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Nano Lett
Nano Lett
nl
nalefd
Nano Letters
1530-6984
1530-6992
American Chemical Society

39171642
10.1021/acs.nanolett.4c02914
Letter
Ultrahigh Néel Temperature Antiferromagnetism and Ultrafast Laser-Controlled Demagnetization in a Dirac Nodal Line MoB3 Monolayer
Gao Zhen †
Ma Fengxian *†
Zhu Ziming ‡
Zhang Qin ‡
https://orcid.org/0000-0002-7164-962X
Liu Ying †
https://orcid.org/0000-0003-3438-8149
Jiao Yalong *†
https://orcid.org/0000-0002-3369-3283
Du Aijun §
† College of Physics, Hebei Key Laboratory of Photophysics Research and Application, Hebei Normal University, 050024 Shijiazhuang, China
‡ Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, 410081 Changsha, China
§ School of Chemistry and Physics and Centre for Materials Science, Queensland University of Technology, Gardens Point Campus, Brisbane, 4000 Queensland, Australia
* E-mail: fengxianma@hebtu.edu.cn.
* E-mail: yalong.jiao@hebtu.edu.cn.
22 08 2024
04 09 2024
24 35 1096410971
20 06 2024
19 08 2024
18 08 2024
© 2024 The Authors. Published by American Chemical Society
2024
The Authors
https://creativecommons.org/licenses/by-nc-nd/4.0/ Permits non-commercial access and re-use, provided that author attribution and integrity are maintained; but does not permit creation of adaptations or other derivative works (https://creativecommons.org/licenses/by-nc-nd/4.0/).

Two-dimensional (2D) antiferromagnetic (AFM) materials boasting a high Néel temperature (TN), high carrier mobility, and fast spin response under an external field are in great demand for efficient spintronics. Herein, we theoretically present the MoB3 monolayer as an ideal 2D platform for AFM spintronics. The AFM MoB3 monolayer features a symmetry-protected, 4-fold degenerate Dirac nodal line (DNL) at the Fermi level. It demonstrates a high magnetic anisotropy energy of 865 μeV/Mo and an ultrahigh TN of 1050 K, one of the highest recorded for 2D AFMs. Importantly, we reveal the ultrafast demagnetization of AFM MoB3 under laser irradiation, which induces a rapid transition from a DNL semimetallic state to a metallic state on the time scale of hundreds of femtoseconds. This work presents an effective method for designing advanced spintronics using 2D high-temperature DNL semimetals and opens up a new idea for ultrafast modulation of magnetization in topological semimetals.

first-principles calculations
antiferromagnetism
Dirac nodal line
Néel temperature
laser pulse
National Natural Science Foundation of China 10.13039/501100001809 11904077 Hebei Province NA C20230509 Hebei Province NA C2022050 Natural Science Foundation of Hebei Province 10.13039/501100003787 A2024205029 Natural Science Foundation of Hebei Province 10.13039/501100003787 A2022205027 Natural Science Foundation of Hebei Province 10.13039/501100003787 A2021205024 National Natural Science Foundation of China 10.13039/501100001809 12204144 document-id-old-9nl4c02914
document-id-new-14nl4c02914
ccc-price
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pmcThe quest to miniaturize spintronic devices, coupled with the need for reduced power consumption and increased operational speeds, has catalyzed the rise of two-dimensional (2D) spintronics.1−7 Recent research in 2D spintronics has increasingly focused on antiferromagnetic (AFM) materials due to their fast dynamic behaviors, absence of stray fields, and robustness against magnetic disturbances.8−10 A key issue for the development of AFM spintronics is the undesirable carrier transport, which significantly hinders its speed for devices. To tackle the issue, the integration of Dirac Fermions within 2D AFM structures has been proven to be a promising strategy. This is because low-energy electrons in such Dirac materials mimic relativistic massless Fermions, showcasing extraordinary transport properties distinct from conventional Schrödinger Fermions.11

While certain 2D AFM systems have been identified with single Dirac points,11−13 materials exhibiting Dirac Nodal Lines (DNL) remain rare. This scarcity largely results from more stringent symmetry requirements such as mirror reflection. DNL semimetals, characterized by multiple Dirac points and a higher density of states at the Fermi level, offer improved conductivity and are thus promising for enhanced device performance. Indeed, such kind of material has been founded in some 2D structures.14−16 Unfortunately, most reported materials cannot be used for practical applications due to the low Néel temperature. Searching for 2D AFM Dirac materials that host room temperature magnetism is of great importance to advance the high-performance AFM spintronics.

To control the magnetic properties of AFM materials, conventional approaches such as gate voltage, electric fields, and strain engineering17−21 are commonly employed strategies, while the spin modulation using ultrafast laser pulses in the femtosecond or picosecond range has not been as extensively explored.22 In contrast to traditional methods that tend to be slower and more energy-consuming, femtosecond laser pulses offer precise, rapid, and minimally dissipative manipulation of material magnetism, potentially revolutionizing quantum information processing.23−25 Understanding the laser-induced spin dynamics provides insights into how spins behave, interact, and evolve over time in response to external stimuli, which is critical for designing materials with optimal magnetic properties. By tailoring the spin dynamics,26 one can enhance the speed, energy efficiency, and reliability of spintronic components, thereby pushing the boundaries of current technology and opening new avenues for ultrafast and low-power electronics.27 Previously, laser-induced spin dynamics were primarily explored in conventional materials, such as three-dimensional (3D) magnetic solids28−30 and 2D magnetic semiconductors.31−33 However, the research regarding light–material interactions in nontrivial 2D materials is still in its infancy. To date, relevant studies have only been reported on a 2D magnetic topological insulator MnBi2Te4,34 while it has yet to be conducted on 2D magnetic topological semimetals.

In this study, utilizing the swarm-intelligence-based structural search,35−37 density functional theory (DFT), and atomistic spin dynamics simulations38 integrated with the two-temperature model,39 we predicted and demonstrated that a highly stable AFM MoB3 monolayer not only hosts nontrivial Dirac Fermions and sustains ultrahigh temperature magnetism, but also exhibits ultrafast spin dynamics induced by laser irradiation. The rapid demagnetization of MoB3 monolayer occurs on a femtosecond time scale and can trigger a transition from a DNL semimetal to a metallic state. This study introduces a novel platform designed to enhance AFM spintronics performance by focusing on the Néel temperature, electronic transport, and laser-induced ultrafast spin dynamics.

The low-energy MoB3 structure was identified through a systematic structure search of the boron-based MonBm sheets, detailed in the Supporting Information. The identified geometric structure of the MoB3 monolayer is illustrated in Figure 1a, revealing a rectangular lattice (space group: Pmmm, No. 47) with lattice constants a = 5.97 and b = 4.99 Å. From the side view in Figure 1a, it is apparent that all atoms in the MoB3 monolayer lie within the same plane. The top view highlights each Mo atom bonded to six B atoms. Among the B atoms, two types exist, designated as B1 and B2. B1 atoms exhibit six-coordinate bonding, whereas B2 atoms display a five-coordinate bonding pattern within the structure. The bond length between Mo–B1 is 2.51 Å, and the bond length between Mo–B2 is 2.25 Å. Additionally, the bond angle formed by Mo–B1–Mo is 180°, while that involving Mo–B2–Mo is approximately 83.28°.

Figure 1 (a) Atomic structure, (b) electron localization function (ELF), and (d) phonon dispersions of the MoB3 monolayer. The isosurface of ELF is 0.6 eÅ–3. (e) Splitting of the degenerate d-orbitals of Mo atom in (c) a square planar ligand field. Up and down arrows denote the spin-up and down electrons, respectively. Δo is the crystal field splitting energy, and the splitting energies of Δ1 and Δ2 are 0.656 Δo and 0.086 Δo, respectively.

To delve into the bonding characteristics of the MoB3 monolayer further, we conducted an analysis of the Electron Localization Function (ELF), depicted in Figure 1b. The analysis revealed that electron localization primarily occurs between B–B bonds, with minimal electron localization between Mo–B bonds. This suggests covalent bonding within B–B bonds and ionic bonding within Mo–B bonds, indicating electron transfer from Mo atoms to B atoms. Bader charge analysis corroborates this, confirming that each Mo atom transfers 1.5e to the B atoms, which is in consistence with the charge density difference plot (Figure S2).

Utilizing a 2 × 2 × 1 supercell, we examined four potential magnetic configurations (Figure S3) to determine the magnetic ground state of MoB3, including one ferromagnetic state (FM) and three antiferromagnetic states (AFM). Table S1 summarizes the relative energies of the MoB3 monolayer in various magnetic states based on different methods. The AFM2 state emerges as the ground state with the lowest energy. The magnetism primarily originates from Mo atoms, as evidenced by the spin charge density (Figure 3c), with each Mo atom exhibiting a magnetic moment of 2.66 μB, close to 3 μB. This value significantly exceeds those of previously reported Mo-based compounds (0.14 and 0.048 μB).40,41

To dissect the origin of this magnetism, we employed crystal field theory to analyze the electron occupancy of the d orbitals for the MoB3. Each Mo atom in the MoB3 lattice is linked with four ligands of B atoms within the x–y plane (Figure 1c), forming a square planar complex in crystal field theory. Consequently, the five d-orbitals split into four energy levels; from the highest energy level to the lowest energy level are dx2–y2, dxy, dz2, and both dxz and dyz. Based on our charge analysis, the oxidation state of Mo is Mo2+, which entails 5 d-electrons filling the low-energy dxz, dyz, dz2, and dxy orbitals, while leaving the highest dx2–y2 state empty. This arrangement yields a net magnetic moment of approximately 3 μB for each Mo atom, consistent with our DFT calculations.

The high stability of the MoB3 monolayer was rigorously confirmed through various analyses, including its formation energy, the phonon spectrum (Figure 1d), ab initio molecular dynamics (AIMD) simulations (Figure S4), and calculating its elastic constants (Table S2). Additionally, its stability under ambient conditions was evaluated by examining its interaction with adsorbed O2 and H2O molecules (Figures S5 and S6).

Without considering spin–orbital coupling (SOC) effects (Figure 2a), our band structure calculations reveal the presence of two linear band crossing points along the X−Γ and Γ–Y paths, denoted as points 1 and 2, respectively. Specifically, point 1 lies 0.308 eV below the Fermi level, while point 2 is situated 0.11 eV above it. These band crossing points exhibit 4-fold degeneracy, characterizing them as Dirac points. Employing the HSE06 method to refine the band structure, we find that the Dirac points persist (Figure S7a). To assess the carrier mobility, we calculated the Fermi velocity (νF) by conducting linear fits on the first derivatives of the bands near the Dirac points.42 The resultant maximum velocities for the MoB3 monolayer amount to 6.43 × 105 m/s for Dirac point 1 and 8.56 × 105 m/s for Dirac point 2. These values are approximately 60–78% of the Fermi velocity in graphene (1.1 × 106 m/s),43 but exceed those of numerous other 2D materials.44−46

Figure 2 (a) Band structure of MoB3 calculated by using the PBE+U method. DP1 and DP2 denote the Dirac point 1 and Dirac point 2, respectively. (b) Band structures derived from specified paths at the K points within (c) the Brillouin zone. (d) 3D band diagram for the MoB3 in the entire Brillouin zone. (e, f) The projected orbital bands for the MoB3 monolayer.

Upon examination of the band structure across the entire Brillouin zone, we find that Dirac point 1 and Dirac point 2 do not exist as isolated points but rather form a nodal line centered at the Γ point (Figure 2b,c). This spatial arrangement is more clearly illustrated in the 3D band dispersion (Figure 2d). To deepen our understanding of the Dirac points, we conducted an analysis of the projected orbital bands of the MoB3 monolayer. As shown in Figure 2e,f, Dirac point 1 primarily arises from B-px and Mo-dx2–y2 orbitals with minor contributions from the B-pz and Mo-dxz orbitals. For Dirac point 2, it is predominantly contributed by B-px and Mo-dyx orbitals, with slight contributions from B-pz and Mo-dxz orbitals.

Subsequently, we discuss the preservation of the nodal line. In the absence of SOC, the spin and orbital degrees of freedom are completely decoupled from each other, leading to their description in two distinct subspaces. Consequently, each spin channel can be treated as a spinless system where an effective time reversal symmetry (T) and all spatial crystal symmetries including inversion symmetry (P), horizontal mirror symmetries Mx and My, as well as vertical mirror symmetry Mz are conserved. The nodal line depicted in Figure 2 manifests two crossed bands with opposite mirror eigenvalues of Mz (+1 and −1), suggesting that it is symmetrically protected. Furthermore, the nodal line is expected to possess a quantized Berry phase (π) owing to the combined PT symmetry, substantiating its topological assurance. Note that under room-temperature conditions, our AIMD simulations reveal a slight buckling in the MoB3 monolayer, indicating a disruption in mirror symmetry. Upon analysis of the band structure, we identified pairs of Dirac points around the Fermi level (Figure S8). However, the spin-up and spin-down channels are not degenerate.

As SOC is turned on, we found that Dirac point 1 opens up a band gap of 31.8 meV, while Dirac point 2 exhibits a band gap of 27.4 meV (Figure S9). This can be attributed to the presence of the same double-group representation (Γ5) in the Γ–Χ and Γ–Y directions, leading to the emergence of a gap at the energy band crossing point. Despite the opening of band gaps at the Dirac points of the MoB3 monolayer, they remain comparatively smaller than those in CaAgAs (∼73 meV)47 and ZrSiTe (∼73 meV),48 indicating the relatively weak impact of SOC on the MoB3 monolayer.

Magnetic anisotropy energy (MAE) serves as a crucial determinant in achieving long-range magnetic ordering in 2D materials. A high MAE signifies the robust thermal stability of the magnetic ordering. The MAE of MoB3 monolayer was evaluated through the equation: MAE(θ, φ) = E(θ, φ) – E(θ = 90°, φ = 0°), where θ is the polar angle and φ is the azimuthal angle. The calculated MAE values for the MoB3 monolayer rotated in the x–y and x–z planes are visualized in Figure 3a and b, respectively. Notably, the MAE is found to display anisotropy in both the in-plane and out-of-plane orientations. Specifically, the out-of-plane orientation exhibits a higher MAE compared to the in-plane configuration, suggesting that the magnetic easy axis of the MoB3 monolayer aligns along the z-axis. The MAE value reaches up to 865 μeV/Mo, which surpasses those of various 2D materials such as CrI3 (685 μeV/Cr),49 CrXTe3 (X = Si, Ge, Sn; 69–209 μeV/Cr),50 GdI2 (553 μeV/Gd),51 CrGa2Se4 (380 μeV/Cr),52 VOF (410 μeV/V),53 Mn2C (25 μeV/Mn),54 and MnP (166 μeV/Mn),55 underscoring the potential of MoB3 for magnetoelectronic applications.

To unravel the origin of magnetism in 2D MoB3, we conducted an analysis of the magnetic exchange interactions within the sheet. Notably, the distance between Mo–B atoms is 2.25 Å, which is even smaller than that in the MoB solid (I41/amd phase, 2.51 Å), suggesting the likelihood of magnetic exchange interactions between Mo···Mo atoms being mediated through the intermediate B atoms due to the short Mo–B bond length. In contrast, the distance between nearest-neighbor Mo–Mo atoms is 2.99 Å, indicating a relatively larger separation compared to the bond length in the Mo solid (Im3M phase, 2.74 Å). This implies while the electron wave functions of Mo atoms may exhibit slight overlap, the direct interaction between Mo···Mo atoms is relatively limited in significance compared to the superexchange interaction. The analysis is consistent with the Goodenough–Kanamori–Anderson rule,56 which posits that the superexchange interaction typically favors AFM ordering.

To develop spintronic devices operable under ambient conditions, their critical temperatures must exceed room temperature. We hence estimated the Néel temperature (TN) of MoB3 monolayer using Monte Carlo (MC) simulations based on Heisenberg model. We have taken into account both the nearest neighbor (J1) and the next-nearest neighbor (J2) interactions. The values estimated using the PBE+U method are J1 = −134.96 meV and J2 = 128.76 meV. These estimates are also consistent with the results obtained from the HSE method, where J1 = −114.74 meV and J2 = 108.97 meV. The temperature-dependent magnetization based on PBE+U method was illustrated in Figure 3d, revealing a TN for the MoB3 monolayer of approximately 1050 K. This value is one of the highest recorded TN to date, surpassing many previously studied materials, such as Mn2C (∼720 K),57 FeAs (ranging from 335 to 710 K),58 Fe2Si (∼780 K),59 penta-MnN2 (∼913 K),60 and Cr2BN (∼874 K).61 This suggests its high feasibility for device applications.

Figure 3 MAE of (a, b) MoB3 monolayer by rotating the spin within the x–y and x–z planes, respectively. (c) The spin charge density distribution with the isosurface value of 0.05 eÅ–3. The yellow and green denote the spin-up and -down polarization, respectively. (d) The normalized magnetic moment of the MoB3 monolayer as a function of temperature by MC simulations.

The ultrafast demagnetization has spurred significant interest as it presents a potential avenue for achieving control over magnetization on an ultrafast time scale.62 The transient temperatures of both electrons and phonons under varying pulse intensities are presented in Figure 4a–c. Initially, the system was equilibrated at 300 K prior to thermalization. Upon exposure to a 50 fs laser pulse, a nonequilibrium distribution of electrons is triggered in the MoB3 sheet. Subsequently, at various time scales, these nonequilibrium electrons redistribute their energy primarily through electron–electron Coulomb interactions. As a result, the temperatures of both electrons and phonons initially increase. However, due to the lower heat capacity of electrons (Ce) compared to phonons (Cp) at room temperature, the temperature increase in electrons is significantly greater than that in phonons. For a pulse power of 5.0 mJ/cm2, the electron temperature begins to decline after 190 fs, as energy is transferred from optically excited “hot” electrons to the lattice during the electron–phonon thermalization process. By τ = 780 fs, both electrons and phonons achieve thermal equilibrium at a temperature of 350 K. Notably, increasing the pulse intensity extends the time required to reach this equilibrium state and, thus, prolongs the electron–phonon thermalization process.

Figure 4 (a–c) Dependence on time of electronic temperatures (Te) and phonon temperatures (Tp) under pulse irradiation. (e, f) Evolution of magnetic moments for spin up and down Mo atoms under pulse irradiation. The laser pulse power is set to 5.0, 7.0, and 9.0 mJ/cm2.

To explore ultrafast demagnetization of MoB3 under laser irradiation, the material was first stabilized at 300 K to allow sufficient time for system thermalization. Gaussian-enveloped laser pulses with powers of 5.0, 7.0, and 9.0 mJ/cm2 were deployed. The dynamic response of the magnetization (M, normalized to the unpumped magnetization, M0), as a function of time, is depicted in Figure 4e,f. Taking the 5.0 mJ/cm2 pulse as an example, the normalized magnetic moment dropped to 0.69 within the time τde of 160 fs, representing a 31% demagnetization. Increased laser intensity boosts the rate of demagnetization; for instance, 44% demagnetization occurs with the 9.0 mJ/cm2 pulse. Furthermore, demagnetization in MoB3 slightly accelerates with increased laser intensity, and it is followed by a remagnetization process (indicated by the green region), typically taking about τre = 300 fs to reach equilibrium.

The rapid and active magnetization response under laser pulses is closely linked to the unique features of the material’s DNL. As a DNL semimetal, MoB3 can provide multiple Dirac points at the Fermi level, where electrons not only possess ultrahigh Fermi velocity but also contribute significantly to the demagnetization process. The extended electronic states near the Fermi level afforded by the DNL result in longer carrier lifetimes, enhancing the interaction between spins and carriers during laser excitation. This interaction can lead to more efficient demagnetization processes. Additionally, DNL semimetals often exhibit spin-momentum locking, whereby the spin direction of electrons is correlated with their momentum direction. This relationship facilitates more efficient spin relaxation processes during laser excitation, subsequently speeding up the demagnetization process. The defined spin direction associated with spin-momentum locking ensures a precise pathway for energy transfer between spins and carriers, enhancing the effectiveness of these processes during laser excitation.

We should note that the ultrafast demagnetization of MoB3 reflects a direct decrease in the magnetic moment, leading to a transition from a DNL semimetal to a metal. For instance, with a 9.0 mJ/cm2 pulse, the magnetic moment of MoB3 is maximally reduced to approximately 1.8 μB per Mo atom at the end of the demagnetization. The reduction in the magnetic moment causes a significant change of the band dispersions, triggering a transition from a DNL semimetal to a trivial metal (Figure S10). This phenomenon is closely tied to changes in orbital hybridization at the Fermi level, especially for the change of the dx2–y2 orbital (Figures S11 and S12). The laser-induced ultrafast electronic state change provides a novel method for manipulating material properties, distinguishing it from traditional methods such as strain, doping, and applying electric fields.

Furthermore, we found that the magnetism and Néel temperature of MoB3 can be modulated through strain engineering. However, the DNL is robust under strain due to its protection by mirror symmetry (Figures S13–S17). We also extended our study to include bilayer configurations, investigating how stacking influences these properties. We discovered that the magnetic ground state, band structure, MAE, and transition temperature can be effectively modifiable by varying the stacking orders. Additionally, the bilayer form exhibits ultrafast spin dynamics when it is subjected to laser pulses. Detailed discussions are provided in the Supporting Information (Figures S18–S21).

In summary, we have established a highly stable MoB3 monolayer with exceptional electronic and magnetic properties. The MoB3 monolayer features an AFM ground state and possesses two 4-fold degenerate Dirac points near the Fermi level, forming a DNL centered at the Γ point within the first Brillouin zone. The DNL is protected by horizontal mirror symmetry, and is further stabilized by the quantized Berry phase due to the inversion symmetry and effective time reversal symmetry. The MoB3 monolayer exhibits a high MAE and an exceptionally high Néel temperature of 1050 K, the highest reported for 2D AFM Dirac semimetals. It also exhibits ultrafast demagnetization under laser irradiation. The unique blend of a high Néel temperature, elevated carrier mobility, and rapid spin dynamics positions the MoB3 monolayer not only as a pivotal material for future spintronic technologies but also as a platform for exploring new quantum functionalities in 2D materials.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.4c02914.Computational methods of this work; stabilities, charge density distribution, charge density difference, magnetic configurations, AIMD simulations, PDOS and HSE band structure for the MoB3 monolayer; Electronic properties, magnetic properties and Néel temperature of the MoB3 monolayer under strain effect; Structural configurations, band structures, Néel temperature, magnetic configurations and spin dynamics for the MoB3 bilayers (PDF)

Supplementary Material

nl4c02914_si_001.pdf

Author Contributions

Y.J.: conceptualization, investigation, validation, writing–review and editing, and funding acquisition. F.M.: resources, supervision, formal analysis, and funding acquisition. Z.G.: investigation, formal analysis, visualization, data curation, and writing–original draft. A.D. and Y.L.: investigation and formal analysis. Q.Z. and Z.Z.: formal analysis (concerning symmetry analysis).

The authors declare no competing financial interest.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 12204144 and 11904077), the Natural Science Fund of Hebei Province (Grant Nos. A2022205027, A2024205029, and A2021205024), and financial support program from Hebei Province (Grant Nos. C20220503 and C20230509).
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