Ternary transition metal chalcogenides (TTMCs), defined as MAXn (M = Mn, Fe, Ni, Cr, etc, A = P, Si, Ge, and X = S, Se, Te, n = 3, 4), are layered intrinsic magnetic materials with weak van der Waals forces, which are nontoxic, nondegradable in ambient temperatures, and easy to synthesize and exfoliate^[1–3]. TTMCs have recently attracted wide attention because of their remarkable electronic, optical, and magnetic properties^[4–6]. Li et al. observed the saturable absorption and reverse saturation absorption at different wavelengths in MnPS3 nanosheets^[7]. Certainly, they have tremendous potential for novel applications of photocatalytic, optoelectronics, water-splitting, and other fields^[8–12]. For example, TTMCs are widely used in saturable absorbers based on excellent one-photon saturable absorption. Liu et al. implemented NiPS3-coated microfiber as a saturable absorber to generate ultrafast laser pulses at picosecond rates^[13]. Similarly, Chen et al. employed MnPSe3 nanosheets to effectuate a stable passively pulsed laser that possessed a repetition rate of 14.62 MHz and a central wavelength of 1602 nm^[14]. TTCMs exhibit promising application prospects for photoelectricity; however, the study of nonlinear optical properties is in the initial stage, and the ultrafast carrier dynamics is inadequate.

Chromium thiophosphate (CrPS4), a member of TTMCs, is a versatile antiferromagnetic material with a Neel temperature of 36 K in bulk^[4,15]. In 1977, Diehl and Carpentier synthesized CrPS4 for the first time and described the atomic arrangement of the crystal structure^[16]. Further, Pei et al. studied the crystallographic, electronic, magnetic, and thermal transport properties of CrPS4 single crystals^[17]. Son et al. reported the local spin ground states of two-dimensional few-layer CrPS4^[1]. The CrPS4 shows excellent performance in magneto-optical and photoelectric cases with excellent stability in air^[1], but the lack of research on nonlinear optical absorption and ultrafast carrier dynamics limits its application in ultrafast optical devices.

In this paper, CrPS4 samples with different thicknesses prepared by the mechanical exfoliation method on sapphire substrate are purchased and used as received. The third-order nonlinear optical responses are studied by the I-scan system at 780 nm, and the nonlinear parameters are obtained by fitting the experimental data. Furthermore, the carrier dynamics of CrPS4 are investigated using transient transmission measurements with the pump laser at 390 nm and the probe laser at 780 nm. The photoinduced absorption and thickness-dependent carrier relaxation time are observed. This work provides a new perspective for developing ultrafast photonic devices.

Atomic force microscopy (AFM, Dimension ICON) was used to measure the thickness of CrPS4. Scanning electron microscopy (SEM, GeminiSEM 300) was used to observe the surface morphology. The optical absorbance spectra were measured by a micro-confocal spectrometer system (Trion, XinYuan Co.). The Raman spectra of CrPS4 from 100 to 700cm−1 were obtained at the excitation wavelength of 532 nm using a Horiba LabRam HR Evolution HR800 in air under ambient conditions. A continuous laser with the power of ∼2mW was focused onto the sample, utilizing an objective (NA=0.5). The reflected light was collected by the same objective and analyzed by a grating spectrometer. The X-ray diffraction (XRD) was used to reveal the crystal structure. The XRD pattern of CrPS4 was obtained by diffractometer (D/MAX2200V PC) with Cu-Kα radiation (power=3kW), and the scanning range was 10° to 80°.

The structure diagram of CrPS4 is given in Fig. 1(a). The six S atoms form a slightly distorted octahedron with the Cr atom coordinates in the middle. Meanwhile, the P atom sits in the center of a tetrahedron consisting of four S atoms. There is a weak van der Waals force between the S layers with the interlayer distance of ∼6.14Å^[18]. The AFM measurement results with the different thicknesses of 105, 510, and 1086 nm are shown in Figs. 1(b)–1(d), respectively. The samples have smooth surfaces observed from SEM images in the insets of Figs. 1(b)–1(d). From the optical absorbance spectra of CrPS4, a weak absorption peak at 740 nm and a strong absorption peak at 410 nm are observed, which is consistent with previous reports^[18]. As shown in Fig. 1(e), the former is attributed to the d-d transition of the Cr ion, and the latter is the ligand-to-metal charge transfer transition from the 3p band of the S atom to the 3d band of the Cr atom^[4,15,19]. At the same time, the bandgap obtained by the Tauc-plot method of the samples increases with the increase of thickness, as shown in Fig. S1 in the Supplemental Material. There are 17 Raman peaks labeled sequentially from A to Q in Fig. 1(f), which are similar to those in Ref. [4] and illustrate the high quality of our CrPS4 samples. As shown in Fig. S2(a) in the Supplemental Material, the surface is identified to be (001) plane, which indicates that the CrPS4 is stacked along the c axis layer by layer^[20,21]. Moreover, we demonstrate the stability of CrPS4 in air under ambient conditions. Figure S2 in the Supplemental Material shows the XRD and Raman data of CrPS4 measured before and after a month of air exposure. In Fig. S2(b) in the Supplemental Material, the two curves are extremely similar, implying the integrity of the crystallization after exposure. In the Raman spectra, all the peaks are clearly observed and there is no Raman shift in exposed and pristine samples. Therefore, the quality and crystal structure have not changed, which reveals the good air stability of CrPS4.

The Z-scan and I-scan systems are commonly used to study the nonlinear optical properties of materials. In the Z-scan system, the sample is moved along the propagation axis of the laser. For the I-scan system, the laser energy is adjusted by controlling the optical attenuator while keeping the position of the sample fixed. This system is beneficial in measuring micro-samples and avoiding the nonuniformity of samples. In this study, the I-scan system is utilized to investigate the nonlinear optical absorption of CrPS4, as shown in Fig. 2(a). The incident femtosecond laser (FS, PHAROS-20 W) beam with a pulse width of 220 fs and a repetition rate of 15 kHz passes through two Glan–Taylor prisms (Thorlabs, GT10-B) with a half-wave plate (HWP, Thorlabs, AHWP10M-580) between them. The first Glan–Taylor prism (GT1) is parallel to the polarization direction of the laser, and the second one (GT2) is perpendicular to GT1. The HWP can be rotated through a motor to change the incident laser intensity. Then, the laser is divided by a beam splitter (BS) into two parts. The reflected one is registered by a Si switchable gain detector (D1, Thorlabs, PDA100A2) as a reference beam, and the transmitted light is focused by an objective lens (Olympus, 20×, NA=0.3) to the sample. Furthermore, another Si switchable gain detector (D2, Thorlabs, PDA100A2) is used to measure the laser transmission after passing through the sample. To ensure that the laser is focused on the same area of the sample and to monitor any damage to the sample, real-time imaging is performed using a white light (WL), an objective lens, and a CCD.

The pump-probe technology is used to study the dynamics of ultrafast processes in materials. The schematic diagram of this method is shown in Fig. 2(b). The laser pulse is divided into two parts by the BS. One of them passes through the beta barium borate (BBO) to generate femtosecond pulses at 390 nm as the pump beam. This pump beam goes into a delay system to ensure that the optical paths of the pump light and the probe light are the same, as indicated by the purple dotted line in Fig. 2(b). Then, the pump light is modulated by an optical chopper. The other one is regarded as the probe beam. The pump and probe beams are combined by a dichroic mirror (DM) and focused onto the sample by an objective lens. After this, the pump beam is blocked by a 450 nm long-pass filter (LPF). The transmitted signal is detected by a Si switchable gain detector and collected by a lock-in amplifier (L-IA, SR830 DSP). Through a white-light imaging system, the position of the pump and probe beam spots can be conveniently operated.

To explore the reverse saturable absorption of CrPS4, it is necessary to ensure that the one-photon energy of the incident laser is less than the bandgap, so the laser of 780 nm (∼1.59eV for one photon) is used. With the increase of sample thickness in our experiment, the linear transmittances are 67%, 61%, and 56%, respectively. Figures 3(a)–3(c) show the I-scan results of CrPS4 samples at 780 nm. The normalized transmission gradually decreases as the incident intensity increases, which implies the TPA effect is observed. Because the CrPS4 is a semiconductor with a bandgap larger than the energy of one photon, the electron can absorb two photons simultaneously to make a transition from the valence band to the conduction band. In previous studies^[22–25], the relationship between the normalized transmission (TNorm) and the incident laser intensity (I) can be utilized to distinguish the nonlinear optical response, which can be written as^[24,25]ln(1−TNorm)=k×ln(I)+C0,(1)where k is the slope and C0 is a constant. For pure TPA, the value of k is 1. Figure S3 in the Supplemental Material shows the plots of ln(1−TNorm) versus ln(I) of CrPS4 films. By linearly fitting the experimental data, the slope k can be extracted. Notably, the slopes are 1.02, 0.98, and 1.01 for 105, 510, and 1086 nm CrPS4, respectively, indicating TPA is the dominant nonlinear optical response in our study.

When comparing Figs. 3(a)–3(c), the value of ΔT (ΔT=T0−Tmin, where T0 and Tmin are the linear transmittance and minimum amplitude of the normalized transmission) increases from ∼4% to ∼13% when the thickness increases. The thickness becomes thicker, resulting from the larger bandgap, and the two-photon excitation energy position (390 nm) is closer to the absorption peak leading to a larger ΔT. In order to exclude the influence of the carrier of the sample, we focused the laser on the sapphire substrate and repeated the nonlinear optical absorption experiments. Other experimental conditions remained unchanged. As shown in Fig. S4 in the Supplemental Material, the normalized transmission of the sapphire substrate is constant, without a nonlinear optical absorption effect. Therefore, the TPA only occurs in CrPS4, and the substrate does not contribute to it in our study.

The I-scan results are fitted using the light attenuation formula expressed as^[26]dI(z′)dz′=−(α0+βI)I,(2)where z′ is the propagation distance in the sample, α0 is the linear absorption coefficient, I is the incident intensity, and β is the nonlinear absorption coefficient. The change of TPA coefficient β with the incident intensity I0 can be expressed as^[27]β(I0)=β01+I0/Isat,(3)where β0 is the nonsaturation TPA coefficient, and Isat is the TPA-induced saturable intensity. The I-scan data are fitted well by Eqs. (2) and (3) in Figs. 3(a)–3(c). When the sample thickness increases, β0 decreases and Isat gradually increases, showing thickness dependence in Fig. 3(d). The saturation intensity of TPA depends on two factors: transition probability and density of states (DOS)^[28]. Approximately, the absorption coefficient for TPA (β0) can reflect the transition probability at different thicknesses. A smaller coefficient at a thicker sample indicates it is more difficult for electrons to jump to a high-energy state. Moreover, the DOS hardly changes, as the band structure remains almost the same for bulk CrPS4. Therefore, the smaller transition probability could contribute to the larger saturation intensity. Moreover, the imaginary part of the third-order nonlinear optical susceptibility Imχ(3) is calculated by^[29]Imχ(3)=10−7cλn296π2β0,(4)where c is the velocity of light, λ is the wavelength of the incident laser, and n is the linear refractive index. According to Eq. (4), β0 and Imχ(3) are proportional, resulting in the same variation trend. The value of Imχ(3) increases when the thickness becomes smaller in Fig. 3(e). The figure of merit (FOM) can reflect the nonlinear optical performance of CrPS4 at different thicknesses by eliminating the discrepancy caused by α0 calculated by the following formula^[29]: FOM=|Imχ(3)/α0|.(5)

In Fig. 3(f), it can be seen that the FOM remains comparatively unaffected, which means that the nonlinear optical performance of CrPS4 is similar under different thicknesses. The TPA parameters of CrPS4 at different thicknesses are summarized in Table 1. The experimental results indicate that the nonlinear optical property of CrPS4 can be flexibly modified and regulated by changing the thickness.

To further study the carrier dynamics of CrPS4, the nondegenerate pump-probe measurements with the pump laser at 390 nm and probe laser at 780 nm of 220 fs are carried out. Figure 4(a) shows the dynamics results of CrPS4 at different incident pump intensities. For all samples, the transient dynamics exhibit photoinduced absorption corresponding to a negative transmission signal (ΔT/T0). The photons of the pump laser can be absorbed by the ground-state electrons of the valence band, which generates multitudinous free carriers in the conduction band. The above free carriers can absorb photons from the probe laser, leading to a decrease in the transmittance. In Fig. 4(b), the transmission signal exhibits thickness dependence at the same pump intensity. Figure 4(c) shows the linear dependence between the amplitude of ΔT/T0 and pump intensity, which can rule out the possibility of higher-order multi-electron scattering processes like Auger recombination^[30–33].

In Fig. 4(d), the ground-state electrons can transit to excited state E2 by absorbing one photon from the pump pulse based on the ligand-to-metal charge transfer from the S atom to the Cr atom^[15,19]. When the pump and probe pulses overlap, the free carriers in E2 can absorb photons of the probe laser jumping to the higher excited state E3; meanwhile, the transition of free carriers achieved by the d-d transition of the Cr ion form E1 to E2^[4,19,24]. Therefore, a multi-exponential model is employed to fit the carrier dynamics^[34,35], ΔT/T0=∑i=1n=3Aiexp(−t/τi)erfc(ω/2τi−t/2ω),(6)where t is the delay time, ω is the laser pulse duration, and erfc ( ) is the integral error function. The excited carriers in E2 relax to the conduction band minimum E1, mainly via carrier–phonon scattering, regarded as the intraband process with the relaxation time τ1. Subsequently, there are excess electrons in the conduction and holes in the valence bands, which can allow interband electron–hole recombination, and the relaxation time is set to τ2^[36]. In the recombination process, the excess energy transfers to phonons and heats the lattice. τ1 (several picoseconds) is associated with the intraband relaxation processes in terms of this time scale, which can be found in various transition metal dichalcogenides^[37–39]. τ2 in the range of tens to a hundred picoseconds corresponds to the typical interband relaxation process in semiconductors^[33]. Specifically, the fitting parameters are shown in Figs. 4(e) and 4(f), Fig. S5 in the Supplemental Material, and Table 2. The τ3 about several nanoseconds is attributed to the energy dissipation of lattice cooling to the substrate^[40,41]. τ3 increases with increasing pump intensity or thickness. In this paper, we mainly concentrate on the relaxation processes about τ1 and τ2.

τ1 can be considered as a constant (∼3.1ps) under different pump intensities or thicknesses. This fast relaxation time is the same order of magnitude of materials, such as WSe2 and PeSe2^[31,33]. In this process, the carriers exchange energy with phonons by carrier–phonon scattering. Furthermore, the anharmonic phonon–phonon scattering by coupling to low-energy phonons modulates the electron–phonon scattering^[42–45], which explains the relaxation time τ1 observed in our measurements.

While τ2 shows thickness-dependent behavior, the relaxation time of 31.5 and 85 ps are found in samples of 105 and 1086 nm, respectively. τ2 can be attributed to phonon-assisted electron–hole recombination. The photoluminescence spectra of the CrPS4 are measured using a 532 nm laser with the monolayer WS2 as a reference. In the experiment, the samples at different thicknesses have no photoluminescence, as shown in Fig. S6 in the Supplemental Material, so the radiative recombination by photon emission is not considered for CrPS4. The strength of interaction between the electron and phonon can be given through a two-temperature model^[46–48], λ⟨ω2⟩=πkBTE3ℏτe−ph,(7)where kB is the Boltzmann’s constant, TE is the electron temperature, ℏ=h/2π, h is the Planck constant, and ω is the phonon frequency. When the thicknesses of CrPS4 increase, the decay time τ2 increases, indicating that the strength of the electron–phonon coupling weakens^[48]. In addition, the increase in thickness can enhance the dielectric screening, leading to diminished electron–phonon coupling^[36,48,49]. The thickness dependence of τ2 can be appropriately explained through the phonon-assisted mechanism.

On the other hand, τ2 increases to 38 ps when the pump intensity increases to 4.8GW/cm2 at 105 nm. Without the influence of other mechanisms, the relaxation time is constant when the pump energy increases. The slower relaxation processes are observed at higher pump intensities in our experiment, as shown in Fig. 5(a), which further implies that the carrier relaxation is phonon-assisted. There are more carriers with increasing pump fluence, resulting in a larger population of nonequilibrium phonons, which increases the phonon reabsorption, reducing the carrier relaxation rate^[50–52].

The Raman results at different powers from 1.1 to 6.5 mW for CrPS4 are shown in Fig. 5(b). Some peak positions are extracted and fitted by linear function in Fig. 5(c). According to the fitting results, the peak position decreases monotonously by increasing the incident laser power, which is consistent with the shift in Fig. S7 in the Supplemental Material. The peak position shifted by about 2cm−1 on average within the range measured in our experiment. In the temperature-dependent Raman spectrum of CrPS4, the Raman peak position decreases when the temperature rises^[53]. Meanwhile, the temperature increases significantly when the incident laser power is increased using Raman thermometry^[54].

In summary, we have studied the thickness dependence third-order nonlinear optical absorption and carrier dynamics of CrPS4. Under the excitation at 780 nm, the TPA phenomena are observed at different thicknesses. β0 and Isat are obtained by fitting the measured data, and Imχ(3) and FOM are further calculated. Specifically, β0 and Imχ(3) are 178.6GW/cm2 and 3.97×10−10esu in CrPS4 of 105 nm, respectively. The nonlinear optical parameters can be modulated by changing the thickness of the sample. Moreover, nondegenerate pump-probe measurements are used to investigate the carrier dynamics in CrPS4. The photoinduced absorption has been observed, and the relaxation processes are phonon-assisted, which is related to thickness and pump intensity. These results provide fundamental insights into the photophysical properties of CrPS4 and highlight its potential as an extraordinary material for optoelectronic application.