Photoexcitation induced magnetic phase transition and spin dynamics in antiferromagnetic MnPS3 monolayer

Antiferromagnetic spin dynamics is the key issue to develop spintronic devices. We adopt ab initio nonadiabatic molecular dynamics with spin–orbit-coupling (SOC) to investigate photoinduced spin dynamics in an antiferromagnetic semiconductor MnPS3 monolayer. Optical doping triggers MnPS3 from Néel antiferromagnetic to ferromagnetic phase at an experimentally achievable electron–hole pair density of 1.11 × 1014 cm−2. This phase transition can be ascribed to the light-induced mid-gap states of S-p orbitals, which lower the electron excitation energy and strengthen the SOC effect between S-p and Mn-d orbitals. The excited S-p electrons first decay to the mid-gap states due to p–p electron–phonon-coupling and then relax to the spin-down Mn-d orbitals via SOC. Such a dramatic relaxation process prolongs the photogenerated carrier lifetime up to 648 fs, providing an explanation for the unusual optoelectronic performance of MnPS3. The reversible switching of magnetic order via optical means gives an important clue for information storage and highly efficient photocatalysts utilizing antiferromagnetic semiconductors.


Introduction
Two-dimensional (2D) magnets have blossomed into one of the most promising areas in condensed matter physics over the past years. Inspired by the successful synthesis of intrinsic 2D magnetic semiconductors, i.e., CrI 3 monolayer and Cr 2 Ge 2 Te 6 bilayer, scientists have vastly broadened the family of potential 2D magnets, including CrX 3 (X = Cl, Br), Fe 3 GeTe 2 , VSe 2 , MnSe 2 , CrSBr, and MPS 3 (M = Fe, Mn, Ni) 1-4 . These emerging 2D magnets provide an ideal platform for manipulating the spin at 2D limit, leading to signi cant advance in low-power-consuming spintronics, quantum computing, and optical communications. Furthermore, there is fast-growing interest in developing effective approaches to control spin structure via electric eld, mechanical strain, defect doping, molecule adsorption, magnetic eld, and so on [5][6][7][8] . Among these approaches, ultrafast laser has unique advantage since it is the fastest, noncontact, and most energy e cient way to manipulate spin.
Speci cally, employing light to control the magnetic order via spin transfer or demagnetization process has attract extensive attention. For MXenes with ferrimagnetic (FiM) order, such as Cr 2 VC 2 F 2 , Mo 2 VC 2 F 2 , Mo 2 VN 2 F 2 , Mo 3 C 2 F 2 and Mo 3 N 2 F 2 , He et al. found that the laser pulse can directly trigger a magnetic transition from FiM to transient FM within a few femtoseconds. Time-dependent density-functional theory (TDDFT) simulations revealed that the microscopic origin of the transient all-optical switching of spin order was the optically induced intersite spin transfer (OSITR) effect 9 . The optically driven magnetic phase transition has also been observed in 2D spin-liquid RuCl 3 , where FM phase was signi cantly stabilized by optical doping at a moderate electron-hole (e-h) density of 1×10 13 cm − 2 10 .
Besides the magnetic phase transition, a drastic change in magnetic anisotropy was achieved in CrI 3 monolayer. The easy magnetization axis switches from out-of-plane to in-plane along with a large magnetic anisotropy energy (MAE) 11 . Using ultrashort laser pulse, Dabrowski et al. demonstrated laserinduced formation of magnetic domain after thermal demagnetization in ultrathin CrI 3 . They also realized helicity-dependent all-optical switch in CrI 3 12 . In few-layer Fe 3 GeTe 2 , both magnetization orientation and amplitude of MAE can be effectively modulated by a laser pulse. The saturation magnetization and coercivity were continuously tunable and the Curie temperature was boosted to room temperature 13 . All these efforts have contributed to the spin control of ferromagnets, while spin dynamics in 2D AFM materials remains largely unexplored 14 . Compared to 2D ferromagnets, the interaction between light and 2D antiferromagnets would pave the way for optically controlling the magnetic materials with faster timescale and promise stronger magneto-transport effects.
In this paper, we focus on the experimentally synthesized transition metal thiophosphate MnPS 3 monolayer as a representative AFM semiconductor [15][16][17] . Its spin dynamics under light illumination is investigated using the time-domain ab initio nonadiabatic molecular dynamics (NAMD) method with inclusion of spin-orbit-coupling (SOC) within spin-diabatic representation. Our results demonstrate that optical doping can convert the magnetic ground state of MnPS 3 monolayer from AFM to ferromagnetic (FM). Accounting for the optically induced mid-gap states, both d-p-d FM superexchange and p-d SOC are strengthened. During the carrier relaxation process, the excited S-p electrons rstly relax to p orbitals by transferring its energy to the lattice through electron-phonon coupling (EPC) and then to Mn-d orbitals to recombine with the holes via SOC. These ndings not only deepen our understanding into spin dynamics of 2D materials but also provide new opportunities for spintronic applications of AFM semiconductors using optical switches.

Results And Discussion
Structural and magnetic properties of MnPS 3 monolayer As shown in Fig. 1(a-b), Mn 2+ cations in MnPS 3 monolayer form a honeycomb lattice with P-P dimers vertically across the center of hexagonal plane. Each P-P dimer is tetrahedrally coordinated with three S atoms to form a [P 2 S 6 ] bipyramid. The calculated lattice parameters for MnPS 3 monolayer are a = 6.15 Å, b = 10.66 Å, slightly larger than the experimental values (a = 6.08 Å, b = 10.52 Å) for bulk MnPS 3 crystal 18 .
To evaluate the magnetic ground state of 2D MnPS 3 , four phases with different long-range magnetic orders, i.e., FM, Néel AFM, zigzag AFM, and stripy AFM, are considered using a 2×1×1 supercell ( Fig. 1(c)). Among them, the Néel AFM phase has lowest energy according to our calculations, while energy of the competing FM phase is about 94.7 meV/f.u. higher, in agreement with previous report 19 . The Mn 2+ ions adopt high-spin states with on-site magnetic moment of about 4.61 µ B .
To further examine the magnetic ground state, exchange coupling between Mn ions has been investigated using the following Heisenberg Hamiltonian: where S is the spin magnetic moment on each atomic site, J 1 , J 2  S atoms are located in separate sublayers ( Fig. 1(b)). However, in the super-superexchange channel for J 3 , the two mediated S atoms are in the same sublayer (Mn-S1···S2-Mn). One can reasonably expect that hybridization of Mn-d states with S-p states within the same sublayer is signi cantly stronger than that between different sublayers. This accounts for the larger magnitude of J 3 in comparison to J 2 despite the longer Mn-Mn distances in the former case. Nevertheless, J 1 is larger than J 3 by a factor of 3, which ensures that the dominating exchange parameter in pristine MnPS 3 monolayer is the Mn-Mn direct AFM exchange.

Effects of optical doping
Before we investigate the optical e-h bipolar doping effect on MnPS 3 monolayer, the role of unipolar doping has been rstly discussed. As shown in Figure S1, the energy difference between Néel AFM ground state and FM state increases with the increase of both electron and hole concentrations. That is to say, the magnetic ground state of MnPS 3 monolayer can be switched from Néel AFM phase to FM one at critical density for electron and hole doping of 1.07×10 14 cm − 2 and 1.52×10 13 cm − 2 , respectively. Unlike the bilayer CrI 3 in which only electron doping can be used to control the magnetic phase transition 21 , the FM phase can be induced by injecting either electrons or holes into AFM MnPS 3 monolayer. This excellent character indicates the possibility of controlling the magnetism simultaneously via photoexcited electron and hole.
The energy difference between the most stable Néel AFM and FM phase as a function of optical doping concentration is plotted in Fig. 2(a). Once the carrier density reaches 1.11×10 14 cm − 2 , corresponding to 0.75 electron/hole per unit cell, the magnetic order will transition from AFM to FM. Remarkably, such critical e-h pairs density in the order of magnitude of 10 14 cm − 2 has already been realized experimentally with laser pump, which ensures the achievement of stable FM MnPS 3 monolayer 22,23 . Moreover, mature experimental technology like time-resolved magneto-Kerr effect also makes the detection and measurement for magnetic phase transition readily available 24 . From the variation of exchange parameters J with optical e-h pairs density ( Fig. 2(b)), we can also obtain the same trend of AFM-to-FM transition. All J values change from negative to positive as the e-h pairs density increases. Depending on their response towards excited e-h pairs, a strong competition is expected between the superexchange Mn-S-Mn FM coupling and direct Mn-Mn AFM one, which in turn leads to the magnetic order transition. Taking (Fig. 3(e, f)). During the process of optical excitation, part of spin density in the spin-down channel on Mn atoms is transferred to the spin-up channel on S atoms, which will be discussed in detail later. The optical pumping induced mid-gap states and change of occupied number have also been found in previous experiments on 1T-TaS 2 , 1T-TiSe 2 , and VO 2 using time-and angle-resolved photoemission spectroscopy. [25][26][27][28] The collapse of their long-range charge order with a frozen lattice is possibly caused by the screening effect due to creation of new intraband electronhole channels. Moreover, the mid-gap states created by optical doping in MnPS 3 monolayer narrows the band gap from 2.34 eV to 1.40 eV. Therefore, the energy difference between S-3p orbitals and Mn-3d orbitals becomes smaller, which will facilitate electron hopping between them by largely lowering the electron excitation energy and enhance the FM superexchange interaction. Consequently, optically controlled magnetic phase transition from AFM to FM can be realized in MnPS 3 monolayer.

Spin dynamic process
The dynamic response of magnetic order to the optical excitation is further investigated using the timedependent Kohn-Sham equation based NAMD simulations, including spin ip mechanism and the carrier relaxation process. Both the spin ip and spin e-h recombination are strongly dependent on the nonadiabatic coupling (NAC) element between the key states ( Fig. 4(a-b)). For electrons with the same spin states, the energy of photoexcited electrons will transfer to phonons directly by EPC. Meanwhile, SOC can induce spin ip between opposite spin states via transferring the spin angular momentum to the orbital angular momentum. In the spin diabatic representation, Fig. 4(a-b) provide a straight line for comparison between the EPC and SOC in the excited MnPS 3 . The SOC is the dominant factor rather than EPC in the p-d interaction. As mentioned above, the stronger SOC offers the channels for the population transfer from the spin-down Mn-d states to the spin-up S-p states after photoexcitation, which is responsible for the magnetic phase transition. Additionally, the lowest unoccupied spin-down state is rough 2 eV higher than the valence band (Fig. 3(c-d)), which makes the electron hopping between spindown d and p states though EPC even more di cult. As a result, the spin is allowed to ip in the process of light excitation. Accordingly, the magnetic order is switched from Néel AFM to FM.
In fact, EPC and SOC always compete with each other during the spin relaxation dynamics process, which synergistically determine the behavior of electrons. The initial states are S-3p orbitals above the Fermi level by about 1.7 eV for spin-up electrons (CB in Fig. 4(c)), while the nal states are Mn-3d near the Fermi level for spin-down electrons (VB in Fig. 4(c)). The photoexcited S-p electrons in CB decay to the mid-gap states of the same spin states in the forbidden band, along with the reduction of electron population in Fig. 4(d) from 1 to 0.5. Our NAC calculations reveal that the EPC between the S-p and S-p orbitals is much stronger than the SOC, which explains why the initial S-p states prefer to relax to the mid-gap states, rather than to the spin-down S-p orbitals with closer energy levels (Fig. 3(c)). However, electron population analysis discloses that most of these spin-up S-p electrons nally relax to the spin-down Mn-d states (VB) to recombinant with holes, due to the larger p-d SOC. Correspondingly, the relaxation process accompanies with spin ip from spin-up to spin-down channel.
Figure 4(e) shows the spin occupation during relaxation. The spin ip nishes within a time scale of 648 fs, which suggests the FM phase can be maintained for a long time. Owing to the mid-gap states induced by photoexcitation, the excited electrons transfer its energy though EPC rstly without spin ip, and then tend to conserve the spin via SOC (Fig. 4(f)). This competitive process gives rise to FM phase of long lifetime, rather than transient one, which makes the experimental realization more convenient. One should note that SOC effect in the present system is so small that it can be treated as a perturbation in the adopted spin-diabatic representation.
The long carrier lifetime of MnPS 3 monolayer also endows it good candidate for charge separation in photovoltaics and optoelectronics. It is also well known that slower recombination is bene cial for the separation of photoexcited electrons and holes participated in the subsequent chemical reactions such as water splitting 29 . Typically, larger bandgap and weaker EPC favor slower dynamics to avoid fast carrier recombination. Moreover, electron spin has non-negligible impact on the control of carrier dynamics. Herein, the enhanced carrier lifetime in MnPS 3 is realized by the joint action of SOC and EPC upon photoexcitation. The optically driven spin state ip via SOC allows MnPS 3 monolayer behaves like an indirect-gap semiconductor during the radiative recombination, simultaneously harnessing larger carrier density of 1.11×10 14 cm − 2 and long lifetimes. The present ndings demonstrate that the AFM MnPS 3 monolayer is not only attractive for spintronics but also a promising light-driven photocatalyst for environmental and energy applications. In fact, exfoliated MnPS 3 from layered bulk phase has already been experimentally explored to achieve stable energy storage and conversion performances 30 .
In summary, we have simulated the spin dynamics of 2D MnPS 3 under light illumination using the SOCincluded NAMD method with spin-diabatic representation. Our computational results have shown that intrinsic MnPS 3 monolayer prefers Néel AFM phase, which can be reversely switched to the stable FM state with an experimentally achievable photoexcited e-h density at 1.11×10 14 cm − 2 . The mechanism for spin dynamics upon photoexcitation has been discussed based on both equilibrium exchange coupling and nonequilibrium NAC. The optical doping introduces mid-gap states that are composed of degenerate S-p orbitals and narrows the bandgap of 2D MnPS 3 from 2.34 eV to 1.40 eV. These mid-gap states decrease the energy difference between Mn-d electrons and S-p electrons, which effectively enhances the superexchange FM coupling though p-d orbital hopping. Moreover, the reduced degeneracy in Mn-d orbitals also weakens the direct AFM interaction. According to NAC calculations, p-p orbitals interact mainly via EPC, while for p-d interaction, it is SOC. The SOC between the S-p and Mn-d states provides a spin ipping channel between opposite spin states, which drives the magnetic phase transition from AFM to FM. During e-h recombination, the excited S-p electrons rstly relax to the mid-gap states with the same spin through EPC channel, which effectively preserve the FM state. Since the S-p electrons relax to the spin-down Mn-d orbitals via spin ip, the FM phase decays with a timescale of 648 fs. The enhanced carrier lifetime by the magnetic phase transition may prompt MnPS 3 a promising photovoltaic material.
Our investigation not only provides unique insight into physical mechanism of optically control magnetism, but also points to new opportunities for the simulation of spin dynamics.

Methods
The calculations were carried out within the framework of DFT, using the projector augmented wave method implemented in Vienna ab inito simulation package (VASP) code 31 . Interactions between ionic cores and valence electrons were descried with the projector augmented wave (PAW) method and a cutoff energy of 500 eV 32 . The generalized gradient approximation with the PBE functional was employed to describe the exchange-correlation interactions 33 . We used Hubbard U term (5 eV for Mn) to account for strong electronic correlation effects as suggested by Dudarew et al 34 . A 15 Å vacuum space was adopted along the perpendicular orientation to suppress the non-physical interaction between the monolayer and its adjacent imaging layer. The atomic coordinates in MnPS 3 monolayer were fully relaxed until the Hellmann-Feynman force and energy were less than 0.001 eV/Å and 10 − 6 eV, respectively. The k-point grids of 2π × 0.02 Å −1 were used for Brillouin-zone sampling. The photogenerated spin dynamics was simulated using SOC-included Hefei-NAMD code, which is mainly based on fewest-switches surface hopping (FSSH) combined with TDDFT [35][36][37][38][39] . The details about the spin dynamic simulations can be found in the Supporting Information.

Supplementary Files
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