Exciton spin structure in lead halide perovskite semiconductors explored via the spin dynamics in magnetic field

TL;DR

This work develops a theoretical framework for exciton spin structure and dynamics in bulk lead halide perovskites across cubic, tetragonal, and orthorhombic phases, highlighting the competition between electron-hole exchange $\Delta_{\rm X}$ and Zeeman splitting governed by $g$-factors. It shows how magnetic-field orientation (Faraday vs. Voigt) and exchange strength qualitatively alter optical signatures, including bright/dark exciton mixing and polarization beats, with clear predictions for strong vs. weak exchange regimes. The authors validate the theory by time-resolved PL measurements on orthorhombic MAPbI$_3$ at 1.6 K, observing bright-exciton quantum beats in both geometries and extracting exchange strengths, $g$-factor values, and small symmetry-induced splittings, thereby establishing a robust method to infer exciton fine structure from spin dynamics. The findings demonstrate coherent exciton spin control in perovskites and suggest broad applicability to other lead-halide systems and confinement-engineered counterparts, underscoring perovskites as a promising platform for exciton-spin physics and spinoptoelectronic applications.

Abstract

We theoretically investigate the spin structure and spin dynamics of excitons in bulk lead halide perovskite semiconductors with cubic, tetragonal, and orthorhombic crystal symmetry. The exciton spin structure and its modification by an external magnetic field are modeled for different regimes defined by the relative magnitude of the electron-hole exchange interaction (splitting between dark and bright states) and the Zeeman spin splitting. The effects of crystal symmetry and magnetic field orientation with respect to the crystal axes are considered for lead halide perovskite crystals with band gaps in the range 1.4 - 3.5 eV, having different ratios of electron and hole g-factors. For cubic symmetry, in a longitudinal magnetic field, our theory predicts quantum beats between the bright exciton states under linearly polarized excitation and detection, while the dark exciton remains optically inactive. In a transverse magnetic field, all exciton spin states become optically active and can be excited by circularly polarized light. Reduction of the crystal symmetry leads to a zero-field offset of the exciton Larmor precession frequencies, modifying the Zeeman splitting energy dependence on magnetic field. This theoretical framework allows for the extraction of the strength of the exchange interaction and the crystal symmetry. Experimentally, we measure the exciton spin coherence via time-resolved photoluminescence at a temperature of 1.6 K in longitudinal and transverse magnetic fields in orthorhombic MAPbI3 crystals. Polarization beats at the frequency of the bright exciton are observed in both configurations. Comparison with theory indicates that the excitons are in the strong exchange interaction regime, and the reduction of symmetry does not lead to a significant splitting of the exciton spin levels.

Figures (11)

• Figure 1: Schematic representation of the exciton spin structure in perovskites with cubic (a), tetragonal (b), and orthorhombic (c) crystal symmetry, shown in the basis of linearly polarized states. $\Delta_{\text{X}}=\Delta_{\text{Y}} < \Delta_{\text{Z}}$ for (b) and $\Delta_{\text{X}}<\Delta_{\text{Y}} < \Delta_{\text{Z}}$ for (c) are assumed.
• Figure 2: (a) Modeling of the $g$-factor dependence on band gap energy for the bright (blue) and dark (red) excitons in lead halide perovskites, taken from Ref. Kopteva_gX_2024. (b) Hole (green) and electron (black) $g$-factor band gap dependences from Ref. kirstein2022nc. Labels I-V indicate the different cases of $g_\text{e}$, $g_\text{h}$, $g_\text{X}$, and $g_\text{DX}$ values and signs listed in Table \ref{['tab:gF']}.
• Figure 3: Exciton spin states in magnetic field $B$, calculated for cubic symmetry $\Delta_\text{X} = 0$ meV (a,c,e,g,i) and $\Delta_\text{X} = 0.5$ meV (b,d,f,h,j) for different cases of exciton $g$-factors shown in Fig. \ref{['fig:EZ']} and listed in Table \ref{['tab:gF']}. The $g_\text{e}$, $g_\text{h}$, $g_\text{X}$, and $g_\text{DX}$ values used for the calculations are given on top of the panels. Symbols and lines represent the modeled values for better visualization.
• Figure 4: (a) Larmor precession frequency (left axis) and Zeeman splitting energy (right axis) of the bright (blue) and dark (red) exciton in longitudinal magnetic field, $B_\text{F}$. (b) Dynamics of P$_\text{lin}$ at $B_\text{F} = 0.3$ T. $g_\text{F,X} = +2.3$, $g_\text{F,DX} = +2.9$, $\Delta_\text{X} = 0.5$ meV.
• Figure 5: (a) Larmor precession frequencies (left axis) and Zeeman splittings (right axis) of the exciton states in a transverse magnetic field for $\Delta_{\text{X}} = 0.5$ meV. (b) Dynamics of $I^\text{+H}$ (red) and $I^\text{+V}$ (blue) after the $\sigma^+$ excitation at $B_{\text{V}} = 0.3$ T. (c) Dynamics of linear polarization degree, $P^{+}_{\text{lin}}$ (green), and $I^\text{+V} - I^\text{+H}$ (black). $g_\text{V,X} = +2.3$, $g_\text{V,DX} = +3.4$, and $\Delta_\text{X} = 0.5$ meV.