Spin dynamics of excitons and carriers in mixed-cation MA$_{x}$FA$_{1-x}$PbI$_{3}$ perovskite crystals: alloy fluctuations probed by optical orientation

TL;DR

This study uses time-resolved optical orientation to probe the spin dynamics of excitons and charge carriers in mixed-cation MA$_{x}$FA$_{1-x}$PbI$_{3}$ perovskites, correlating alloy fluctuations with spin relaxation behavior. By modeling two coexisting spin systems—excitons and spatially separated electron-hole pairs—the authors extract initial spin polarizations and spin-relaxation times, and show that alloy disorder modulates energy-relaxation pathways near the band edge. The results reveal high initial optical orientation across compositions (60–80% for excitons; 35–70% for e--h pairs) with a pronounced minimum at $x=0.4$, where alloy fluctuations are strongest, and g-factors that scale with the band gap in agreement with universal perovskite trends. The findings highlight the role of alloy fluctuations in dictating spin dynamics via acoustic-phonon scattering and localization, and suggest further experiments to dissect localization, hyperfine effects, and symmetry-breaking mechanisms in these materials.

Abstract

Optical spin orientation measured by time-resolved photoluminescence provides a powerful tool to probe the spin dynamics of excitons and charge carriers in perovskite semiconductors. The impact of alloy fluctuations on the spin dynamics of mixed-cation \MAFAPI{} perovskite single crystals is studied here experimentally. The optical orientation is measured under nonresonant excitation for crystals with $x = 0.1$, $0.4$, and $0.8$ at cryogenic temperatures and compared with data on \MAPI{} crystals. The high degree of exciton optical orientation of $75-80$\% for $x = 0.1$ and $0.8$ reduces to about 60\% for $x = 0.4$. A similar trend is observed for the carrier spin optical orientation. This behavior is attributed to enhanced scattering of free excitons and carriers in the alloys with increased compositional and structural disorder. From the Larmor spin precession measured from spin dynamics in an external magnetic field applied in the Voigt geometry, the electron and hole $g$-factors are evaluated. Their dependence on the band gap energy in \MAFAPI{} crystals follows the universal trend previously established for lead halide perovskites.

Figures (15)

• Figure 1: Time-integrated photoluminescence spectra of the studied MA$_{x}$FA$_{1-x}$PbI$_{3}$ crystals measured at $T = 1.6$ K using the laser photon energy $E_{\rm exc} = 1.77$ eV for excitation with power density $P = 0.5$ W/cm$^{2}$ for $x= 0.1$ (a), $x= 0.4$ (b), and $x= 0.8$ (c). Photoluminescence spectra measured at the moment of pulse arrival are shown by the dashed lines. $E_\text{X}$ denotes the exciton resonance.
• Figure 2: Exciton energies $E_{\rm X}$ in MA$_{x}$FA$_{1-x}$PbI$_{3}$ crystals at $T = 1.6$ K, measured in this work (blue dots) and in Ref. kopteva_bayer2025PRB_MAPbI3_OO (blue square), plotted against MA content. The blue line is a linear fit of these data. Data for polycrystalline films at $T = 2$ K are shown by black empty squares (Ref. galkowski_nicholas2016enenvsci_FAPI_MAPI_Eg_Ex, magneto-optical band gap measurement) and empty diamond (Ref. fang_anoniettaLoi2016lightSciAppl_FAPI_film_spectra, estimate of band gap from optical spectra). The solid red line is a linear fit of room-temperature band gap measurements as reported in Ref. weber_weller2016jmatchemA_FAMAPbI3_phase_transitions. The exciton binding energy is about $15$ meV for both FAPbI$_3$ and MAPbI$_3$ at $T=2$ K galkowski_nicholas2016enenvsci_FAPI_MAPI_Eg_Ex.
• Figure 3: Photoluminescence dynamics measured at $T = 1.6$ K in a MA$_{0.4}$FA$_{0.6}$PbI$_3$ crystal. (a) Spectrally-resolved photoluminescence dynamics excited by $100$ fs pulses with excitation at $E_{\rm exc} = 1.70$ eV using $P = 0.5$ W/cm$^{2}$ laser fluence. The horizontal dashed lines mark the temporal ranges used for the time-integrated data presented in panel (b). The vertical dashed lines mark the the high- and low-energy boundaries of the spectral ranges for the long-lived dynamics (LL, $1.525-1.536$ eV), exciton (X, $1.536-1.545$ eV), and the high energy range (HE, $1.5405-1.545$ eV) (shown by solid lines) used for the time-resolved data in panels (c, d). (b) PL spectra measured in a 40 ps time window at different delays as marked by the horizontal dashed lines in panel (a). The signal at $t < 0$ is measured at $t = -50$ ps and is equivalent to $t \approx 12.5$ ns. The spectra are shifted vertically for clarity. (c) Photoluminescence dynamics, spectrally integrated across the LL, X, and HE ranges. (d) Recombination dynamics in MA$_{x}$FA$_{1-x}$PbI$_{3}$ crystals measured with $E_{\rm exc} = 1.77$ eV and $P = 0.5$ W/cm$^{2}$, averaged over the X spectral range (see Section \ref{['SI:trpl']} in the Supplementary Information for the exact ranges in the other samples). The black lines are biexponential fits.
• Figure 4: Optical orientation of excitons and carriers in a MA$_{0.4}$FA$_{0.6}$PbI$_3$ crystal at $T = 1.6$ K, measured using $\sigma^+$ polarized excitation. $E_{\rm exc} = 1.70$ eV and $P= 0.5$ W/cm$^2$ at $T = 1.6$ K. (a) Spectrally-resolved dynamics of the optical orientation degree. The dashed lines show the temporal and spectral ranges used to average the data presented in panels (b,c) and (d,e), respectively. (b) PL spectra detected in $\sigma^+$ and $\sigma^-$ circular polarization at the moment of pulse arrival. (c) Spectral dependence of the optical orientation degree at $t=0$ calculated from the data in panel (b). The horizontal dashed line gives the maximum optical orientation degree. (d) Spectrally-integrated ($1.536-1.545$ eV) PL dynamics detected in $\sigma^+$ and $\sigma^-$ circular polarization. (e) Dynamics of the optical orientation degree calculated from the data in panel (d). The black line is a biexponential fit giving estimates for the exciton and $\rm{e}$--$\rm{h}$-pair initial optical orientation degrees of $P_{\rm oo}^{\rm X}(0) = 0.50$ and $P_{\rm oo}^{\rm eh}(0) = 0.35$ and their decay times of 15 ps and 460 ps, respectively.
• Figure 5: (a) Experimental PL dynamics (dots) in a MA$_{0.4}$FA$_{0.6}$PbI$_3$ crystal measured with $E_{\rm exc} = 1.70$ eV and $P= 0.5$ W/cm$^2$ at $T = 1.6$ K. The black line shows a biexponential fit yielding ${\tau_{\rm R}^{\rm X}} = 25$ ps, ${\tau_{\rm R}^{\rm eh}} = 340$ ps, and $I_{\rm X}(0)/I_{\rm eh}(0) = 1.3$. The exciton (blue line) and $\rm{e}$--$\rm{h}$ (dashed red line) components are also shown. (b) Experimental dynamics of the optical orientation degree (dots) in a MA$_{0.4}$FA$_{0.6}$PbI$_3$ crystal. The black line is a fit within the two-component model using Eq. \ref{['SI:eq:P_oo_def']} and the parameters obtained from panel (a). The exciton and $\rm{e}$--$\rm{h}$ contributions are shown by the solid blue and dashed red lines, respectively. The following parameters are evaluated from the fit: $P_{\rm oo}^{\rm X}(0) = 0.60$, ${\tau_{\rm s}^{\rm X}} = 60$ ps, $P_{\rm oo}^{\rm eh}(0) = 0.35$, and ${\tau_{\rm s}^{\rm eh}} = 450$ ps. Note that $P_{\rm oo}^{\rm eh}(0) < P_{\rm oo}(0) < P_{\rm oo}^{\rm X}(0)$, with the total initial optical orientation degree $P_{\rm oo}(0)=0.55$.