1. INTRODUCTION

Lead iodide (${\rm PbI}_2$), which has large bandgap (${\gt}{2}\;{\rm eV}$), high environmental stability, and low production cost, is an intriguing semiconductor for applications in optoelectronic technologies, such as $\gamma$- and $ x $-radiation detectors [1–3]. It adopts the graphene type of layered structure, which can be easily exfoliated into a monolayer possessing novel 2D electronic properties. In addition, ${\rm PbI}_2$ is an essential precursor for hybrid lead halide perovskites, which emerged as the third-generation solar cell with efficiency exceeding 25% [4–7]. Therefore, in recent years, various forms of ${\rm PbI}_2$ including thin films, nanoclusters, nanotubes, and graphitic-like layered structures have been fabricated [8–12], and their electronic and optical properties have been widely explored [9,12–14]. Given the strong spin-orbital coupling (SOC) in Pb and I, the spin generation and relaxation in ${\rm PbI}_2$ are as intriguing as those shown in Pb-based materials such as ${\rm CH}_3{\rm NH}_3{\rm PbI}_3$ and Ruddlesden–Popper type of multiquantum wells [15–18]. However, until now, as far as we know, there is a lack of the study of the spin physics in ${\rm PbI}_2$.

In this work, we present a systematic study on the electronic and spin dynamics of ${\rm PbI}_2$ thin film by using transient reflectance (TR) and time-resolved Kerr rotation (TRKR) spectroscopy. While TR spectroscopy monitors the fate of the photogenerated electrons, TRKR probes the dynamics of the spins carried by these electrons without the necessity of applying any external magnetic field. In the latter technique, the Kerr rotation (${\theta _K}$) is proportional to the difference of the refractive index for the right ($ n_r $) and left ($ n_l $) circular polarization components: ${\theta _K} \propto |{n_r} - {n_l}|$. By combining these two techniques, we are able to reveal the processes governing the spin relaxation. We find that ${\rm PbI}_2$ film possesses large Kerr rotation angle and subpicosecond spin relaxation lifetime around the bandgap. Therefore, it has great promise in spin-based applications, such as full optical isolators and switches, owing to the excellent optical and electronic properties.

2. SAMPLE PREPARATION AND EXPERIMENTAL SETUPS

Quartz substrates was cleaned by ultrasonication for 10 min in acetone solution, followed by UV ozone treatment for 10 min. The film was deposited by spin-coating ${\rm PbI}_2$ solution in dimethylformamide (DMF) with a concentration of 575 mg/ml on the cleaned quartz substrate at 3000 revolutions per minute (rpm). The as-casted films were then annealed at 70°C for 5 min. The thickness of the ${\rm PbI}_2$ film is ${\sim}{200}\;{\rm nm}$. All the processes were performed under ambient conditions.

The absorption spectroscopy was measured by a UV/Vis/NIR spectrometer (Shimadzu UV-2600). In the TR measurements, the film was excited by femtosecond pump pulses (Spitfire Pro, Spectra-Physics), which were frequency-doubled using a beta-barium borate (BBO) crystal (${\sim}{35}\;{\rm fs}$, 400 nm, 1 kHz). The probe beam was a white light continuum generated by passing the 800 nm femtosecond laser pulses through a 1 mm thick sapphire crystal. The TRKR setup is similar to a typical degenerate pump-probe setup, except that the pump polarization is set to circular polarization. The linearly polarized probe beam, which is reflected by the sample, passes through a half-wave plate with its fast axis fixing at an angle 45° to the polarization of the probe beam and then is split into the $ s $-polarized and $ p $-polarized components by a Wollaston prism. The intensity of the probe beam was detected by a balanced optical bridge and subtracted through a differential amplification circuit. The output $ s $-polarized and $ p $-polarized components were further input into a lock-in amplifiers. The Kerr rotation was measured by calculating the difference of the probe beam reflectance changes of the $ s $-polarized and $ p $-polarized components. All the measurements were performed at room temperature.

3. RESULTS AND DISCUSSION

Figure 1(a) shows the scanning electron microscope (SEM) image of the cross section of ${\rm PbI}_2$ film. It can be seen that the film has a smooth surface and uniform thickness of about 200 nm. Figure 1(b) shows the steady-state absorption spectrum of the ${\rm PbI}_2$ film, which can be well fitted using the Elliott formula, taking into account of the exciton absorption and continuous state absorption [19]. We extracted from the fitting the bandgap energy of 2.48 eV (500 nm) and the exciton binding energy of 12.8 meV (503 nm), which are in good agreement with the values obtained within the framework of the empirical pseudopotential method [13]. According to the theoretical calculations by considering SOC caused by heavy atom Pb, the bandgap appears at the surface of the Brillouin zone at point ${\boldsymbol A}$ between the nondegenerate state ${\boldsymbol A}_1^ +$ (the top of the valence band) and the twofold-degenerate level ${\boldsymbol A}_3^ -$ (the bottom of the conduction band). The third $ p $-like level ${\boldsymbol A}_2^ -$ appears about 0.6 eV higher in energy than level ${\boldsymbol A}_3^ -$. The simplified level is given in the inset of Fig. 1(b). In our work, only the transition from level ${\boldsymbol A}_1^ +$ to ${\boldsymbol A}_3^ -$ is excited because we used the pump energy just around the bandgap ($480 \sim 510\;{\rm nm}$), which cannot excite the transition from level ${\boldsymbol A}_1^ +$ to ${\boldsymbol A}_2^ -$. Therefore, we can obtain an instantaneous excitation of near 100% spin polarized population in ${\rm PbI}_2$ film photoexcited by a circular polarization laser based on the mentioned band structure.

 

Fig. 1. (a) Scanning electron microscope image of the cross section of the ${\rm PbI}_2$ film. (b) Absorption spectrum of the ${\rm PbI}_2$ film. The black circle line is the experimentally measured absorption data. The red solid line is the fitted curve using the Elliott formula, including the exciton and continuum contributions. The inset is the theoretically calculated energy band structure diagram of ${\rm PbI}_2$ at the $ A $ point in the Brillouin zone.

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The carrier dynamics of the ${\rm PbI}_2$ film were first explored using TR spectroscopy. Figure 2(a) shows the pseudo-color TR image of the ${\rm PbI}_2$ film with 400 nm excitation at a moderate pump fluence of around ${20.7}\;\unicode{x00B5} {{{\rm J}/{\rm cm}}^2}$. In the TR measurement, the pump penetration depth is about 66.7 nm (absorption coefficient ${\alpha _0} = 1.5 \times {{10}^5}/{\rm cm}$), while the effective detecting depth is $\lambda /{4}n\pi \sim 15.5$ ($ n $ is the refractive index, 2.55) for probe photon energies near the bandgap [19]. If we neglect the change in transmission, the change of reflectivity is opposite to the change of absorption, namely, $\Delta \alpha /\alpha = - \Delta R/R$. In Fig. 2(b), the representative TR curves at five different decay times (0, 0.5, 1, 2, and 5 ps) were extracted, showing an asymmetrical peak near the band edge. Based on our experimental data, it can be seen that the positions of photoinduced absorption (PIA) and photoinduced bleach (PB) are approximately centered at 485 nm and 503 nm, respectively. The position of the PB peak is consistent with the exciton absorption spectrum. Figure 2(c) shows a few decay curves at selected probing wavelengths including the PB (495, 500, and 505 nm) and PIA (480 and 490 nm) bands. The kinetics at the exciton resonance (${\sim}{503}\;{\rm nm}$) are fitted by triple exponential function shown in Fig. 2(d), which yields three characteristic lifetimes: ${{t}_1} = 1.86\pm{0.09}\;{\rm ps}$, ${{t}_2} = 25.1\pm{0.8}\;{\rm ps}$, and ${{t}_3} = 667\pm{74}\;{\rm ps}$. Herein, ${{t}_1}$ is assigned to the Auger recombination, ${{t}_2}$ originates from the trapping process, and ${{t}_3}$ is related to the radiative recombination [9,20].

 

Fig. 2. (a) Pseudo-color TR spectra of the ${{\rm PbI} _2}$ film upon 400 nm excitation. The pump fluence is ${20.7}\;\unicode{x00B5} {{{\rm J}/{\rm cm}}^2}$. (b) The TR selected spectra at different times (0, 0.5, 1, 2, and 5 ps) extracted from (a). (c) The probe wavelength (480, 490, 495, 500, and 505 nm) dependent TR dynamics. (d) The TR dynamics at 503 nm (the blue hollow point) and the fitted curve by the tri-exponential decay function (the red curve). The lifetimes obtained by fitting are ${t_1} = 1.86\pm{0.09}\;{\rm ps}$, ${t_2} = 25.1\pm{0.8}\;{\rm ps}$, and ${t_3} = 667\pm{74}\;{\rm ps}$, respectively.

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We further probe the dynamics of spin polarization using TRKR, which allows one to address the spin states of the polarized carriers photoexcited by a circular polarization pulse laser. Figure 3(a) shows typical TRKR kinetics of the ${\rm PbI}_2$ film excited at 490 nm with right-handed circular polarization and pump fluence of ${78}\;\unicode{x00B5} {{{\rm J}/{\rm cm}}^2}$. The black and red scatter lines are from two separate detectors probing the $ s $- and $ p $-polarized components, which show striking differences owing to the varied populations of the spin-up and spin-down states. The signals of the $ s $- and $ p $-polarized components excited at 490 nm are negative because the probe wavelength is at the PIA band mentioned in Fig. 2(b). Half of the sum of $ s $ and $ p $ components [$({\rm S} + {\rm P})/{2}$], as shown by the magenta scatter line in Fig. 3(a), shows a sharp rise followed by an approximately constant level within the measurement time window. The $({\rm S} + {\rm P})/{2}$ signal cancels the spin information and is only relevant to the carrier dynamics. Therefore, we observed almost the same dynamical behavior here for the $({\rm S} + {\rm P})/{2}$ signal as that shown in TR spectra probed at 490 nm [red line in Fig. 2(c)]. In what follows, we focus on the difference of $ s $- and $ p $-polarized components (S-P), namely, Kerr rotation signal [the blue scatter line in Fig. 3(a)]. The positive Kerr rotation signal excited by the right-handed circular polarization only represents the rotation direction. The Kerr rotation directions obtained by the excitation using the right- and left-handed circular polarization light are reversed, but the rotation angles are almost the same [Fig. 3(b)]. The symmetrical Kerr rotation signals upon the right- and left-handed polarization light excitation indicate that the Kerr rotation directions are inverse because the transient effective magnetic fields generated by the circular polarization pulse lasers have opposite directions. The maximum of Kerr rotation at zero time is 0.54 deg. By globally fitting the Kerr rotation spectroscopy with the single exponential decay function [magenta solid line in Fig. 3(b)], we extracted a spin lifetime as short as $1.08 \pm 0.01\;{\rm ps} $, which indicates that the ${\rm PbI}_2$ film is a promising candidate for ultrafast spin switch.

 

Fig. 3. (a) Typical time-resolved Kerr rotation spectroscopy photoexcited with the wavelength of 490 nm at pump fluence of ${78}\;\unicode{x00B5} {{{\rm J}/{\rm cm}}^2}$. (b) Kerr rotation from left- (blue hollow scatter line) and right- (red hollow scatter line) handed circular polarization light. The magenta solid line is the fitting line using a single exponential function. Kerr rotation and spin lifetime are 0.52 deg and $1.08 \pm 0.01\;{\rm ps} $, respectively.

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To further deeply understand the spin relaxation and rotation properties, the Kerr rotation and the characteristic spin lifetime were measured as a function of the pump fluence in the range of 13–${234}\;\unicode{x00B5} {{{\rm J}/{\rm cm}}^2}$. As shown in Fig. 4(a), the Kerr rotation (blue scatter line) first grows rapidly at low pump fluence (${\lt}{78}\;\unicode{x00B5} {{{\rm J}/{\rm cm}}^2}$), then increases slowly, and eventually reaches a saturation value of ${\sim}{0.8}\;{\rm deg}$ for 200 nm thickness ${\rm PbI}_2$ film (${\sim}{4}\;{\rm deg}/\unicode{x00B5}{\rm m}$). This trend is similar to that for periodic gold nanowires structured on a thin layer of bismuth iron garnet [21]. The saturable Kerr rotation reflects that the film was completely polarized under high pump fluence. The large Kerr rotation angle, ${\sim}{4}\;{\rm deg}/\unicode{x00B5}{\rm m}$, is much larger than CdSe quantum dot at 630 nm [22] and slightly smaller than ${\rm CH}_3{\rm NH}_3{\rm PbI}_3$ film (10 deg/µm, pump fluence of ${19}\;\unicode{x00B5} {{{\rm J}/{\rm cm}}^2}$) at 200 K [23]. The SOC effect is responsible for such a large Kerr rotation angle. Due to the SOC effect, the conduction band splits into two states, the twofold-degenerate level ${\boldsymbol A}_3^ -$ and the level ${\boldsymbol A}_2^ -$ that appears above ${\boldsymbol A}_3^ -$ with energy difference of $\Delta = 0.6\;{\rm eV}$, while the valence band still remains a nondegenerate state ${\boldsymbol A}_1^ +$. The degree of spin polarization after being excited by the circular polarization laser can reach 100% for ${\rm PbI}_2$ with the nondegenerate top valence band and the twofold-degenerate bottom conduction band. The maximal net spin polarized population for the compound semiconductors is only 50% because of its fourfold-degenerate levels at the top of the valence band [24].

 

Fig. 4. (a) Pump dependence of Kerr rotation and spin lifetime upon 490 nm excitation with the fluence in the range of ${13 - 234}\;\unicode{x00B5} {{{\rm J}/{\rm cm}}^2}$. The cyan line is fitted by ${\tau _s} \propto {F^{- 1/3}}$. (b) Kerr rotation and spin lifetime as a function of the pump wavelength. The pump fluence is fixed at ${156}\;\unicode{x00B5} {{{\rm J}/{\rm cm}}^2}$.

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The spin lifetime [red scatter line in Fig. 4(a)] decreases gradually from 2.24 to 0.48 ps with the increase of the pump fluence. All spin lifetime is on the order of picoseconds (ps) in the range under investigation, which is much shorter than that of conventional semiconductors such as GaAs. The ultrafast magneto-optical response of the ${\rm PbI}_2$ film is also caused by the strong SOC effect, which provides a path for spin flip and accelerates the spin relaxation process. The spin polarization relaxes via a few mechanisms including the Elliot–Yafet (EY) [25,26], the D’yakonov–Perel (DP) [27] and Bir–Aronov–Pikus (BAP) mechanisms [28]. The BAP mechanism originates from the electron spin flip scattering as the electron spin interacts with the hole spin, which is a dominant process in heavily $ p $-doped semiconductors. We can first exclude the BAP mechanism, as the sample used in this work is not intentionally doped. The DP process is the dominant mechanism in GaAs-like materials without center of inverse symmetry, where both Dresselhaus and Rashba effects might induce spin precession randomized by scattering. However, the lowest conduction band of ${\rm PbI}_2$ is dominated by the $ p $ orbit of Pb as confirmed by density function theory calculations [13]. Owing to the strong SOC [29], we conclude that the dominant mechanism in the ${\rm PbI}_2$ film is the EY process similar to that in ${\rm CH}_3{\rm NH}_3{\rm PbI}_3$ [23]. In the EY mechanism, the spin lifetime $\tau _s^{{\rm EY}}$ can be expressed as [30]

The wavelength dependence of the Kerr rotation and spin relaxation time were measured around the bandgap energy with a fixed pump fluence of ${156}\;\unicode{x00B5} {{{\rm J}/{\rm cm}}^2}$. As shown in Fig. 4(b), the longest response time occurs at the exciton absorption peak. In addition, the Kerr signal decreases rapidly when the probe wavelength is away from the bandgap, which suggests that ${\rm PbI}_2$-based spintronic devices may possess high sensitivity just around the bandgap. These results can be well interpreted according to the data shown in Fig. 2(b). As we know, the refractive index $n(\hbar \omega)$ is usually much larger than the extinction coefficient $\kappa (\hbar \omega)$ for typical semiconductors. Since $\Delta R(\hbar \omega)/R$ is small (${\lt}{0.007}$) in our studied spectral region, the TR signal $\Delta R(\hbar \omega)/R$ is proportional to the change in refractive index $\Delta n(\hbar \omega)$ [32], namely,

4. CONCLUSIONS

We carried out a systematic study of carrier and spin dynamics around the band edge on solution-processed ${\rm PbI}_2$ film using transient reflection spectroscopy and time-resolved Kerr rotation technique. With the increase of pump fluence, the Kerr rotation angle ${\theta _K}$ increases linearly at first, followed by a sublinear rise until reaching a saturated value of ${\sim}{4}\;{\rm deg}/\unicode{x00B5}{\rm m}$. At the same time, the spin relaxation lifetime gradually decreases to a minimum value of ${\sim}{1.6}\;{\rm ps}$. The spin relaxation mechanism in ${\rm PbI}_2$ thin films is attributed to the EY process, owing to the strong spin-orbital coupling. In addition, we find that the Kerr effect has a large signal just around the bandgap, which suggests that the spintronic device made of ${\rm PbI}_2$ is sensitive to the probe wavelength. Our work highlights the potentiality of ${\rm PbI}_2$ film as a new candidate for spintronic applications in the range of 480–510 nm, such as ultrafast spin switches and spin isolators, owing to giant Kerr rotation angle and ultrafast spin flip lifetime.