-ns, 6-ns, and 4500-ns delay times. The photoinduced phase segregation is highlighted by the red dashed lines. All the images in this figure are plotted on a linear scale.

Figure 3B shows the XRD beam profiles corresponding to the (222), (220), and (400) planes under laser-off conditions. Despite the compositional complexity of CNAIC, the crystal quality is high as each diffraction spot is extremely sharp—nearly limited to a single detector pixel in width. The elongated shape of the spots arises from the geometry of the x-ray source at the beamline. Figure S13 shows the rocking curves of the three peaks of CNAIC measured under laser-off conditions. All three peaks exhibit narrow full widths at half maximum of only ∼0.01 Å⁻¹, supporting the exceptional crystalline quality of CNAIC. Inelastic x-ray scattering (IXS) data (figs. S9 to S11 and Supplementary Note 4) reveal almost identical acoustic phonon branches between CNAIC and CAIC, suggesting excellent long-wavelength structural uniformity in the doped system, consistent with the sharp XRD peak.

We first used a 1-kHz laser repetition rate to probe the lattice dynamics within several microsecond delay time windows after photoexcitation. On the basis of the TA data, under these conditions, the metastable phase could not fully decay before the arrival of the next laser pulse; however, within the microsecond timescale of interest, the millisecond-long decay component can be considered as a constant, pump-induced background. Figure 3C presents the temporal evolution of the total integrated intensity of the (222), (220), and (400) diffraction peaks following the 360-nm pump excitation. All three diffraction peaks exhibit an instantaneous increase in intensity after photoexcitation, followed by a gradual decay. Single-exponential fitting of the decay dynamics yields time constants on the order of several microseconds, comparable to the STE lifetime. These data indicate that STE formation enhances the total XRD intensity, a phenomenon previously reported for photoexcited perovskites (41).

Focusing on the early-time response (fig. S16) and comparing the diffraction intensity at 3 ns before laser excitation with that under dark conditions reveals a slightly weaker signal at −3 ns, suggesting that the presence of the metastable phase—after the STE and photothermal contributions have largely vanished—reduces the overall diffraction intensity. Figure 3D presents the temporal evolution of the diffraction peak center-of-mass positions following photoexcitation. A transient decrease in Q is observed immediately after photoexcitation, indicating a prompt lattice expansion, followed by a gradual recovery. The recovery dynamics are well described by a single-exponential decay similar to their intensity decay, demonstrating that STE formation induces a transient lattice expansion.

To further elucidate the signature of the metastable phase in the TR-XRD data, we closely examined the diffraction profiles on the detector, as displayed in Fig. 3E and fig. S17, using linear and logarithmic color scales, respectively. The measurements correspond to −3 ns (when STEs generated by the previous laser pulse have fully decayed, leaving only the residual metastable phase), 6 ns (when both STEs and metastable phases coexist before their decay), 4500 ns (when most STEs have decayed while the metastable phase remains largely intact), and under laser-off conditions (where neither STEs nor metastable phases are present). Under dark conditions, the (222) peak appears as a single-pixel-width narrow line, whereas under illumination, a weaker secondary diffraction spot consistently emerges on the right side of the main spot. As discussed in Supplementary Notes S6 and S7, the peak on the right side corresponds to a larger Q value, corresponding to a smaller lattice constant. Notably, this additional peak persists even at a negative delay time of −3 ns. Given the laser repetition rate of 1 kHz, this observation reconfirms that the structural response induced by the previous laser pulse persists for over 1 ms before fully relaxing, consistent with the long-lived PIA shown in Fig. 2. The emergence of this distinct, photoinduced peak thus provides further evidence for the existence of a photoinduced metastable phase.

Moreover, the diffraction peak corresponding to the metastable phase exhibits nearly identical shape and position on the detector as that of the original double perovskite, suggesting that it retains the same space group (Fm$\overline{3}$m) and differs only in lattice constant. Specifically, the photoinduced peak is displaced by ∼4 pixels along the x direction from the main peak. On the basis of the linear correlation between the detector x-pixel position and the scattering vector Q established in fig. S15, it corresponds to a Q shift of 0.0045 Å⁻¹, and the lattice constant of the metastable phase is estimated to be 10.477 Å, slightly smaller than that of the parent double perovskite (10.500 Å) by 0.023 Å.

Figure 3F shows the diffraction peak profile of the (220) reflection at the same pump-probe delays as in Fig. 3E. A similar peak splitting caused by phase segregation is observed, exhibiting consistent temporal characteristics. The diffraction spot of the (400) peak likewise exhibits photoinduced distortion (fig. S18), although the segregation is less pronounced compared to the (222) and (220) reflections. Therefore, this metastable phase accompanied by the long-lived PIA can be identified as a photoinduced phase segregation in double perovskites. In addition, by comparing the diffraction spot profiles under dark conditions at different temperatures (fig. S19), we demonstrate that temperature has a negligible effect on the XRD profile.

The lattice dynamics correlated to the B-site disordering

Our TA and TR-XRD results both indicate that the relaxation of the photoinduced phase recovers over hundreds of microseconds to single-digit milliseconds, exceeding the continuously variable pump-probe delay range of the APS beamline. To capture the slower dynamics, we reduced the pump laser repetition rate to 167 Hz to ensure complete relaxation of the metastable phase between adjacent pump pulses. Furthermore, by adjusting the x-ray detector gating pulse (note that x-ray probe pulses are thousands of times higher in repetition rate than the optical pump), we achieved extended, but discrete, pump-probe time delays.

Figure 4A shows the (222) diffraction peak profiles under laser-on and laser-off conditions at a delay time of 147 μs. At this delay time, when STEs are fully relaxed, the metastable phase leads to a reduction in intensity at the peak center and an increase on the shoulders. Figure 4B displays the temporal evolution of Bragg peak intensity on the high-Q side, highlighting the contrasts between laser-on and laser-off conditions. Upon photoexcitation, a pronounced intensity enhancement appears in this region, which gradually decays over several hundred microseconds. This decay characteristic is consistent with the PIA observed in TA experiments.

Fig. 4. TR-XRD response in the millisecond time range.

(A) Rocking curve of the (222) plane without pulsed laser excitation (blue) and with pulsed laser excitation captured at a delay time of 147 μs (red). (B) Temporal evolution of the Bragg peak intensity upon laser excitation, integrated from 2.076 to 2.08 Å⁻¹. (C) Temporal evolution of the diffraction images on the x-ray detector, which is obtained by integrating diffraction spots within the Q range of 2.060 to 2.065 Å⁻¹. (D) x-directional diffraction intensity profile with (top)/without (bottom) laser excitation, obtained by integrating the 2D diffraction pattern along the y axis. (E) Time evolution of the SD (σ) along the x direction, extracted from Gaussian fits to the diffraction intensity profiles.

We further compared the diffraction spot profiles at various delay times. As shown in the first panel of Fig. 4C, the diffraction spot before time-zero appeared symmetric, confirming that the metastable phase fully decays before the arrival of the next laser pulse. Note that the spot shape is more circular, owing to improved beam coherence and change in focusing optics after the APS upgrade. Nevertheless, after time zero, an intensity enhancement appears on the right side of the main spot, corresponding to the formation of the metastable phase as seen in Fig. 3 (E and F).

Because the x coordinate of the detector correlates with Q for the (222) reflection whereas the y coordinate does not convey information about lattice constant, we integrated the raw 2D diffraction data along the y direction to obtain the intensity distribution along the 2θ direction (Fig. 4D). Compared with the laser-off condition, the laser-on curve exhibits a clear intensity enhancement on the right side associated with the metastable phase. Figure 4E shows the temporal evolution of the standard deviation (SD) of the diffraction-spot distribution along the 2θ direction under laser-on and laser-off conditions. The SD increases upon photoexcitation and gradually decays over several hundred microseconds, whereas it exhibits only random fluctuations in the laser-off state. It should be noted that the diffraction signals of the original and metastable phases overlap substantially, rendering peak deconvolution and extraction of independent dynamics of the metastable phase experimentally less practical.

The role of STEs in the metastable phase formation and recovery

By combining TA and TR-XRD measurements, we confirmed the existence of a photoinduced metastable phase segregation in CAIC and CNAIC, evidenced by the optical PIA signal and the XRD peak splitting. In perovskite materials, ionic substitution typically occurs between isovalent ions (42–44). For instance, in MAPbI_xBr_1–x (x = 0∼1), phase segregation under illumination leads to the formation of I-rich and Br-rich regions (45, 46). Considering the structure of Cs₂B⁺B³⁺Cl₆, the exchange between B⁺ and B³⁺ cations is a plausible process responsible for the observed phase segregation, as detailed below.

We illustrate the photodynamic cation swapping mechanism in Fig. 5A. The swapping process induces phase segregation, which underpins the metastable phase in CAIC and its derivative CNAIC. In the ground state, the Ag-centered and In-centered octahedra are ordered. Upon photoexcitation, electron-hole pairs are generated, and within several hundred femtoseconds, the hole oxidizes Ag⁺ into Ag²⁺. Accompanying this, the originally symmetric octahedron undergoes a Jahn-Teller distortion and, through strong electron-phonon coupling, forms an STE. Immediately afterward (within subnanoseconds), Ag²⁺ undergoes a site exchange with a neighboring In³⁺. This cationic swapping results in the formation of locally Ag-enriched and In-enriched domains, with the Ag domains exhibiting a substantially reduced bandgap. Together with the STEs, the aggregated domains contribute to the observed broadband PIA. Following this, the STEs recombine over a few microseconds, emitting broadband PL, whereas Ag²⁺ is reduced back to Ag⁺. The size-mismatched Ag⁺ and In³⁺ then gradually return to their original, ordered lattice positions over several milliseconds, driven by thermal fluctuations with a large energy barrier, completing the full photodynamic cycle.

Fig. 5. Schematic depiction of the photodriven lattice dynamics and TR-XAS results.

(A) Schematic drawing of the photoinduced structural rearrangements in CAIC, ranging from the subpicosecond to the millisecond timescales. (B) XAS captured at the Ag K-edge in the ground-state (dark) condition. (C) Differential XAS spectra due to photoexcitation (the pump-probe delay time is 150 ps). The cyan curve shows the measured spectrum from TR-XAS experiments; the orange curve shows the differential XAS spectrum obtained by manually shifting the dark spectrum in (B) by 35 meV.

As discussed in Supplementary Note S8, density functional theory (DFT) calculations were performed to determine the lattice constants of In-rich and Ag-rich domains. Compared with the Ag-In ordered double perovskite structure, the In-rich domain exhibits a smaller lattice constant, whereas the Ag-rich domain shows a larger one. This indicates that the photoinduced diffraction peak observed in TR-XRD corresponds to the In-rich domain, despite that Ag-rich and In-rich domains coexist. This is rationalized by the fact that the measured CNAIC sample contains both Ag⁺ and Na⁺ cations at the B⁺ sites; under the condition of B⁺-rich and B³⁺-rich domains, the multicomponent (Ag-Na) B⁺-composition reduces the crystallinity and thus the XRD intensity of the B⁺-rich domains but not the B³⁺-rich domains. Therefore, only the diffraction from the compositionally purer In-rich domain was experimentally observed. It should be noted that, due to limitations in the excitation wavelength (360 nm, where CAIC has a weak absorption), TR-XRD measurements on CAIC could not be performed to directly observe the Ag-rich domain signal. In future work, pulsed electron-beam excitation may provide a viable approach to overcome this limitation and yield more direct experimental evidence. Furthermore, as shown in Supplementary Note S9, a single Ag-In exchange in a 2 by 2 by 2 CAIC supercell is sufficient to reduce the bandgap by at least 1.19 eV, which is consistent with the broadband PIA feature across the entire visible range observed in TA spectroscopy (Fig. 2).

The process exhibits an asymmetric temporal behavior: It forms within a subnanosecond timescale but decays on the millisecond timescale. In contrast, photoinduced phase transitions in lead halide perovskites—whether driven by photothermal effects or photogenerated charge carriers—do not show such an asymmetric response (47). Instead, the forward and recovery phase-change processes in both 3D and 2D metal halide perovskites occur within tens to hundreds of nanoseconds (47, 48). We attribute this pronounced temporal asymmetry observed here to the unique nature of STEs. Specifically, in CAIC and CNAIC, the electron and hole wave functions of the STEs are asymmetric: The hole is highly localized on Ag⁺, whereas the electron is delocalized over several unit cells (21). Therefore, the locally STE-associated Ag⁺ is oxidized into Ag²⁺. This oxidation process is critical as cation swapping processes are more favorable between ions with more similar valence states; the smaller charge difference between Ag²⁺ and In³⁺ lowers the energy barrier for cation exchange, when compared with Ag⁺-In³⁺ swapping. In addition, Ag⁺ (1.15 Å) has a larger ionic radius than In³⁺ (0.8 Å); upon oxidation to Ag²⁺, its radius decreases, reducing the energy barrier for swapping. After STEs recombine, Ag²⁺ reverts back to Ag⁺, and the large charge and ionic radius differences between Ag⁺ and In³⁺ increase the energy barrier for relaxation of the metastable phase, giving rise to the asymmetric relaxation behavior.

The influence of ionic radii difference on energy barrier provides a compelling explanation for the contrasting B⁺-B³⁺ cation exchange behaviors observed in Cs₂AgBiBr₆ and CAIC. In Cs₂AgBiBr₆, diffuse scattering signals have been observed in single crystals, which is a hallmark of short-range B-site arrangement induced by Ag⁺-Bi³⁺ exchange, in line with its thermochromic behavior (49, 50). In contrast, CAIC does not exhibit thermochromic behavior (fig. S8), and our high dynamic-range reciprocal space mapping of CAIC and CNAIC, across a range of temperatures, reveals a consistently high degree of crystallographic order, with no evidence of diffuse scattering (figs. S24 and S25). This discrepancy between Cs₂AgBiBr₆ and CAIC can be partly explained by the different ionic radii of Ag⁺ (1.15 Å), Bi³⁺ (1.03 Å), and In³⁺ (0.8 Å): Ag⁺ is 43.7% larger than In³⁺ but only 11.6% larger than Bi³⁺. The larger mismatch between Ag⁺ and In³⁺ radii leads to a higher energy barrier for their exchange, thereby suppressing thermal disorder in CAIC.

The photodriven redox process involving Ag⁺ is central to the complete photodynamic pathway described above. However, Ag²⁺ is an unstable, rare oxidation state. Thus far, the oxidation of Ag⁺ by STEs has been proposed only through theoretical calculations and lacks direct experimental evidence (21). To experimentally verify the STE-induced oxidation of Ag⁺, we directly probe the electronic structure of Ag cation in CNAIC nanocrystals with TR-XAS. The TR-XAS measurements were performed under 355-nm, pulsed laser excitation (∼10-ps pulse width) and ∼150-ps x-ray pulses as the probe at the APS. Figure 5B displays the Ag K-edge x-ray absorption near-edge structure (XANES) spectrum of CNAIC acquired without laser excitation. This spectrum features a prominent white-line transition at 25.5232 keV, attributed to the dipole-allowed 1s→5p transition (51). With a 150-ps time delay after the 355-nm laser excitation, the XANES spectrum shows a clear difference signal: A negative feature observed at 25.5205 keV indicates a shift of the absorption edge toward higher energy, as shown in Fig. 5C. By manually shifting the absorption spectrum and calculating the difference, we further determined this blue shift to be ∼35 meV. Thermal effects on XAS are generally minimal and tend to cause red shifts (toward lower energies), instead of blue shifts (52). Therefore, this observed blue shift provides direct experimental evidence that STEs induce the oxidation of Ag⁺ into Ag²⁺.

DISCUSSION

By combining optical spectroscopy and synchrotron XRD and XAS experiments, we reveal that in addition to STEs, the highly emissive double perovskites CAIC and CNAIC exhibit a photoinduced, metastable B-site cationic reorganization. This process leads to phase segregation into Ag-rich and In-rich domains, leading to a notably reduced electronic bandgap of the material. This metastable phase persists for several to tens of milliseconds, far exceeding the STE lifetimes, highlighting a distinct, long-lived contribution to these materials’ photodynamics. The B-site disorder mechanism unveiled from this study may be more broadly applicable across double perovskites, where similar lattice-driven bandgap narrowing could explain the widely observed thermochromic effects (53–55). We propose that photochromic behavior driven by B-site cation disorder is likely to occur in systems that satisfy two key conditions: (i) the presence of a Jahn-Teller active or distortion-prone octahedron (e.g., [AgX₆] or [CuX₆]) and (ii) a substantial ionic radii mismatch between the two B-site cations, such that cation exchange is not thermally activated but can be selectively triggered under photoexcitation. On the basis of these considerations, compositions such as Cs₂AgSbCl₆ may exhibit similar photoinduced lattice dynamics. The presence of such photoinduced cation disorder can be identified through a combination of spectroscopic and structural signatures. These include (i) the emergence of broadband sub-bandgap PIA distinct from STE-related features, (ii) long-lived metastable dynamics extending well beyond excitonic lifetimes, and (iii) the absence of corresponding thermally driven phase transitions in steady-state temperature-dependent measurements.

Moreover, the metastable nature of the segregated phase allows it to accumulate under continuous excitation, particularly approaching liquid helium temperatures and potentially accounting for anomalous optical phenomena such as high-order Raman scattering (56). Although this bandgap reduction can hinder these materials for obtaining optical gain and stimulated emission, it offers a potential advantage for photodetection. We point out that sustained excitation with sub-bandgap light can enhance photoresponse through increased carrier generation. This concept has already been successfully applied in detecting weak infrared signals, suggesting an alternative strategy for optimizing lead-free perovskite photodetectors (57, 58).

MATERIALS AND METHODS

Single crystal growth

Cesium chloride (CsCl; 99.99%), silver chloride (AgCl; 99%), sodium chloride (NaCl; 99.99%), anhydrous indium chloride (InCl₃; 99.99%), and anhydrous bismuth chloride (BiCl₃; 99.99%) were purchased from Alfa Aesar without further purification. Anhydrous InCl₃ (1 mmol), anhydrous BiCl₃ (0.005 mmol), and CsCl (2 mmol) were first dissolved in 10 ml of a 10 M HCl solution in a 25-ml Teflon autoclave. Then, 0.6 mmol of AgCl and 0.4 mmol of NaCl were added and the solution was heated at 180°C for 12 hours in a stainless steel Parr autoclave for CNAIC (1 mmol of AgCl was used for CAIC without any NaCl). The solution was then steadily cooled to 50°C at a speed of 1°C·hour⁻¹. The as-prepared crystals were then filtered out, washed with isopropanol, and dried in a furnace at 60°C.

Nanocrystal synthesis

Bismuth acetate (99.99%), silver acetate (99.99%), indium acetate (99.99%), cesium carbonate (99.9%), sodium acetate (99.0%), dioctyl ether (99%), oleylamine (70%), oleic acid (90%), and benzoyl chloride (99.0%) were obtained from Sigma-Aldrich. Chemicals were used as received. Silver acetate was stored under foil. Synthesis of Bi-doped Cs₂Ag_1−xNa_xInCl₆ nanocrystals followed literature procedures (59) with a scale-up by a factor of 4. The value of x in the formula was 0.4 (i.e., 40% Na). Briefly, 1 mmol of cesium carbonate, 1 mmol of indium acetate, 0.6 mmol of silver acetate, 0.4 mmol of sodium acetate, and 0.005 mmol of bismuth acetate were added to a three-neck flask held under an air atmosphere with 16 ml of dioctyl ether, 2.4 ml of oleylamine, and 4.8 ml of oleic acid, stirring vigorously. The reaction was heated to 115°C, held for 5 min, and then heated to 145°C. Separately, dioctyl ether was degassed by sparging with nitrogen. Once the reaction reached 145°C, an injection solution of 0.8 ml of benzoyl chloride and 2.4 ml of degassed dioctyl ether was rapidly injected. The reaction vessel was immediately cooled with an ice bath, and the reaction contents were centrifuged at 4500 rpm for 5 min, discarding the supernatant. The remaining pellet was redispersed in hexane and precipitated with ethyl acetate (1:2, v/v) and centrifuged again for 5 min at 6000 rpm. The solid pellet was redispersed in hexanes for further studies. Transmission electron microscopy (TEM) imaging was performed using a JEOL 2100F TEM operated at 200 keV.

Ultrafast ps-ns pump-probe TA spectroscopy

Femtosecond pump pulses were generated using an optical parametric amplifier (OPA; Orpheus-F), driven by a Pharos femtosecond laser amplifier operating at a 2-kHz repetition rate. The amplifier produced 1030-nm fundamental pulses with a 170-fs pulse width, of which 0.5 mJ per pulse was used to power the OPA. The OPA outputs 740-nm pulses, which were frequency doubled using a Beta-Barium Borate (BBO) crystal to produce 370-nm pump pulses. The pump beam was focused on the sample using a 250-mm focal length CaF₂ lens, producing a ∼1-mm-diameter spot. Supercontinuum probe pulses were generated by focusing a small portion of the 1030-nm output onto a 4-mm-thick sapphire window and delayed using a retroreflector. The pump and probe pulses operated at 1 and 2 kHz, respectively. Probe spectra were acquired at 2 kHz using a USB spectrometer (Avantes).

Longer delay time pump-probe TA spectroscopy

The pump pulses were identical to that used in ultrafast pump-probe spectroscopy. For delay times up to 50 μs, the pump and probe lasers were operated at 1 and 2 kHz, respectively; the probe laser (Leukos Disco-UV) was electrically triggered by a digital delay generator (Stanford Research, DG645). For delay time windows up to several milliseconds, the pump repetition rate was further reduced to 100 Hz using a 10% duty cycle optical chopper (Thorlabs MC2000B), enabling full recovery of the sample between adjacent pump pulses. The probe was operated at 200 Hz. Pump-probe delay was achieved using a digital delay generator. The samples were mounted in a liquid nitrogen cryostat (Lake Shore VPF-100) with a vacuum level better than 1 × 10⁻⁴ torr.

Time-resolved PL

The PL excitation pulses were identical to the pump pulses used in the pump-probe spectroscopy experiments. The samples were mounted in a closed-cycle liquid helium cryostat (ARS) with a vacuum level higher than 1 × 10⁻⁵ torr. The PL photons were steered into a spectrograph, which is equipped with an electron-multiplying charge-coupled device (EMCCD) camera for time-integrated spectral acquisition, and a streak camera (Hamamatsu) for time-resolved and wavelength-resolved measurements.

Time-resolved x-ray diffraction

TR-XRD measurements were performed at the Beamline 7-ID-C of the APS at Argonne National Laboratory (ANL). A Ti:sapphire laser amplifier’s output (Legend, Coherent Inc., with a 1-kHz repetition rate, a 70-fs pulse width, and 1.8 mJ at 800 nm) was fed into an OPA system (Opera Solo, Coherent Inc). The fourth harmonic of the OPA signal output (360 nm, 1 kHz, and 70 fs) was then routed to the sample surface. The sample was positioned at the center of rotation of a six-circle Huber diffractometer. Pump pulses at a 360-nm wavelength impinged onto the sample surface close to normal incidence. The size of the elliptical laser spot was 220 μm by 200 μm in diameters. Hybrid pixel photon-counting area detectors (Eiger2 500k and Pilatus 100k, Dectris Inc.) were used to collect the XRD signals from the sample. The area detector was electronically gated to single x-ray pulses matching the repetition rate of the laser pulses. Experiments took place during the 24-bunch mode operation of the APS with monochromatic x-ray energy at 10 keV and pulse width of ∼80 ps in full width at half maximum before the upgrade and ∼150 ps after the upgrade. The time delay between the laser pump and x-ray probe pulses was continuously varied by digital delay generator (DG 645, Stanford Research Systems) for data in Fig. 3 and varied in steps by moving the gating time of the x-ray detector for data in Fig. 4.

Time-resolved x-ray absorption spectroscopy

The Ag K-edge TR-XAS spectra of 1.0 mM Cs₂Ag_0.6Na_0.4InCl₆ nanocrystals dissolved in hexane were collected at the beamline 25-ID-E of the APS at ANL. Detailed descriptions of the experimental setup and data acquisition are provided in prior publications (60, 61). The sample was photoexcited using a 355-nm laser (∼10-ps pulse duration), generated from the third harmonic output of a Duetto laser (Time-Bandwidth), operating at a repetition rate of 54.56 kHz. The x-ray probe pulses with an ∼150-ps pulse width were derived from the 48-bunch timing mode of the APS, which delivers evenly spaced x-ray pulses at 13.03 MHz with 76.7-ns intervals. The pump and probe beams intersected at a free-flowing liquid jet (∼500 μm in diameter) enclosed in a nitrogen atmosphere. The x-ray probe pulse synchronized with the laser pump was delayed by 150 ps relative to the pump.

The laser and x-ray spot sizes (H × V) at the sample position were ∼600 μm by 80 μm and 450 μm by 30 μm, respectively. Fluorescence signals from Ag were collected at a 90° angle relative to the incident x-ray beam using two avalanche photodiodes (APDs) positioned on either side. A customized combination of Soller slits and a 25-μm-thick Rh filter, which was designed to match the sample chamber geometry and detector distance, was placed between the sample jet and the APDs. Sample integrity was monitored periodically via UV-visible spectroscopy, so that the solution was refreshed once any sign of degradation was detected. The APD signals were digitized using a high-speed analyzer card (Agilent), triggered by a 54.56-kHz transistor-transistor logic (TTL) pulse synchronized with the laser. The card recorded the x-ray fluorescence with a 1-ns time resolution per point and averaged signals over a 4-s integration window. All individual x-ray pulses occurring between two laser pulses were captured. To minimize systematic error from pulse-to-pulse intensity fluctuations, the fluorescence signal from the sample was normalized to a reference signal obtained by measuring the air scattering intensity from the x-ray beam upstream of the sample. The laser-off spectrum was obtained by averaging the fluorescence signals from six x-ray probe pulses recorded before photoexcitation, representing the ground-state absorption profile.

Full reciprocal space mapping

Synchrotron XRD experiments were performed on the ID4B (QM2) beamline at the Cornell High Energy Synchrotron Source (CHESS). The incident x-ray energy was 50 keV (λ = 0.248 Å), which was selected using a double-bounce diamond monochromator. An area detector (Pilatus 6M) was used to collect the scattering intensities in a reflection geometry. The sample was rotated with three tilted 360° rotations, sliced into 0.1° frames. Geometric parameters of the Pilatus 6M detector such as detector distance, tilting, rotation, and direct beam position were extracted using standard CeO₂ powder, and data were processed and analyzed using the in-house software. The data visualization was performed with the NeXpy software package.

Microspectroscopic ellipsometry experiments

Imaging spectroscopic ellipsometry was conducted to extract the dielectric function of perovskite using the Accurion EP4 system (Park Systems). Measurements were performed across the 250- to 1000-nm spectral range with a 7× objective lens. To ensure measurement reliability and accurately determine material properties, multiangle incidence measurements were performed over an angular range of 40° to 60°. The ellipsometric coefficients maps (Ψ and Δ) were obtained with a spatial resolution of ∼1 μm within the region of interest. The map data were analyzed using the EP4 model and DataStudio software provided with the EP4 system.

For ellipsometric coefficients analysis (Ψ and Δ), coefficients were extracted from the target flakes in map data using the DataStudio software and subsequently analyzed using the EP4 model software. For modeling the excitonic behavior of perovskite, we used the multi-Lorentz oscillator model as: $\mathrm{\epsilon }\left(E\right)={\mathrm{\epsilon }}_{\infty }+\sum _i\frac{A_i}{E_{0,i}^2-E^2-i{\mathrm{\Gamma }}_{i}E}$, where ${\mathrm{\epsilon }}_{\infty }$ is a background permittivity, E_0,i denotes the resonance energy of the ith oscillator, A_i represents its oscillator strength, and Γ_i is its damping factor. On the basis of the crystal structure of perovskite, the material was modeled as an isotropic material. The parameters of each Lorentz oscillator and background permittivity were fitted to the experimental data to determine the complex refractive indices.

Inelastic x-ray scattering

The IXS was conducted at beamline 10-ID at the NSLS-II (IXS) (62). The highly monochromatic x-ray beam of incident energy E_i = 9.13 keV (λ = 1.36 Å) was focused on the sample with a beam cross section of ∼10 μm by 10 μm. The total energy resolution was ΔE ∼ 1.4 meV (full width at half maximum). The measurements were performed in reflection geometry on the sample’s (222) surface.

DFT calculations

For the lattice constant, DFT calculations were performed with Vienna Ab initio Simulation Package (VASP) (63–65) using the projector-augmented wave (PAW) method (66). A plane-wave cutoff energy of 400 eV and a Γ-centered 4 by 4 by 4 Monkhorst-Pack k-point mesh were used. Structural relaxations used the PBEsol exchange-correlation functional (67, 68) until the residual forces on all atoms were less than 0.01 eV/Å.

To obtain the projected density of states (DOS) (fig. S22), DFT calculations were performed within the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) (67) as implemented in Quantum ESPRESSO (69), using a fully relativistic spinor formalism and norm-conserving PseudoDojo pseudopotentials (70) to account for spin-orbit coupling from heavy elements. To model defects, we constructed 2 by 2 by 2 supercells of CAIC (320 atoms) with and without defects. Self-consistent and non-self-consistent runs used a 3 by 3 by 3 Monkhorst-Pack k-point grid and a plane-wave kinetic energy cutoff of ∼50 rydbergs. PBE typically underestimates the bandgap; however, it is sufficiently reliable for qualitatively analyzing bandgap changes induced by structural variations.

Supplementary Materials

This PDF file includes:

Supplementary Notes S1 to S10

Figs. S1 to S25

References