High Throughput Discovery of 2D Ferromagnetic and Multiferroic Transition Metal Oxyhalides and Nitrogen Halides 

High Throughput Discovery of 2D Ferromagnetic and Multiferroic Transition Metal Oxyhalides and Nitrogen Halides | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article High Throughput Discovery of 2D Ferromagnetic and Multiferroic Transition Metal Oxyhalides and Nitrogen Halides Shaowen Xu, Fanhao Jia, Ning Dai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5980980/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 10 Oct, 2025 Read the published version in npj Computational Materials → Version 1 posted 10 You are reading this latest preprint version Abstract Two-dimensional (2D) transition metal oxyhalides and nitrogen-halides (TMBXs, where TM = transition metal, B = O-group and N-group elements, X = halogen) have emerged as promising candidates for exploring multiferroic orders and spintronic applications. In this study, we conduct a systematic first-principles high-throughput screening combined with machine learning to identify novel 2D ferromagnetic and multiferroic materials within TMBX family. From a comprehensive dataset comprising 672 TMBX monolayers, we identify 78 ferromagnetic systems, of which 38 exhibit high Curie temperatures (TC ≥ 200 K), significantly expanding the known library of 2D magnetic materials. A machine learning model is developed to elucidate the key factors governing ferromagnetism, revealing that the second-nearest neighbor exchange interaction (J2) plays a dominant role in determining TC. Furthermore, we discover seven ferromagnetic-ferroelectric multiferroic systems, revealing unique polarization switching pathways. Notably, spin transport simulations using the nonequilibrium Green's function formalism demonstrate exceptional spin filtering capabilities (~ 100 %) and giant bias-dependent tunneling magnetoresistance (> 105 %). These findings deepen the fundamental understanding of 2D multiferroics and establish a solid platform for future experimental exploration and the development of next-generation spintronic devices. Physical sciences/Physics/Condensed matter physics/Electronic properties and materials Physical sciences/Physics/Condensed matter physics/Ferroelectrics and multiferroics Physical sciences/Physics/Condensed matter physics/Ferromagnetism Physical sciences/Physics/Condensed matter physics/Magnetic properties and materials Physical sciences/Physics/Condensed matter physics/Spintronics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Two-dimensional (2D) magnetic materials have garnered significant attention as promising candidates for next-generation high-density spintronics applications 1,2 . Various 2D magnetic materials have been discovered and synthesized, including transition metal halides 3,4 , chalcogenides 5 , carbonitrides 6 , covalent organic framework 7 , and their heterostructures 8,9 . However, a persistent challenge undermining their practical utility is their intrinsically low intrinsic Curie temperature ( T C ), typically below 200 K, as exemplified by materials such as CrI 3 3 , Cr 2 Ge 2 Te 6 10 and Fe 3 GeTe 2 11 , which greatly limits their potential for room-temperature device applications. The Heisenberg model offers foundational insights into strategies for enhancing the T C , emphasizing the importance of strengthening the exchange interaction J and magnetic anisotropy energy (MAE) or increasing the coordination number of neighboring spins. In honeycomb lattice systems, such as CrI 3 and Cr 2 Ge 2 Te 6 , the limited coordination number of three nearest neighbors constrains the cumulative magnetic interaction strength. Conversely, triangular lattice systems, with six nearest neighbors, benefit from a potentially higher interaction density; however, their high symmetry often diminishes MAE, reducing the magnetic stability. Moreover, the exchange interactions in most triangular lattice materials remain relatively weak, further limiting their capacity to achieve high T C . In comparison, rectangular lattice magnetic materials remain significantly underexplored relative to their honeycomb and triangular counterparts. These systems may offer a promising avenue for achieving an optimal trade-off among the number of nearest neighbors, exchange interaction strength, and MAE, potentially facilitating the design of high- T C 2D magnets. Among the prospective candidates, ternary transition metal oxyhalides and nitrogen-halides T M BXs (where T M represents transition metals; B denotes elements form the oxygen or nitrogen groups; and X denotes halogen elements), emerge as a compelling system for investigating rectangular magnetic lattices. Bulk T M BX materials exhibit a layered orthorhombic structure characterized by a variety of magnetic ground states. Their rectangular monolayer derivatives display pronounced uniaxial in-plane magnetic anisotropy, attributable to substantial in-plane lattice anisotropy 12 . Despite this promise, the T C of experimentally synthesized T M BX monolayers has yet to surpass 200 K, a constraint primarily arising from the limited diversity of systems explored thus far. A notable example is the CrSBr monolayer 13,14 , a ferromagnetic semiconductor with a T C of ~ 150 K 15 . This material has revealed lots of intriguing properties, including magnetoelastic coupling 16 , a magnetic high-order topological insulator phase 17 , multiferroic behavior 18,19 , magnetic bimerons 20 , giant magnetoresistance 21 and spin-spiral magnetic ordering 22,23 . Meanwhile, theoretical studies have intermittently predicted T C values exceeding room temperature for certain T M BX monolayers, such as MnNI (~310 K) and VNI (~ 500 K) 24,25 , suggesting significant untapped potential within this material family. Given the challenges associated with fast experimental synthesis, first-principles high-throughput calculation could greatly accelerate the study of the fundamental electronic and magnetic properties of T M BX system. Several primary questions of this ternary system could be answered through the calculations, including the upper bound of the ferromagnetic T C , the magnetic phase diagram, the key physical parameters governing magnetism, and possible couplings with ferroelectric polarization. By systematically mapping these properties, this study aims to unlock the full potential of rectangular lattice T M BX materials, paving the way for the rational design of 2D magnetic materials with enhanced T C and functionalities for spintronics applications. High-throughput density functional theory (DFT) calculations were performed for 672 T M BX monolayers, in which we screened out 78 ferromagnetic and 38 ferromagnetic candidates with T C ≥ 200 K. Contemporary data mining techniques were employed to analyze the principal physical and chemical factors influencing T C . Additionally, a predictive model was developed using the sure independence screening and sparsifying operator (SISSO) method 26 to predict T C for this ternary system. Among these high- T C candidates, six systems were identified as multiferroic, concurrently displaying ferromagnetism and in-plane ferroelectricity. Their ferroelectric switching pathways and the interplay between their ferroelectric and magnetic properties were thoroughly assessed. Furthermore, a two-probe spin transistor based on T M BXs was designed, and its spin-polarized transport properties were investigated using the non-equilibrium Green’s function (NEGF) formalism. The results demonstrate remarkable spin-filtering efficiency and substantial tunneling magnetoresistance, highlighting the considerable promise of these materials for advanced nanomagnetic device applications. Results High-throughput and data screening T M BXs monolayer manifests a rectangle lattice as shown in Fig. 1a. Its monolayer comprises four atomic layers, with transition metal atoms adopting a distorted octahedron coordination. The structure follows the prototype structure of CrSBr system (with point group symmetry of D 2h ), where the oxygen-group and nitrogen-group atoms are located in the middle two atomic layers and forming ionic bonds with the transition metal, while the halogen atoms are located in the outermost atomic layer. The unequal bond lengths of T M - B and T M - X lead to a large distortion of the octahedron and strong in-plane anisotropy. As a result, the doubly degenerate e g orbitals spilt into two distinct orbitals, while the triply degenerate t 2g orbitals split into three separate orbitals. For example, in VSeF system, e g orbitals split into two a 1 orbitals, and t 2g orbitals split into b 1 , b 2 , and a 2 orbitals 19 . The detailed d -state splitting configurations of various T M element can be found in Table S1 (Supporting Information). Fig. 1b gives the workflow of the high-throughput calculations and data screening for the large T M BX family. Due to this study focus on the magnetic properties, we only select the element set of {V, Cr, Mn, Fe, Co, Ni, Cu, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Ta, W, Re, Os, Ir, Pt, Au} with 21 elements for the T M site. It should be pointed out that Tc is a radioactive element. Here, for the continuity of the element's properties, we did not exclude T c for data analysis. While 4 oxygen-group and 4 nitrogen-group elements were selected for the B site, and 4 halogen elements were used for the X site, as shown in the inset element table of Fig. 1b. In this way, 672 T M BX s can be constructed as the initial compound set through element substitution based on the prototype rectangular structure of CrSBr. We discarded those nonmagnetic (NM) systems and applied formation energy stability filtering to the entire set (see Fig. S1), leaving 310 stable T M BX s, among which 78 FM compounds and 232 AFM compounds were identified. Fig. 1c shows the relative stability and magnetic property distributions of the entire set. After the electronic structure calculation, 78 FM compounds can be further divided into 41 FM half metal/metal and 37 FM semiconductors (Fig. S2). The second branch of the high-throughput workflow is to identify the possible ferroelectric (FE)/multiferroic materials. We introduced artificial slight distortion into the nonpolar high symmetry structure (with point group of D 2h ), as a result the structure symmetry was reduced to a polar symmetry of C 2v . By comparing the relative energy, we screened out 7 ferroelectric and 4 antiferroelectric (AFE) T M BX s from the 78 FM compounds. The 2D ferroelectric T M BX s possess in-plane polarization along the b -axis as shown in the inset of Fig. 1d. Then, we calculated their spin exchange interaction parameters (listed in Table S2). The Monte Carlo (MC) simulations of anisotropic Heisenberg model were performed for all 78 FM systems. Three nearest-neighbor interactions were considered, which have been roughly labeled in Fig. 1a, respectively. The details of the MC simulation and spin exchange interaction were given in section 2.1 of the Supporting Information . In the end, we screened out 38 high- T C FM candidates with T C ≥ 200 K (listed in Table S3). Among them, 7 compounds possess polar structures, whose dynamical and thermodynamic stabilities were confirmed (Fig. S3-S5). Ferromagnetism and High- T C In Fig.2a, 672 T M BX compounds were divided into FM, AFM and NM subsets according to their T M -site elements. In line with the cognition, common NM transition metal systems, such as those containing noble metals and Cu, Nb, etc., do not appear magnetism, while Mo and Ta are the exceptions. To surprise, T M BX s with Fe, Co and Os are all AFM. As for Ni BX s, the number of AFM cases is also more than twice that of FM cases. Moreover, the number of AFM materials accounts for 34.2% of the total T M BX , while FM materials only account for 11.6%. As shown in Fig.2b, AFM is almost three times the number of FM. In contrary, from existing crystal databases, such as the Materials Project 27 , AFM materials account for less than 10% of magnetic materials. This implies that the rectangle T M BX lattice system must have super exchange characteristics that are more suitable for AFM. In addition, these AFM T M BX s all favor the high-symmetry D 2h lattice, while FM T M BX s allows for polar distortions. Among those FM compounds, the proportions of 3 d -, 4 d - and 5 d- T M -based systems are 74%, 22% and 4%, respectively. Fig. 2c shows the specific T C of 38 screened-out high- T C ( T C ³ 200 K) FM candidates, which are 15 semiconductors and 23 half-metals, respectively. It’s worth mentioning that 26 of them are room-temperature ferromagnets with T C ³ 300 K. Due to the strongest localization of 3d electrons, 89% of high- T C compounds are 3 d - T M BX , i.e., T M = {V, Cr, Mn, Ni}-based compounds. The left 11% are MoN Xs , where each Mohas the magnetic moment of 2 μ B . The MoN X s were also predicted to be high T C monolayers in previous works 28 . Another interesting trend is that, for most T M BX s that have the same T M and B , the larger the electronegativity of halogen X , the lower the T C , indicating the important role of charge transfer in determining the T C (Table S4). In addition, as the electronegativity of X increases, the system tends to transform from a metal to a semiconductor (Fig. S2). For the example shown in Fig. S6, the band gaps of MnO X s increase from 0 to 1.5 eV. Though the analysis of the electronic structure(Fig. S7-S9), when B is oxygen-group element, the bands near the Fermi level are primarily contributed by T M - d orbitals, B and X-p orbitals. Conversely, when B is nitrogen-group element, the dominant contributions are only from the T M and B . Machine learning models in predicting T C and J To gain a more comprehensive understanding of the T C of the 78 FM T M BXs , we used the gradient boosting method 29 to evaluate the relative importance of the parameters in the effective Hamiltonian and the fundamental properties of the elements. As shown in Fig. 3a, the second-nearest exchange parameter J 2 plays a dominating role in determining the T C , rather than the J 1 . For most T M BXs , J 2 manifests the diagonal supe-exchange interaction along the T M - X - T M path. Thereby, we see the significant effect of halogen elements on modulating the T C as we discussed in the last section. However, even J 2 itself contains too much information, including from the electronic structure, occupancy and lattice. In Fig. 3b, we see that the intensity of J 2 relates to the magnet moment ( M ), nearest-neighbor T M - T M distance length ( L 1 ) and band gap at the same time, so it’s hard to quantify J 2 with a few simple parameters. Therefore, we derived two SISSO machine learning models to predict the T C and J 2 , respectively. These model allows us to maximize the data utilization of a small dataset by constructing high-dimensional descriptors from simple fundamental features 26 . 15 simple features, including the electronic, lattice- and element-related features, were used for SISSO, which were summarized in Table S5. The produced high-dimensional descriptors were given in Supplementary Materials . Then, linear model using these SISSO descriptors can be constructed. For predicting T C and J 2 , our linear models reach well accuracy with the root mean square error (RMSE) of 33.59 K and 5.36 meV, respectively. Multiferroic properties The T M BX family also provides an ideal setting for studying 2D multiferroic and exploring the coupling between electric, magnetic, and structural order parameters 30 . To make the discussion more concise, we will refer to these polar metallic structures as “FEs” just for discussions despite that their polarization cannot be switched by an electric field. The AFE-FM systems are also called multiferroics for discussions, whose polarization cannot be switched as well. Table 1 has listed 11 selected high- T C T M BXs that possess rich order parameters. They are VN X s ( X = F and Cl), CrNF, MnO X s, and MoN X s ( X = F, Cl, Br, and I), respectively. Among them, MnO X s and MoNCl are conventional FE-FM multiferroics with the band gaps ranging from 0.16 to 1.58 eV. VN X s ( X = F and Cl) and MoN X s ( X = Br and I) are AFE-FM multiferroics. Here, MoNF is more special than other systems. Its ground state coexists FE-FM and AFE-FM multiferroics, which will be addressed in detail later. The in-plane polarizations of these FE T M BX systems range from 2.4 to 9.0 μ C/cm², and they need overcome moderate energy barriers from 16 to 252 meV/ f.u. to switch the polarization. Switching the polarization of metallic T M BX s need overcome a much higher energy barrier. To our surprise, the switching energy barrier of AFE systems are even lower than most FE systems. The magnetic easy axes, MAE and T C are also given in Table 1. Interestingly, these 11 high- T C multiferroic systems happen to be the only ones with low lattice symmetry ( C 2h and C 2v ) among the 78 FM systems. Fig. 4a shows three types of the polarization switching path existing in T M BX systems, which are FE-PE-FE, FE-AFE-FE, and AFE-PE-AFE. MnO X ( X = F, Cl, and Br) systems favor the FE-AFE-FE path, while MoO X ( X = F, Br, and I) systems favor the AFE-PE-AFE path (Fig. S10). The envelope of the polarization switching energy of MnOF and MoNF selected as examples were displayed in Fig. 4b. For MnOF, the energy barrier Δ E of the FE-AFE-FE path is much lower than the FE-PE-FE path. Moreover, the middle point of its switching path (corresponds to the AFE phase) possess similar energy with respect to its ground-state FE structure, indicating the polymorphism nature of this system. The comparation of two switching paths for MnOCl and MnOBr were displayed in Fig. S11, which possess similar characteristics to that of MnOF. The MoNF system exhibits unique characteristics that distinguish it from other systems. The relative energy difference between the FE and AFE phases is remarkably small, within 10 meV per formula unit ( f.u. ). The ground-state structure of MoNF is identified as a ferroelectric phase, as illustrated in Fig.S10. The ferroelectric polarization is oriented along the b -axis, determined by analyzing the imaginary mode of the paraelectric (PE) structure. Both the FE and AFE phases are dynamically stable. The FE phase possesses a 9.0 μ C/cm² in-plane polarization, and favors the FE-PE-FE switching path with an energy barrier of 114 meV/ f.u. . While the AFE phase favors the AFE-PE-AFE switching path, which has a much lower energy barrier of 55 meV/ f.u. . It is also worth mentioning that there are numerous AFM-FE systems with large net polarizations, such as PtOCl, OsOCl, PdOF, and MoOF, which also deserves further in-depth investigations to fully understand their properties and potential applications. From the perspective of magnetic properties, the magnetic easy axes of T M BX systems also have diverse orientations, enabling them to display distinct magnetoelectric coupling behaviors. For MnO X systems, their magnetic easy axes are along the c -axis but with a small canting in the bc -plane. The easy axes of the VNF and CrNF are along the b -axis (polar axis). The magnetic easy axis of AFE-MoN X systems is along the a- axis, while that of FE-MoNF is along the b -axis (polar axis). This means that if the ferroelectric polarization of FE MoNF is switched, the magnetic easy axis will also be switched. The simulated T C of FE and AFE MoNF are shown in Fig. 4c, and their MAE and exchange coupling parameters were listed in Table 2. The FE MoNF shows a T C of480 K, while the AFE MoNF shows a lower T C of 360 K. This is due to that FE shows a much larger J 2 and MAE, which play the dominate role in determining T C . More interesting, AFE MoNF could form stable Bloch and Néel type merons near the domain wall at approximately 110 K as shown in Fig. 4d and Fig. S12. Spin-polarized transport Next, we investigate the spin-polarized transport properties of T M BX s. A two-probe spin transistor was constructed, comprising a central region made of a FM semiconductor CrSBr monolayer sandwiched by left and right electrodes made of a FM half metal CrNF, as shown in Fig.5a. The electrodes extend to y = ±∞ where the current is collected. The transport direction of Fig.5 is along the b -axis, while the transport simulation along the a -axis was given in Fig. S13. Two types of magnetic configuration of the CrNF electrodes were considered, which are spin parallel configuration (PC) and spin anti-parallel configuration (APC), respectively. The current-voltage dependences of two spin configurations were shown in Fig.5c. We have considered a bias voltage from 0.0 to 0.6 V, where the linear current-voltage relationship was maintained. On the other hand, compared to the PC device, APC device exhibits significantly higher resistance due to the existing tunnel magnetoresistance effect. The parallel spin carriers can easily tunnel through the semiconductor layer, indicating the great potential of T M BX systems in spin filtering applications. To quantify the spin transport performance, we defined the spin injection efficiency (SIE) and tunneling magnetoresistance (TMR) as following: where I ↑ , I ↓ , I PC , and I APC are the spin-up current, the spin-down current, the current of PC device and the current of APC device, respectively. Since I ↓ is almost equal to zero in our systems, a nearly fully spin-polarized current is generated (SIE ~ 100%, shown in the inset of Fig. 5d). Then, TMR shows a large dependence on the bias voltage (Fig. 5d). There is a maximum TMR of 5.2×10 5 % along a -axis and 2.5×10 6 % along b -axis when under a bias of 0.1 V, which is much larger than those measured in the ZrTe 2 /CrOCl/CrOCl/ZrTe 2 (2.5×10 4 %) 31 , graphene/CrI 3 /graphene (1.9×10 4 %) 32 and (Fe 0.8 Co 0.2 ) 3 GaTe 2 /WSe 2 /Fe 3 GaTe 2 (1.8×10 2 %). The transmission spectra under a bias of 0.1 V were presented in Fig. 5e and 5f. Under a bias of 0.1 V, the transmission coefficient T PC approaches 0.5, while T APC approximately equals to 0. Moreover, the transmission spectrum implies that almost completely spin-polarized transmission can be achieved in a broad energy window from -0.8 to 3 eV. Discussion In this work, we have conducted a comprehensive high-throughput investigation of the T M BX s, uncovering a rich landscape of ferromagnetic and multiferroic properties. By screening 672 T M BX systems, 78 ferromagnetic monolayers were identified, 38 of which had high Curie temperatures ( T C ≥ 200 K), greatly expanding the known 2D magnets. Machine learning models were developed to reveal the critical role of the second-nearest neighbor exchange interaction in determining T C , offering a new insight for designing 2D magnets. Additionally, we discovered seven FM-FE multiferroics, exhibiting unique polarization switching mechanisms. Spin transport simulations demonstrate that T M BX monolayers exhibit exceptional spin filtering and tunneling magnetoresistance (>10 5 %), making them highly promising for spintronic applications. These findings provide a solid foundation for future experimental studies and the development of next-generation 2D multiferroics. Methods Density Functional Theory First-principles calculations were performed within generalized gradient approximation (GGA) in the form proposed by Perdew, Burke, and Ernzerhof (PBE) 33 using Vienna ab initio simulation package (VASP) 34 . The lattice relaxations adopted a vdW functional optB88-vdW 35 . Atomic positions were relaxed until the maximum force on each atom was less than 10 -3 eV/Å. A 600 eV energy cutoff and a 10´10´1 Γ-centered k grid of were used. And a vacuum layer more than 25 Å was applied to avoid the interaction between periodic images. To reduce the self-interaction error of T M - d orbitals, we have considered the Hubbard correction 36 . The effective Hubbard U parameter ( U eff ) for V, Cr, Mn, Fe, Co, Ni and Mo are 3.3 eV, 3.7 eV, 4.0 eV, 5.3 eV, 4.0, 6.2, and 4.0 eV, respectively. The Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional was used to correct the problem of severe underestimation of the band gap by PBE 37 method. Spin-orbit coupling (SOC) was taken into account in determining the magnetization easy axis. Phonon dispersion was calculated using density-functional perturbation theory (DFPT) with VASP-PHONOPY interface 38,39 . The Born effective tensor is defined as: in which e is the charge of electron, p is polarization, and u is the atomic displacement from its high-symmetry nonpolar position. The calculated polarization of 2D materials strongly depends on the thickness of slab we chose. Here, we added two extra 1 Å thcikness along the c -axis on both sides of T M BX monolayers when calcauling the volume W . The polarization was calcualted using Born effective charge method. Quantum transport Transport properties of the device were calcualted using Nanodcal 40 within the NEGF-DFT framwork 41 . The DZP atomic orbital basis is used to expand all the physical quantities; the exchange and correlation are treated at the level of PBE functional; and atomic cores are defined by the standard norm conserving nonlocal pseudopotentials, and 16 × 16× 1 k-points were used. Under certain bias V b , the spin current I was calcualted as follows: is the spin index. The integration is over the bias window between m L and m R which are the electrochemical potentials of the top/bottom leads. The total current is given by I total = I ↑ + I ↓ . Declarations Competing interests The authors declare no conflict of interest. Author Contribution S.X. carried out the calculations and wrote the manuscript under the supervision of F.J. and N.D. All authors reviewed the manuscript. F.J. and N.D. conceived and led the entire scientific project. Acknowledgement The work was supported by the National Science Foundation of China (Grant No. 12347115), China Postdoctoral Science Foundation (No. 2024M760690), and Hangzhou Science and Technology Bureau of Zhejiang Province (No. TD2020002). Work at HDU was supported by Zhejiang Provincial Natural Science Foundation (QN25A040026), and the Foundation of Hangzhou Dianzi University (KYS075624288). We gratefully acknowledge HZWTECH for providing computation facilities. S. Xu thanks Taozhen Fu (from HZWTECH) for help and discussions on this study. Data availability The data that support the findings of this study are available from the corresponding author upon reasonable request. Code availability The code is available from the corresponding author upon reasonable request. Additional information Supplementary information The online version contains supplementary material available at XXX . Correspondence and requests for materials should be addressed to Fanhao Jia. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. References Jia, Z. et al. Spintronic Devices upon 2D Magnetic Materials and Heterojunctions. ACS Nano 19 , 9452-9483 (2025). Ahn, E. C. 2D materials for spintronic devices. npj 2D Materials and Applications 4 , 17 (2020). Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546 , 270-273 (2017). Bedoya-Pinto, A. et al. Intrinsic 2D-XY ferromagnetism in a van der Waals monolayer. Science 374 , 616-620 (2021). Chua, R. et al. Room temperature ferromagnetism of monolayer chromium telluride with perpendicular magnetic anisotropy. Advanced Materials 33 , 2103360 (2021). Balasubramanian, K., Khare, S. V. & Gall, D. Valence electron concentration as an indicator for mechanical properties in rocksalt structure nitrides, carbides and carbonitrides. Acta Materialia 152 , 175-185 (2018). Li, W., Zhu, D., Dong, S. & Zhang, J.-J. Two-dimensional multiferroic NbPc covalent organic framework with strong magnetoelectric coupling and room-temperature ferroelectricity. Physical Review B 111 , 035439 (2025). Papavasileiou, A. V. et al. Ferromagnetic Elements in Two‐Dimensional Materials: 2D Magnets and Beyond. Advanced Functional Materials 34 , 2309046 (2024). Zhang, Z., Sun, R. & Wang, Z. Recent Advances in Two-Dimensional Ferromagnetic Materials-Based van der Waals Heterostructures. ACS Nano 19 , 187-228 (2025). Zhuo, W. et al. Manipulating ferromagnetism in few‐layered Cr2Ge2Te6. Advanced Materials 33 , 2008586 (2021). Wu, Y. et al. Interlayer engineering of Fe3GeTe2: From 3D superlattice to 2D monolayer. Proceedings of the National Academy of Sciences 121 , e2314454121 (2024). Villalpando, G. et al. Chemical exfoliation toward magnetic 2D VOCl monolayers. ACS Nano 16 , 13814-13820 (2022). Rizzo, D. J. et al. Visualizing atomically layered magnetism in CrSBr. Advanced Materials 34 , 2201000 (2022). Boix‐Constant, C. et al. Programmable Magnetic Hysteresis in Orthogonally‐Twisted 2D CrSBr Magnets via Stacking Engineering. Advanced Materials , 2415774 (2025). Tschudin, M. A. et al. Imaging nanomagnetism and magnetic phase transitions in atomically thin CrSBr. Nature Communications 15 , 6005 (2024). Fei, F. et al. Spin-mechanical coupling in 2D antiferromagnet CrSBr. Nano Letters (2024). Guo, Z. et al. Magnetic high-order topological insulator in 2D layered CrOCl. Materials Today Physics 36 , 101153 (2023). Xu, S. et al. Intrinsic multiferroic MnOF monolayer with room-temperature ferromagnetism. Materials Today Physics 27 , 100775 (2022). Li, Y. et al. Nonvolatile electrical control of spin polarization in the 2D bipolar magnetic semiconductor VSeF. npj Computational Materials 9 , 50 (2023). Yang, B., Han, X. & Picozzi, S. Emergence of topological bimerons in monolayer CrSBr. arXiv preprint arXiv:2406.17495 (2024). Chen, Y. et al. Twist-assisted all-antiferromagnetic tunnel junction in the atomic limit. Nature 632 , 1045-1051 (2024). Zhang, T. et al. Magnetism and optical anisotropy in van der Waals antiferromagnetic insulator CrOCl. ACS Nano 13 , 11353-11362 (2019). Yang, S., Zhang, T. & Jiang, C. van der Waals magnets: Material family, detection and modulation of magnetism, and perspective in spintronics. Advanced Science 8 , 2002488 (2021). Hu, M. et al. First-principles prediction of a room-temperature ferromagnetic and ferroelastic 2D multiferroic MnNX (X= F, Cl, Br, and I). Nanoscale 12 , 24237-24243 (2020). Zhu, Y. et al. Prediction of 2D ferromagnetic metal VNI monolayer with tunable topological properties. Journal of Applied Physics 132 (2022). Ouyang, R., Curtarolo, S., Ahmetcik, E., Scheffler, M. & Ghiringhelli, L. M. SISSO: A compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates. Physical Review Materials 2 , 083802 (2018). Jain, A. et al. Commentary: The Materials Project: A materials genome approach to accelerating materials innovation. APL Materials 1 , 011002 (2013). Wu, F. et al. Atomically thin transition-metal dinitrides: high-temperature ferromagnetism and half-metallicity. Nano Letters 15 , 8277-8281 (2015). Pedregosa, F. et al. Scikit-learn: Machine learning in Python. the Journal of Machine Learning Research 12 , 2825-2830 (2011). Mostovoy, M. Multiferroics: Different routes to magnetoelectric coupling. npj Spintronics 2 , 18 (2024). Zhang, X. et al. Van der Waals Magnetic Heterojunctions with Giant Zero‐Bias Tunneling Magnetoresistance and Photo‐Assisted Magnetic Memory. Advanced Functional Materials 32 , 2200154 (2022). Song, T. et al. Giant tunneling magnetoresistance in spin-filter van der Waals heterostructures. Science 360 , 1214-1218 (2018). Perdew, J. P. JP Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). Physical Review Letter 77 , 3865 (1996). Kresse, G. G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996). Physical Review B 54 , 11169 (1996). Klimeš, J., Bowler, D. R. & Michaelides, A. Van der Waals density functionals applied to solids. Physical Review B 83 , 195131 (2011). Kan, M., Zhou, J., Sun, Q., Kawazoe, Y. & Jena, P. The intrinsic ferromagnetism in a MnO2 monolayer. The Journal of Physical Chemistry Letters 4 , 3382-3386 (2013). Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. The Journal of Chemical Physics 118 , 8207-8215 (2003). Togo, A., Oba, F. & Tanaka, I. First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures. Physical Review B 78 , 134106 (2008). Togo, A. & Tanaka, I. First principles phonon calculations in materials science. Scripta Materialia 108 , 1-5 (2015). Taylor, J., Guo, H. & Wang, J. Ab initio modeling of quantum transport properties of molecular electronic devices. Physical Review B 63 , 245407 (2001). Stradi, D., Martinez, U., Blom, A., Brandbyge, M. & Stokbro, K. General atomistic approach for modeling metal-semiconductor interfaces using density functional theory and nonequilibrium Green's function. Physical Review B 93 , 155302 (2016). Additional Declarations No competing interests reported. Supplementary Files cleansupporting.pdf Cite Share Download PDF Status: Published Journal Publication published 10 Oct, 2025 Read the published version in npj Computational Materials → Version 1 posted Editorial decision: Accepted 22 Apr, 2025 Reviews received at journal 15 Apr, 2025 Reviews received at journal 11 Apr, 2025 Reviewers agreed at journal 10 Apr, 2025 Reviews received at journal 10 Apr, 2025 Reviewers agreed at journal 10 Apr, 2025 Reviewers agreed at journal 10 Apr, 2025 Reviewers invited by journal 10 Apr, 2025 Submission checks completed at journal 04 Apr, 2025 First submitted to journal 18 Mar, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5980980","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":441406933,"identity":"49630e1c-636d-4763-a61a-1806afd1b625","order_by":0,"name":"Shaowen Xu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYHACNgjF3kCyFp4DJGuRSCBSvcGN9GcPflQcljOXfGP44ccfBnn+BuZnD/BpkZyRY27Yc+awseXsHGPJ3jYGwxkH2MwN8Gnhl8hhk+Btu5244XaOGQNvAwPjBgYeNgm8HpFIfyb5t+12/YabZ8wY//xhsCeohV8iwUwaaEuCwQ0eM2YeNoZEgloke96YScuc+W+44UxasbRsm0TyjMNsZni1GBwHOuxNRZq8wfHDGz+++WNj29/e/AyvFnQAVMxMivpRMApGwSgYBVgBAOnnQdNkGaUxAAAAAElFTkSuQmCC","orcid":"","institution":"Hangzhou Institute for Advanced Study, University of Chinese Academy of Science","correspondingAuthor":true,"prefix":"","firstName":"Shaowen","middleName":"","lastName":"Xu","suffix":""},{"id":441406934,"identity":"a21f5d3a-f8ca-4750-a0a7-0030d4c5eece","order_by":1,"name":"Fanhao Jia","email":"","orcid":"","institution":"Hangzhou Dianzi University","correspondingAuthor":false,"prefix":"","firstName":"Fanhao","middleName":"","lastName":"Jia","suffix":""},{"id":441406935,"identity":"33edcb59-cc4c-4d70-ba57-13a9157ea124","order_by":2,"name":"Ning Dai","email":"","orcid":"","institution":"Hangzhou Institute for Advanced Study, University of Chinese Academy of Science","correspondingAuthor":false,"prefix":"","firstName":"Ning","middleName":"","lastName":"Dai","suffix":""}],"badges":[],"createdAt":"2025-02-07 12:08:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5980980/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5980980/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41524-025-01620-7","type":"published","date":"2025-10-10T15:57:05+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":80368235,"identity":"7d3b87cb-5f98-46ba-bdf5-cb086cc6583e","added_by":"auto","created_at":"2025-04-11 06:06:29","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":692524,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eHigh-throughput and screening workflows\u003c/strong\u003e. a) Schematic diagram of \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eBX\u003c/em\u003e monolayer structure, where the blue, red and yellow balls are transition metal, oxygen or nitrogen groups and halogen atoms. \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, and \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e are the spin exchange interactions. b) Workflow diagram of high-throughput calculation and the screening of magnetic/multiferroic materials. c) The phase diagram of ferromagnetic (FM), antiferromagnetic (AFM) and non-magnetic (NM) monolayers. Red, gold, and dark cyan squares represent FM, AFM and NM, respectively. The white square represents unstable systems. The inserted diamond marker represent that they are semiconductors. d) The number of paraelectric (PE), ferroelectric (FE) and antiferroelectric (AFE) structures. The arrow corresponds to the in-plane polar displacement.\u003c/p\u003e","description":"","filename":"Figure1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5980980/v1/cda6c343c76f384c9393c0f6.jpg"},{"id":80368928,"identity":"28c0aeea-4977-4dc1-85ca-8219b2f8dbf3","added_by":"auto","created_at":"2025-04-11 06:14:29","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":793814,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFerromagnetic properties of \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eT\u003c/strong\u003e\u003c/em\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003eM\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e\u003cstrong\u003eBX\u003c/strong\u003e\u003c/em\u003e monolayers. a) The number of FM, AFM and NM \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eBXs\u003c/em\u003e with the same \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e. b) The proportion of FM, AFM and NM \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eBXs\u003c/em\u003e. The occurrence of 3\u003cem\u003ed\u003c/em\u003e-4\u003cem\u003ed T\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e in FM systems. c) High-\u003cem\u003eT\u003c/em\u003e\u003csub\u003eC \u003c/sub\u003e(\u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e \u0026gt; 200 K) FM \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eBX\u003c/em\u003e monolayers simulated using the anisotropic Heisenberg model.\u003c/p\u003e","description":"","filename":"Figure2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5980980/v1/5574d8ed3c8a51f4e66e78ad.jpg"},{"id":80368929,"identity":"7b2f43cb-e6fd-4c04-a28a-7818ce41dd1b","added_by":"auto","created_at":"2025-04-11 06:14:29","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":423968,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMachine learning of the magnetic ground states\u003c/strong\u003e. Featuring relative importance in predicting a) \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e and b) \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, respectively. The descriptions of the features were given in Table S5. Inset is the corresponding Pearson correlation (pc) coefficients between the feature and \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e (\u003cem\u003eJ\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e). The comparation of SISSO predicted and DFT calculated c) \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e and d) \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, respectively.\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/p\u003e","description":"","filename":"Figure3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5980980/v1/93dc038de3a42999ce377af8.jpg"},{"id":80368927,"identity":"e1e095c8-4b8e-4b22-8d1a-d52fa93a26dc","added_by":"auto","created_at":"2025-04-11 06:14:29","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":940981,"visible":true,"origin":"","legend":"\u003cp\u003eMultiferroic properties. a) Three types of switching paths of the displacement mode (indicated with the arrows). b) Free energy envelope of the displacement switching. c) The normalized magnetic moment as a function of temperature of AFE and FE MoNF monolayer. d) Selected snapshots of AFE MoNF during the Monte-Carlo (MC) simulations as the temperature decreases from 500 K to 0.1 K. The right panels are enlarged local magnetic vortex and antivortex. Here, red and blue represent spin up and spin down, respectively, while the arrows are the in-plane spin projections.\u003c/p\u003e","description":"","filename":"Figure4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5980980/v1/824feb96e38058030258b510.jpg"},{"id":80368932,"identity":"77584a19-8a9c-455d-acb0-c6cac0ee8b53","added_by":"auto","created_at":"2025-04-11 06:14:29","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":726318,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSpin transport properties\u003c/strong\u003e. Schematic diagram of the two-probe spin transistor of CrNF/CrSBr/CrNF with a) spin parallel configuration(PC) and b) spin antiparallel configuration (APC). c) \u003cem\u003eI\u003c/em\u003e-\u003cem\u003eV\u003c/em\u003e curves of PC (dark green circles) and APC (dark orange squares) devices. d) Tunneling magnetoresistance (TMR) as a function of the bias voltage. Inset is the corresponding spin injection efficiency (SIE). The spin-polarized transmission spectra of e) PC and f) APC devices under 0.1 V bias.\u003c/p\u003e","description":"","filename":"Figure5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5980980/v1/c8a948f25557e3447bebfe19.jpg"},{"id":93419726,"identity":"6b19418d-8d3b-4d03-8a71-4e5daa69c9f1","added_by":"auto","created_at":"2025-10-13 16:06:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4464368,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5980980/v1/bb456f66-5b33-4ea1-9232-592996ed3d30.pdf"},{"id":80368243,"identity":"2d9c8925-6800-4ec3-9bfa-e7521c00d813","added_by":"auto","created_at":"2025-04-11 06:06:29","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":3948427,"visible":true,"origin":"","legend":"","description":"","filename":"cleansupporting.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5980980/v1/9468bb625c057d0770a860cd.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"High Throughput Discovery of 2D Ferromagnetic and Multiferroic Transition Metal Oxyhalides and Nitrogen Halides ","fulltext":[{"header":"Introduction","content":"\u003cp\u003eTwo-dimensional (2D) magnetic materials have garnered significant attention as promising candidates for next-generation high-density spintronics applications\u003csup\u003e1,2\u003c/sup\u003e. Various 2D magnetic materials have been discovered and synthesized, including transition metal halides\u003csup\u003e3,4\u003c/sup\u003e, chalcogenides\u003csup\u003e5\u003c/sup\u003e, carbonitrides\u003csup\u003e6\u003c/sup\u003e, covalent organic framework\u003csup\u003e7\u003c/sup\u003e, and their heterostructures\u003csup\u003e8,9\u003c/sup\u003e. However, a persistent challenge undermining their practical utility is their intrinsically low intrinsic Curie temperature (\u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e), typically below 200 K, as exemplified by materials such as CrI\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e3\u003c/sup\u003e, Cr\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e6\u003c/sub\u003e\u003csup\u003e10\u003c/sup\u003e and Fe\u003csub\u003e3\u003c/sub\u003eGeTe\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e11\u003c/sup\u003e, which greatly limits\u0026nbsp;their potential for room-temperature device applications.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;The Heisenberg model offers foundational insights into strategies for enhancing the \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e, emphasizing the importance of strengthening the exchange interaction \u003cem\u003eJ\u003c/em\u003e and magnetic anisotropy energy (MAE) or increasing the coordination number of neighboring spins. In honeycomb lattice systems, such as CrI\u003csub\u003e3\u003c/sub\u003e and Cr\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e6\u003c/sub\u003e, the limited coordination number of three nearest neighbors constrains the cumulative magnetic interaction strength. Conversely, triangular lattice systems, with six nearest neighbors, benefit from a potentially higher interaction density; however, their high symmetry often diminishes MAE, reducing the magnetic stability. Moreover, the exchange interactions in most triangular lattice materials remain relatively weak, further limiting their capacity to achieve high \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e. In comparison, rectangular lattice magnetic materials remain significantly underexplored relative to their honeycomb and triangular counterparts. These systems may offer a promising avenue for achieving an optimal trade-off among the number of nearest neighbors, exchange interaction strength, and MAE, potentially facilitating the design of high- \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e 2D magnets.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAmong the prospective candidates, ternary transition metal oxyhalides and nitrogen-halides\u003cem\u003e\u0026nbsp;T\u003csub\u003eM\u003c/sub\u003eBXs\u0026nbsp;\u003c/em\u003e(where \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003e\u003c/em\u003e represents transition metals; \u003cem\u003eB\u003c/em\u003e denotes elements form the oxygen or nitrogen groups; and \u003cem\u003eX\u0026nbsp;\u003c/em\u003edenotes halogen elements), emerge as a compelling system for investigating rectangular magnetic lattices. Bulk \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u0026nbsp;\u003c/em\u003ematerials exhibit a layered orthorhombic structure characterized by a variety of magnetic ground states. Their rectangular monolayer derivatives display pronounced uniaxial in-plane magnetic anisotropy, attributable to substantial in-plane lattice anisotropy\u003csup\u003e12\u003c/sup\u003e. Despite this promise, the \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e of experimentally synthesized \u003cem\u003eT\u003c/em\u003e\u003csub\u003eM\u003c/sub\u003e\u003cem\u003eBX\u003c/em\u003e monolayers has yet to surpass 200 K, a constraint primarily arising from the limited diversity of systems explored thus far. A notable example is the CrSBr monolayer\u003csup\u003e13,14\u003c/sup\u003e, a ferromagnetic semiconductor with a \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e of ~ 150 K\u003csup\u003e15\u003c/sup\u003e. This material has revealed lots of intriguing properties, including magnetoelastic coupling\u003csup\u003e16\u003c/sup\u003e, a magnetic high-order topological insulator phase\u003csup\u003e17\u003c/sup\u003e, multiferroic behavior\u003csup\u003e18,19\u003c/sup\u003e, magnetic bimerons\u003csup\u003e20\u003c/sup\u003e,\u0026nbsp;giant magnetoresistance\u003csup\u003e21\u003c/sup\u003e and \u0026nbsp;spin-spiral magnetic ordering\u003csup\u003e22,23\u003c/sup\u003e. Meanwhile, theoretical studies have intermittently predicted\u003cem\u003e\u0026nbsp;T\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e values exceeding room temperature for certain \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e monolayers, such as MnNI (~310 K) and VNI (~ 500 K)\u003csup\u003e24,25\u003c/sup\u003e, suggesting significant untapped potential within this material family.\u003c/p\u003e\n\u003cp\u003eGiven the challenges associated with fast experimental synthesis, first-principles high-throughput calculation could greatly accelerate the study of the fundamental electronic and magnetic properties of \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e system. Several primary questions of this ternary system could be answered through the calculations, including the upper bound of the ferromagnetic \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e, the magnetic phase diagram, the key physical parameters governing magnetism, and possible couplings with ferroelectric polarization. By systematically mapping these properties, this study aims to unlock the full potential of rectangular lattice \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e materials, paving the way for the rational design of 2D magnetic materials with enhanced \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e and functionalities for spintronics applications.\u003c/p\u003e\n\u003cp\u003eHigh-throughput density functional theory (DFT) calculations were performed for 672\u0026nbsp;\u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e monolayers, in which we\u0026nbsp;screened out 78\u0026nbsp;ferromagnetic\u0026nbsp;and\u0026nbsp;38 ferromagnetic candidates with\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e \u0026ge; 200 K. Contemporary data mining techniques were employed to analyze the principal physical and chemical factors influencing \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e. Additionally, a predictive model was developed using the sure independence screening and sparsifying operator (SISSO) method\u003csup\u003e26\u003c/sup\u003e to predict \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e for this ternary system. Among these high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e candidates, six systems were identified as multiferroic, concurrently displaying ferromagnetism and in-plane ferroelectricity. Their ferroelectric switching pathways and the interplay between their ferroelectric and magnetic properties were thoroughly assessed. Furthermore, a two-probe spin transistor based on\u0026nbsp;\u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBXs\u003c/em\u003e was designed, and its spin-polarized transport properties were investigated using the non-equilibrium Green\u0026rsquo;s function (NEGF) formalism. The results demonstrate remarkable spin-filtering efficiency and substantial tunneling magnetoresistance, highlighting the considerable promise of these materials for advanced nanomagnetic device applications.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eHigh-throughput and data screening\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBXs\u003c/em\u003e monolayer manifests a rectangle lattice as shown in Fig. 1a. Its monolayer comprises four atomic layers, with transition metal atoms adopting a distorted octahedron coordination. The structure follows the prototype structure of CrSBr system (with point group symmetry of \u003cem\u003eD\u003c/em\u003e\u003csub\u003e2h\u003c/sub\u003e), where the oxygen-group and nitrogen-group atoms are located in the middle two atomic layers and forming ionic bonds with the transition metal, while the halogen atoms are located in the outermost atomic layer. The unequal bond lengths of \u003cem\u003eT\u003c/em\u003e\u003csub\u003eM\u003c/sub\u003e-\u003cem\u003eB\u003c/em\u003e and \u003cem\u003eT\u003c/em\u003e\u003csub\u003eM\u003c/sub\u003e-\u003cem\u003eX\u003c/em\u003e lead to a large distortion of the octahedron and strong in-plane anisotropy. As a result, the doubly degenerate \u003cem\u003ee\u003c/em\u003e\u003csub\u003eg\u003c/sub\u003e orbitals spilt into two distinct orbitals, while the triply degenerate \u003cem\u003et\u003c/em\u003e\u003csub\u003e2g\u003c/sub\u003e orbitals split into three separate orbitals. For example, in VSeF system, \u003cem\u003ee\u003c/em\u003e\u003csub\u003eg\u003c/sub\u003e orbitals split into two \u003cem\u003ea\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e orbitals, and \u003cem\u003et\u003c/em\u003e\u003csub\u003e2g\u003c/sub\u003e orbitals split into \u003cem\u003eb\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003eb\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, and \u003cem\u003ea\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e orbitals\u003csup\u003e19\u003c/sup\u003e. The detailed \u003cem\u003ed\u003c/em\u003e-state splitting configurations of various \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003e\u003c/em\u003e element can be found in Table S1 (Supporting Information).\u003c/p\u003e\n\u003cp\u003eFig. 1b gives the workflow of the high-throughput calculations and data screening for the large \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e family. Due to this study focus on the magnetic properties, we only select the element set of {V, Cr, Mn, Fe, Co, Ni, Cu, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Ta, W, Re, Os, Ir, Pt, Au} with 21 elements for the \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003e\u003c/em\u003e site. It should be pointed out that Tc is a radioactive element. Here, for the continuity of the element\u0026apos;s properties, we did not exclude \u003cem\u003eT\u003c/em\u003ec for data analysis. While 4 oxygen-group and 4 nitrogen-group elements were selected for the \u003cem\u003eB\u003c/em\u003e site, and 4 halogen elements were used for the \u003cem\u003eX\u003c/em\u003e site, as shown in the inset element table of Fig. 1b. In this way, 672 \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003es can be constructed as the initial compound set through element substitution based on the prototype rectangular structure of CrSBr. We discarded those nonmagnetic (NM) systems and applied formation energy stability filtering to the entire set (see Fig. S1), leaving 310 stable \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003es, among which 78 FM compounds and 232 AFM compounds were identified. Fig. 1c shows the relative stability and magnetic property distributions of the entire set. After the electronic structure calculation, 78 FM compounds can be further divided into 41 FM half metal/metal and 37 FM semiconductors (Fig. S2).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe second branch of the high-throughput workflow is to identify the possible ferroelectric (FE)/multiferroic materials. We introduced artificial slight distortion into the nonpolar high symmetry structure (with point group of \u003cem\u003eD\u003c/em\u003e\u003csub\u003e2h\u003c/sub\u003e), as a result the structure symmetry was reduced to a polar symmetry of \u003cem\u003eC\u003c/em\u003e\u003csub\u003e2v\u003c/sub\u003e. By comparing the relative energy, we screened out 7 ferroelectric and 4 antiferroelectric (AFE) \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003es from the 78 FM compounds. The 2D ferroelectric \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003es possess in-plane polarization along the \u003cem\u003eb\u003c/em\u003e-axis as shown in the inset of Fig. 1d. Then, we calculated their spin exchange interaction parameters (listed in Table S2). The Monte Carlo (MC) simulations of anisotropic Heisenberg model were performed for all 78 FM systems. Three nearest-neighbor interactions were considered, which have been roughly labeled in Fig. 1a, respectively. The details of the MC simulation and spin exchange interaction were given in section 2.1 of the \u003cem\u003eSupporting Information\u003c/em\u003e. In the end, we screened out\u0026nbsp;38 high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e FM candidates with\u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e \u0026ge; 200 K (listed in Table S3). Among them, 7 compounds possess polar structures, whose dynamical and thermodynamic stabilities were confirmed (Fig. S3-S5).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFerromagnetism and High-\u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn Fig.2a, 672 \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e compounds were divided into FM, AFM and NM subsets according to their \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003e\u003c/em\u003e-site elements. In line with the cognition, common NM transition metal systems, such as those containing noble metals and Cu, Nb, etc., do not appear magnetism, while Mo and Ta are the exceptions. To surprise, \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003es\u0026nbsp;with Fe, Co and Os are all AFM. As for Ni\u003cem\u003eBX\u003c/em\u003es, the number of AFM cases is also more than twice that of FM cases. Moreover, the number of AFM materials accounts for 34.2% of the total \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e, while FM materials only account for 11.6%. As shown in Fig.2b, AFM is almost three times the number of FM. In contrary, from existing crystal databases, such as the \u003cem\u003eMaterials Project\u003c/em\u003e\u003csup\u003e27\u003c/sup\u003e, AFM materials account for less than 10% of magnetic materials. This implies that the rectangle \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e lattice system must have super exchange characteristics that are more suitable for AFM. In addition, these AFM \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003es all favor the high-symmetry \u003cem\u003eD\u003c/em\u003e\u003csub\u003e2h\u003c/sub\u003e lattice, while FM \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003es allows for polar distortions.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAmong those FM compounds, the proportions of 3\u003cem\u003ed\u003c/em\u003e-, 4\u003cem\u003ed\u003c/em\u003e- and 5\u003cem\u003ed-\u003c/em\u003e\u003cem\u003eT\u003csub\u003eM\u003c/sub\u003e\u003c/em\u003e-based systems are 74%, 22% and 4%, respectively. Fig. 2c shows the specific \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e of 38 screened-out high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e (\u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e \u0026sup3; 200 K) FM candidates, which are 15 semiconductors and 23 half-metals, respectively. It\u0026rsquo;s worth mentioning that 26 of them are room-temperature ferromagnets with \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e \u0026sup3; 300 K. Due to the strongest localization of \u003cem\u003e3d\u003c/em\u003e electrons, 89% of high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e compounds are 3\u003cem\u003ed\u003c/em\u003e-\u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e, i.e., \u003cem\u003eT\u003c/em\u003e\u003csub\u003eM\u003c/sub\u003e = {V, Cr, Mn, Ni}-based compounds. The left 11% are MoN\u003cem\u003eXs\u003c/em\u003e, where each Mohas the magnetic moment of 2 \u003cem\u003e\u0026mu;\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e. The MoN\u003cem\u003eX\u003c/em\u003es were also predicted to be high \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e monolayers in previous works\u003csup\u003e28\u003c/sup\u003e. Another interesting trend is that, for most \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003es that have the same \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003e\u003c/em\u003e and \u003cem\u003eB\u003c/em\u003e, the larger the electronegativity of halogen \u003cem\u003eX\u003c/em\u003e, the lower the \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e, indicating the important role of charge transfer in determining the \u003cem\u003eT\u003csub\u003eC\u003c/sub\u003e\u003c/em\u003e (Table S4). In addition, as the electronegativity of \u003cem\u003eX\u003c/em\u003e increases, the system tends to transform from a metal to a semiconductor (Fig. S2). For the example shown in Fig. S6, the band gaps of MnO\u003cem\u003eX\u003c/em\u003es increase from 0 to 1.5 eV. Though the analysis of the electronic structure(Fig. S7-S9), when \u003cem\u003eB\u003c/em\u003e is oxygen-group element, the bands near the Fermi level are primarily contributed by \u003cem\u003eT\u003c/em\u003e\u003csub\u003eM\u003c/sub\u003e-\u003cem\u003ed\u003c/em\u003e orbitals, \u003cem\u003eB\u0026nbsp;\u003c/em\u003eand \u003cem\u003eX-p\u003c/em\u003e orbitals. Conversely, when \u003cem\u003eB\u003c/em\u003e is nitrogen-group element, the dominant contributions are only from the \u003cem\u003eT\u003c/em\u003e\u003csub\u003eM\u003c/sub\u003e and \u003cem\u003eB\u003c/em\u003e.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eMachine learning models in predicting \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e\u003c/strong\u003e \u003cstrong\u003eand \u003cem\u003eJ\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo gain a more comprehensive understanding of the \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e of the 78 FM \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBXs\u003c/em\u003e, we used the gradient boosting method\u003csup\u003e29\u003c/sup\u003e to evaluate the relative importance of the parameters in the effective Hamiltonian and the fundamental properties of the elements. As shown in Fig. 3a, the second-nearest exchange parameter \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e plays a dominating role in determining the \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e, rather than the \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e. For most \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBXs\u003c/em\u003e, \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e manifests the diagonal supe-exchange interaction along the \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003e\u003c/em\u003e-\u003cem\u003eX\u003c/em\u003e-\u003cem\u003eT\u003csub\u003eM\u003c/sub\u003e\u003c/em\u003e path. Thereby, we see the significant effect of halogen elements on modulating the \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e as we discussed in the last section. However, even \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e itself contains too much information, including from the electronic structure, occupancy and lattice. In Fig. 3b, we see that the intensity of \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e relates to the magnet moment (\u003cem\u003eM\u003c/em\u003e), nearest-neighbor \u003cem\u003eT\u003c/em\u003e\u003csub\u003eM\u003c/sub\u003e-\u003cem\u003eT\u003c/em\u003e\u003csub\u003eM\u0026nbsp;\u003c/sub\u003edistance length (\u003cem\u003eL\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e) and band gap at the same time, so it\u0026rsquo;s hard to quantify \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e with a few simple parameters.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTherefore, we derived two SISSO machine learning models to predict the \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e and \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, respectively. These model allows us to maximize the data utilization of a small dataset by constructing high-dimensional descriptors from simple fundamental features\u003csup\u003e26\u003c/sup\u003e. 15 simple features, including the electronic, lattice- and element-related features, were used for SISSO, which were summarized in Table S5. The produced high-dimensional descriptors were given in \u003cem\u003eSupplementary Materials\u003c/em\u003e. Then, linear model using these SISSO descriptors can be constructed. For predicting \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e and \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, our linear models reach well accuracy with the root mean square error (RMSE) of 33.59 K and 5.36 meV, respectively.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMultiferroic properties \u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e family also provides an ideal setting for studying 2D multiferroic and exploring the coupling between electric, magnetic, and structural order parameters\u003csup\u003e30\u003c/sup\u003e. To make the discussion more concise, we will refer to these polar metallic structures as \u0026ldquo;FEs\u0026rdquo; just for discussions despite that their polarization cannot be switched by an electric field. The AFE-FM systems are also called multiferroics for discussions, whose polarization cannot be switched as well. \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTable 1 has listed 11 selected high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBXs\u003c/em\u003e that possess rich order parameters. They are VN\u003cem\u003eX\u003c/em\u003es (\u003cem\u003eX\u003c/em\u003e = F and Cl), CrNF, MnO\u003cem\u003eX\u003c/em\u003es, and MoN\u003cem\u003eX\u003c/em\u003es (\u003cem\u003eX\u003c/em\u003e = F, Cl, Br, and I), respectively. Among them, MnO\u003cem\u003eX\u003c/em\u003es and MoNCl are conventional FE-FM multiferroics with the band gaps ranging from 0.16 to 1.58 eV. VN\u003cem\u003eX\u003c/em\u003es (\u003cem\u003eX\u003c/em\u003e = F and Cl) and MoN\u003cem\u003eX\u003c/em\u003es (\u003cem\u003eX\u003c/em\u003e = Br and I) are AFE-FM multiferroics. Here, MoNF is more special than other systems. Its ground state coexists FE-FM and AFE-FM multiferroics, which will be addressed in detail later. The in-plane polarizations of these FE \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u0026nbsp;\u003c/em\u003esystems range from 2.4 to 9.0 \u003cem\u003e\u0026mu;\u003c/em\u003eC/cm\u0026sup2;, and they need overcome moderate energy barriers from 16 to 252 meV/\u003cem\u003ef.u.\u003c/em\u003e to switch the polarization. Switching the polarization of metallic \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003es need overcome a much higher energy barrier. To our surprise, the switching energy barrier of AFE systems are even lower than most FE systems. The magnetic easy axes, \u003cem\u003eMAE\u0026nbsp;\u003c/em\u003eand \u003cem\u003eT\u003csub\u003eC\u003c/sub\u003e\u003c/em\u003e are also given in Table 1. Interestingly, these 11 high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u0026nbsp;\u003c/sub\u003emultiferroic systems happen to be the only ones with low lattice symmetry (\u003cem\u003eC\u003c/em\u003e\u003csub\u003e2h\u003c/sub\u003e and\u003cem\u003e\u0026nbsp;C\u003c/em\u003e\u003csub\u003e2v\u003c/sub\u003e) among the 78 FM systems.\u003c/p\u003e\n\u003cp\u003eFig. 4a shows three types of the polarization switching path existing in \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e systems, which are FE-PE-FE, FE-AFE-FE, and AFE-PE-AFE. MnO\u003cem\u003eX\u003c/em\u003e (\u003cem\u003eX\u003c/em\u003e = F, Cl, and Br) systems favor the FE-AFE-FE path, while MoO\u003cem\u003eX\u003c/em\u003e (\u003cem\u003eX\u003c/em\u003e = F, Br, and I) systems favor the AFE-PE-AFE path (Fig. S10). The envelope of the polarization switching energy of MnOF and MoNF selected as examples were displayed in Fig. 4b. For MnOF, the energy barrier \u0026Delta;\u003cem\u003eE\u003c/em\u003e of the FE-AFE-FE path is much lower than the FE-PE-FE path. Moreover, the middle point of its switching path (corresponds to the AFE phase) possess similar energy with respect to its ground-state FE structure, indicating the polymorphism nature of this system. The comparation of two switching paths for MnOCl and MnOBr were displayed in Fig. S11, which possess similar characteristics to that of MnOF.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe MoNF system exhibits unique characteristics that distinguish it from other systems. The relative energy difference between the FE and AFE phases is remarkably small, within 10 meV per formula unit (\u003cem\u003ef.u.\u003c/em\u003e). The ground-state structure of MoNF is identified as a ferroelectric phase, as illustrated in Fig.S10. The ferroelectric polarization is oriented along the \u003cem\u003eb\u003c/em\u003e-axis, determined by analyzing the imaginary mode of the paraelectric (PE) structure. Both the FE and AFE phases are dynamically stable. The FE phase possesses a 9.0 \u003cem\u003e\u0026mu;\u003c/em\u003eC/cm\u0026sup2; in-plane polarization, and favors the FE-PE-FE switching path with an energy barrier of 114 meV/\u003cem\u003ef.u.\u003c/em\u003e. While the AFE phase favors the AFE-PE-AFE switching path, which has a much lower energy barrier of 55 meV/\u003cem\u003ef.u.\u003c/em\u003e. It is also worth mentioning that there are numerous AFM-FE systems with large net polarizations, such as PtOCl, OsOCl, PdOF, and MoOF, which also deserves further in-depth investigations to fully understand their properties and potential applications.\u003c/p\u003e\n\u003cp\u003eFrom the perspective of magnetic properties, the magnetic easy axes of \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e systems also have diverse orientations, enabling them to display distinct magnetoelectric coupling behaviors. For MnO\u003cem\u003eX\u003c/em\u003e systems, their magnetic easy axes are along the \u003cem\u003ec\u003c/em\u003e-axis but with a small canting in the \u003cem\u003ebc\u003c/em\u003e-plane. The easy axes of the VNF and CrNF are along the \u003cem\u003eb\u003c/em\u003e-axis (polar axis). The magnetic easy axis of AFE-MoN\u003cem\u003eX\u003c/em\u003e systems is along the \u003cem\u003ea-\u003c/em\u003eaxis, while that of FE-MoNF is along the \u003cem\u003eb\u003c/em\u003e-axis (polar axis). This means that if the ferroelectric polarization of FE MoNF is switched, the magnetic easy axis will also be switched. The simulated \u003cem\u003eT\u003c/em\u003e\u003csub\u003eC\u003c/sub\u003e of FE and AFE MoNF are shown in Fig. 4c, and their MAE and exchange coupling parameters were listed in Table 2. The FE MoNF shows a \u003cem\u003eT\u003csub\u003eC\u003c/sub\u003e\u003c/em\u003e of480 K, while the AFE MoNF shows a lower \u003cem\u003eT\u003csub\u003eC\u003c/sub\u003e\u003c/em\u003e of 360 K. This is due to that FE shows a much larger \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e and MAE, which play the dominate role in determining \u003cem\u003eT\u003csub\u003eC\u003c/sub\u003e\u003c/em\u003e. More interesting, AFE MoNF could form stable Bloch and N\u0026eacute;el type merons near the domain wall at approximately 110 K as shown in Fig. 4d and Fig. S12.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSpin-polarized transport\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNext, we investigate the spin-polarized transport properties of \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003es. A two-probe spin transistor was constructed, comprising a central region made of a FM semiconductor CrSBr monolayer sandwiched by left and right electrodes made of a FM half metal CrNF, as shown in Fig.5a. The electrodes extend to \u003cem\u003ey\u0026nbsp;\u003c/em\u003e= \u0026plusmn;\u0026infin; where the current is collected. The transport direction of Fig.5 is along the \u003cem\u003eb\u003c/em\u003e-axis, while the transport simulation along the \u003cem\u003ea\u003c/em\u003e-axis was given in Fig. S13. Two types of magnetic configuration of the CrNF electrodes were considered, which are spin parallel configuration (PC) and spin anti-parallel configuration (APC), respectively. The current-voltage dependences of two spin configurations were shown in Fig.5c. We have considered a bias voltage from 0.0 to 0.6 V, where the linear current-voltage relationship was maintained. On the other hand, compared to the PC device, APC device exhibits significantly higher resistance due to the existing tunnel magnetoresistance effect. The parallel spin carriers can easily tunnel through the semiconductor layer, indicating the great potential of \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e systems in spin filtering applications. To quantify the spin transport performance, we defined the spin injection efficiency (SIE) and tunneling magnetoresistance (TMR) as following: \u003cimg src=\"data:image/png;base64,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\" width=\"115\" height=\"41\"\u003e\u0026nbsp;\u003cimg src=\"data:image/png;base64,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\" height=\"37\" width=\"153\"\u003e where \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u0026uarr;\u003c/sub\u003e, \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u0026darr;\u003c/sub\u003e,\u003cem\u003e\u0026nbsp;I\u003c/em\u003e\u003csub\u003ePC\u003c/sub\u003e, and \u003cem\u003eI\u003c/em\u003e\u003csub\u003eAPC\u003c/sub\u003e are the spin-up current, the spin-down current, the current of PC device and the current of APC device, respectively. Since \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u0026darr;\u003c/sub\u003e is almost equal to zero in our systems, a nearly fully spin-polarized current is generated (SIE ~ 100%, shown in the inset of Fig. 5d). Then, TMR shows a large dependence on the bias voltage (Fig. 5d). There is a maximum TMR of 5.2\u0026times;10\u003csup\u003e5\u003c/sup\u003e % along \u003cem\u003ea\u003c/em\u003e-axis and 2.5\u0026times;10\u003csup\u003e6\u003c/sup\u003e % along \u003cem\u003eb\u003c/em\u003e-axis when under a bias of 0.1 V, which is much larger than those measured in the ZrTe\u003csub\u003e2\u003c/sub\u003e/CrOCl/CrOCl/ZrTe\u003csub\u003e2\u003c/sub\u003e (2.5\u0026times;10\u003csup\u003e4\u003c/sup\u003e %)\u003csup\u003e31\u003c/sup\u003e, graphene/CrI\u003csub\u003e3\u003c/sub\u003e/graphene (1.9\u0026times;10\u003csup\u003e4\u003c/sup\u003e %)\u003csup\u003e32\u003c/sup\u003e and (Fe\u003csub\u003e0.8\u003c/sub\u003eCo\u003csub\u003e0.2\u003c/sub\u003e)\u003csub\u003e3\u003c/sub\u003eGaTe\u003csub\u003e2\u003c/sub\u003e/WSe\u003csub\u003e2\u003c/sub\u003e/Fe\u003csub\u003e3\u003c/sub\u003eGaTe\u003csub\u003e2\u0026nbsp;\u003c/sub\u003e(1.8\u0026times;10\u003csup\u003e2\u003c/sup\u003e %). The transmission spectra under a bias of 0.1 V were presented in Fig. 5e and 5f. Under a bias of 0.1 V, the transmission coefficient \u003cem\u003eT\u003c/em\u003e\u003csub\u003ePC\u003c/sub\u003e approaches 0.5, while \u003cem\u003eT\u003c/em\u003e\u003csub\u003eAPC\u003c/sub\u003e approximately equals to 0. Moreover, the transmission spectrum implies that almost completely spin-polarized transmission can be achieved in a broad energy window from -0.8 to 3 eV.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eIn this work, we have conducted a comprehensive high-throughput investigation of the\u003cem\u003e\u0026nbsp;T\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003es, uncovering a rich landscape of ferromagnetic and multiferroic properties. By screening 672 \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e systems, 78 ferromagnetic monolayers were identified, 38 of which had high Curie temperatures (\u003cem\u003eT\u003csub\u003eC\u003c/sub\u003e\u003c/em\u003e\u003csub\u003e\u0026nbsp;\u003c/sub\u003e\u0026ge; 200 K), greatly expanding the known 2D magnets. Machine learning models were developed to reveal the critical role of the second-nearest neighbor exchange interaction in determining \u003cem\u003eT\u003csub\u003eC\u003c/sub\u003e,\u0026nbsp;\u003c/em\u003eoffering a new insight for designing 2D magnets. Additionally, we discovered seven FM-FE multiferroics, exhibiting unique polarization switching mechanisms. Spin transport simulations demonstrate that \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e monolayers exhibit exceptional spin filtering and tunneling magnetoresistance (\u0026gt;10\u003csup\u003e5\u0026nbsp;\u003c/sup\u003e%), making them highly promising for spintronic applications. These findings provide a solid foundation for future experimental studies and the development of next-generation 2D multiferroics.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eDensity Functional Theory\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/strong\u003eFirst-principles calculations were performed within generalized gradient approximation (GGA) in the form proposed by Perdew, Burke, and Ernzerhof (PBE)\u003csup\u003e33\u003c/sup\u003e using Vienna \u003cem\u003eab initio\u003c/em\u003e simulation package (VASP)\u003csup\u003e34\u003c/sup\u003e. The lattice relaxations adopted a vdW functional optB88-vdW \u003csup\u003e35\u003c/sup\u003e.\u0026nbsp;Atomic positions\u0026nbsp;were\u0026nbsp;relaxed until the maximum force on each atom was less than 10\u003csup\u003e-3\u003c/sup\u003e eV/\u0026Aring;. A 600 eV energy cutoff and a 10\u0026acute;10\u0026acute;1 \u0026Gamma;-centered \u003cem\u003ek\u003c/em\u003e grid of were used. And a vacuum layer more than 25 \u0026Aring; was applied to avoid the interaction between periodic images. To reduce the self-interaction error of \u003cem\u003eT\u003c/em\u003e\u003csub\u003eM\u003c/sub\u003e-\u003cem\u003ed\u003c/em\u003e orbitals, we have considered the Hubbard correction\u003csup\u003e36\u003c/sup\u003e. The effective Hubbard \u003cem\u003eU\u003c/em\u003e parameter (\u003cem\u003eU\u003c/em\u003e\u003csub\u003eeff\u003c/sub\u003e) for V, Cr, Mn, Fe, Co, Ni and Mo are 3.3 eV, 3.7 eV, 4.0 eV, 5.3 eV, 4.0, 6.2, and 4.0 eV, respectively.\u0026nbsp;The Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional was\u0026nbsp;used to correct the problem of severe underestimation of the band gap by PBE\u003csup\u003e37\u003c/sup\u003e method. Spin-orbit coupling (SOC) was taken into account in determining the magnetization easy axis. Phonon dispersion was calculated using density-functional perturbation theory (DFPT) with VASP-PHONOPY interface\u003csup\u003e38,39\u003c/sup\u003e. The Born effective tensor is defined as: \u003cimg src=\"data:image/png;base64,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\" width=\"79\" height=\"43\"\u003e in which \u003cem\u003ee\u003c/em\u003e is the charge of electron, \u003cem\u003ep\u0026nbsp;\u003c/em\u003eis polarization, and \u003cem\u003eu\u003c/em\u003e is the atomic displacement from its high-symmetry nonpolar position. The calculated polarization of 2D materials strongly depends on the thickness of slab we chose. Here, we added two extra 1 \u0026Aring; thcikness along the \u003cem\u003ec\u003c/em\u003e-axis on both sides of \u003cem\u003eT\u003csub\u003eM\u003c/sub\u003eBX\u003c/em\u003e monolayers when calcauling the volume \u003cem\u003eW\u003c/em\u003e. The polarization was calcualted using Born effective charge method.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eQuantum transport\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTransport properties of the device were calcualted using \u003cem\u003eNanodcal\u003c/em\u003e\u003csup\u003e40\u003c/sup\u003e within the NEGF-DFT framwork\u003csup\u003e41\u003c/sup\u003e.\u0026nbsp;The DZP atomic orbital basis is used to expand all the physical quantities; the exchange and correlation are treated at the level of PBE functional; and atomic cores are defined by the standard norm conserving nonlocal pseudopotentials, and 16 \u0026times; 16\u0026times; 1 k-points were used.\u0026nbsp;Under certain bias V\u003csub\u003eb\u003c/sub\u003e, the spin current \u003cem\u003eI\u003c/em\u003e was calcualted as follows:\u003cimg src=\"data:image/png;base64,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\" height=\"34\" width=\"398\"\u003e\u003csub\u003e\u0026nbsp;\u003c/sub\u003eis the spin index. The integration is over the bias window between \u003cem\u003em\u003c/em\u003e\u003csub\u003eL\u003c/sub\u003e and \u003cem\u003em\u003c/em\u003e\u003csub\u003eR\u003c/sub\u003e which are the electrochemical potentials of the top/bottom leads. The total current is given by \u003cem\u003eI\u003c/em\u003e\u003csub\u003etotal\u003c/sub\u003e = \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u0026uarr;\u0026nbsp;\u003c/sub\u003e+ \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u0026darr;\u003c/sub\u003e.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eS.X. carried out the calculations and wrote the manuscript under the supervision of F.J. and N.D. All authors reviewed the manuscript. F.J. and N.D. conceived and led the entire scientific project.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe work was supported by the National Science Foundation of China (Grant No. 12347115), China Postdoctoral Science Foundation (No. 2024M760690), and Hangzhou Science and Technology Bureau of Zhejiang Province (No. TD2020002). Work at HDU was supported by Zhejiang Provincial Natural Science Foundation (QN25A040026), and the Foundation of Hangzhou Dianzi University (KYS075624288). We gratefully acknowledge HZWTECH for providing computation facilities. S. Xu thanks Taozhen Fu (from HZWTECH) for help and discussions on this study.\u003c/p\u003e\u003ch2\u003eData availability\u003c/h2\u003e \u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\u003ch2\u003eCode availability\u003c/h2\u003e \u003cp\u003eThe code is available from the corresponding author upon reasonable request.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eAdditional information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplementary information\u0026nbsp;\u003c/strong\u003eThe online version contains supplementary material available at\u0026nbsp;\u003cem\u003eXXX\u003c/em\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorrespondence\u003c/strong\u003e and requests for materials should be addressed to Fanhao Jia.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eReprints and permissions information\u0026nbsp;\u003c/strong\u003eis available at http://www.nature.com/reprints.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePublisher\u0026rsquo;s note\u003c/strong\u003e Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eOpen Access\u003c/strong\u003e This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third-party material in this article are included in the article\u0026rsquo;s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article\u0026rsquo;s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eJia, Z.\u003cem\u003e et al.\u003c/em\u003e Spintronic Devices upon 2D Magnetic Materials and Heterojunctions. \u003cem\u003eACS Nano\u003c/em\u003e \u003cstrong\u003e19\u003c/strong\u003e, 9452-9483 (2025).\u003c/li\u003e\n\u003cli\u003eAhn, E. C. 2D materials for spintronic devices. \u003cem\u003enpj 2D Materials and Applications\u003c/em\u003e \u003cstrong\u003e4\u003c/strong\u003e, 17 (2020).\u003c/li\u003e\n\u003cli\u003eHuang, B.\u003cem\u003e et al.\u003c/em\u003e Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. \u003cem\u003eNature\u003c/em\u003e \u003cstrong\u003e546\u003c/strong\u003e, 270-273 (2017).\u003c/li\u003e\n\u003cli\u003eBedoya-Pinto, A.\u003cem\u003e et al.\u003c/em\u003e Intrinsic 2D-XY ferromagnetism in a van der Waals monolayer. \u003cem\u003eScience\u003c/em\u003e \u003cstrong\u003e374\u003c/strong\u003e, 616-620 (2021).\u003c/li\u003e\n\u003cli\u003eChua, R.\u003cem\u003e et al.\u003c/em\u003e Room temperature ferromagnetism of monolayer chromium telluride with perpendicular magnetic anisotropy. \u003cem\u003eAdvanced Materials\u003c/em\u003e \u003cstrong\u003e33\u003c/strong\u003e, 2103360 (2021).\u003c/li\u003e\n\u003cli\u003eBalasubramanian, K., Khare, S. V. \u0026amp; Gall, D. Valence electron concentration as an indicator for mechanical properties in rocksalt structure nitrides, carbides and carbonitrides. \u003cem\u003eActa Materialia\u003c/em\u003e \u003cstrong\u003e152\u003c/strong\u003e, 175-185 (2018).\u003c/li\u003e\n\u003cli\u003eLi, W., Zhu, D., Dong, S. \u0026amp; Zhang, J.-J. Two-dimensional multiferroic NbPc covalent organic framework with strong magnetoelectric coupling and room-temperature ferroelectricity. \u003cem\u003ePhysical Review B\u003c/em\u003e \u003cstrong\u003e111\u003c/strong\u003e, 035439 (2025).\u003c/li\u003e\n\u003cli\u003ePapavasileiou, A. V.\u003cem\u003e et al.\u003c/em\u003e Ferromagnetic Elements in Two‐Dimensional Materials: 2D Magnets and Beyond. \u003cem\u003eAdvanced Functional Materials\u003c/em\u003e \u003cstrong\u003e34\u003c/strong\u003e, 2309046 (2024).\u003c/li\u003e\n\u003cli\u003eZhang, Z., Sun, R. \u0026amp; Wang, Z. Recent Advances in Two-Dimensional Ferromagnetic Materials-Based van der Waals Heterostructures. \u003cem\u003eACS Nano\u003c/em\u003e \u003cstrong\u003e19\u003c/strong\u003e, 187-228 (2025).\u003c/li\u003e\n\u003cli\u003eZhuo, W.\u003cem\u003e et al.\u003c/em\u003e Manipulating ferromagnetism in few‐layered Cr2Ge2Te6. \u003cem\u003eAdvanced Materials\u003c/em\u003e \u003cstrong\u003e33\u003c/strong\u003e, 2008586 (2021).\u003c/li\u003e\n\u003cli\u003eWu, Y.\u003cem\u003e et al.\u003c/em\u003e Interlayer engineering of Fe3GeTe2: From 3D superlattice to 2D monolayer. \u003cem\u003eProceedings of the National Academy of Sciences\u003c/em\u003e \u003cstrong\u003e121\u003c/strong\u003e, e2314454121 (2024).\u003c/li\u003e\n\u003cli\u003eVillalpando, G.\u003cem\u003e et al.\u003c/em\u003e Chemical exfoliation toward magnetic 2D VOCl monolayers. \u003cem\u003eACS Nano\u003c/em\u003e \u003cstrong\u003e16\u003c/strong\u003e, 13814-13820 (2022).\u003c/li\u003e\n\u003cli\u003eRizzo, D. J.\u003cem\u003e et al.\u003c/em\u003e Visualizing atomically layered magnetism in CrSBr. \u003cem\u003eAdvanced Materials\u003c/em\u003e \u003cstrong\u003e34\u003c/strong\u003e, 2201000 (2022).\u003c/li\u003e\n\u003cli\u003eBoix‐Constant, C.\u003cem\u003e et al.\u003c/em\u003e Programmable Magnetic Hysteresis in Orthogonally‐Twisted 2D CrSBr Magnets via Stacking Engineering. \u003cem\u003eAdvanced Materials\u003c/em\u003e, 2415774 (2025).\u003c/li\u003e\n\u003cli\u003eTschudin, M. A.\u003cem\u003e et al.\u003c/em\u003e Imaging nanomagnetism and magnetic phase transitions in atomically thin CrSBr. \u003cem\u003eNature Communications\u003c/em\u003e \u003cstrong\u003e15\u003c/strong\u003e, 6005 (2024).\u003c/li\u003e\n\u003cli\u003eFei, F.\u003cem\u003e et al.\u003c/em\u003e Spin-mechanical coupling in 2D antiferromagnet CrSBr. \u003cem\u003eNano Letters\u003c/em\u003e (2024).\u003c/li\u003e\n\u003cli\u003eGuo, Z.\u003cem\u003e et al.\u003c/em\u003e Magnetic high-order topological insulator in 2D layered CrOCl. \u003cem\u003eMaterials Today Physics\u003c/em\u003e \u003cstrong\u003e36\u003c/strong\u003e, 101153 (2023).\u003c/li\u003e\n\u003cli\u003eXu, S.\u003cem\u003e et al.\u003c/em\u003e Intrinsic multiferroic MnOF monolayer with room-temperature ferromagnetism. \u003cem\u003eMaterials Today Physics\u003c/em\u003e \u003cstrong\u003e27\u003c/strong\u003e, 100775 (2022).\u003c/li\u003e\n\u003cli\u003eLi, Y.\u003cem\u003e et al.\u003c/em\u003e Nonvolatile electrical control of spin polarization in the 2D bipolar magnetic semiconductor VSeF. \u003cem\u003enpj Computational Materials\u003c/em\u003e \u003cstrong\u003e9\u003c/strong\u003e, 50 (2023).\u003c/li\u003e\n\u003cli\u003eYang, B., Han, X. \u0026amp; Picozzi, S. Emergence of topological bimerons in monolayer CrSBr. \u003cem\u003earXiv preprint arXiv:2406.17495\u003c/em\u003e (2024).\u003c/li\u003e\n\u003cli\u003eChen, Y.\u003cem\u003e et al.\u003c/em\u003e Twist-assisted all-antiferromagnetic tunnel junction in the atomic limit. \u003cem\u003eNature\u003c/em\u003e \u003cstrong\u003e632\u003c/strong\u003e, 1045-1051 (2024).\u003c/li\u003e\n\u003cli\u003eZhang, T.\u003cem\u003e et al.\u003c/em\u003e Magnetism and optical anisotropy in van der Waals antiferromagnetic insulator CrOCl. \u003cem\u003eACS Nano\u003c/em\u003e \u003cstrong\u003e13\u003c/strong\u003e, 11353-11362 (2019).\u003c/li\u003e\n\u003cli\u003eYang, S., Zhang, T. \u0026amp; Jiang, C. van der Waals magnets: Material family, detection and modulation of magnetism, and perspective in spintronics. \u003cem\u003eAdvanced Science\u003c/em\u003e \u003cstrong\u003e8\u003c/strong\u003e, 2002488 (2021).\u003c/li\u003e\n\u003cli\u003eHu, M.\u003cem\u003e et al.\u003c/em\u003e First-principles prediction of a room-temperature ferromagnetic and ferroelastic 2D multiferroic MnNX (X= F, Cl, Br, and I). \u003cem\u003eNanoscale\u003c/em\u003e \u003cstrong\u003e12\u003c/strong\u003e, 24237-24243 (2020).\u003c/li\u003e\n\u003cli\u003eZhu, Y.\u003cem\u003e et al.\u003c/em\u003e Prediction of 2D ferromagnetic metal VNI monolayer with tunable topological properties. \u003cem\u003eJournal of Applied Physics\u003c/em\u003e \u003cstrong\u003e132\u003c/strong\u003e (2022).\u003c/li\u003e\n\u003cli\u003eOuyang, R., Curtarolo, S., Ahmetcik, E., Scheffler, M. \u0026amp; Ghiringhelli, L. M. SISSO: A compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates. \u003cem\u003ePhysical Review Materials\u003c/em\u003e \u003cstrong\u003e2\u003c/strong\u003e, 083802 (2018).\u003c/li\u003e\n\u003cli\u003eJain, A.\u003cem\u003e et al.\u003c/em\u003e Commentary: The Materials Project: A materials genome approach to accelerating materials innovation. \u003cem\u003eAPL Materials\u003c/em\u003e \u003cstrong\u003e1\u003c/strong\u003e, 011002 (2013).\u003c/li\u003e\n\u003cli\u003eWu, F.\u003cem\u003e et al.\u003c/em\u003e Atomically thin transition-metal dinitrides: high-temperature ferromagnetism and half-metallicity. \u003cem\u003eNano Letters\u003c/em\u003e \u003cstrong\u003e15\u003c/strong\u003e, 8277-8281 (2015).\u003c/li\u003e\n\u003cli\u003ePedregosa, F.\u003cem\u003e et al.\u003c/em\u003e Scikit-learn: Machine learning in Python. \u003cem\u003ethe Journal of Machine Learning Research\u003c/em\u003e \u003cstrong\u003e12\u003c/strong\u003e, 2825-2830 (2011).\u003c/li\u003e\n\u003cli\u003eMostovoy, M. Multiferroics: Different routes to magnetoelectric coupling. \u003cem\u003enpj Spintronics\u003c/em\u003e \u003cstrong\u003e2\u003c/strong\u003e, 18 (2024).\u003c/li\u003e\n\u003cli\u003eZhang, X.\u003cem\u003e et al.\u003c/em\u003e Van der Waals Magnetic Heterojunctions with Giant Zero‐Bias Tunneling Magnetoresistance and Photo‐Assisted Magnetic Memory. \u003cem\u003eAdvanced Functional Materials\u003c/em\u003e \u003cstrong\u003e32\u003c/strong\u003e, 2200154 (2022).\u003c/li\u003e\n\u003cli\u003eSong, T.\u003cem\u003e et al.\u003c/em\u003e Giant tunneling magnetoresistance in spin-filter van der Waals heterostructures. \u003cem\u003eScience\u003c/em\u003e \u003cstrong\u003e360\u003c/strong\u003e, 1214-1218 (2018).\u003c/li\u003e\n\u003cli\u003ePerdew, J. P. JP Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). \u003cem\u003ePhysical Review Letter\u003c/em\u003e \u003cstrong\u003e77\u003c/strong\u003e, 3865 (1996).\u003c/li\u003e\n\u003cli\u003eKresse, G. G. Kresse and J. Furthm\u0026uuml;ller, Phys. Rev. B 54, 11169 (1996). \u003cem\u003ePhysical Review B\u003c/em\u003e \u003cstrong\u003e54\u003c/strong\u003e, 11169 (1996).\u003c/li\u003e\n\u003cli\u003eKlime\u0026scaron;, J., Bowler, D. R. \u0026amp; Michaelides, A. Van der Waals density functionals applied to solids. \u003cem\u003ePhysical Review B\u003c/em\u003e \u003cstrong\u003e83\u003c/strong\u003e, 195131 (2011).\u003c/li\u003e\n\u003cli\u003eKan, M., Zhou, J., Sun, Q., Kawazoe, Y. \u0026amp; Jena, P. The intrinsic ferromagnetism in a MnO2 monolayer. \u003cem\u003eThe Journal of Physical Chemistry Letters\u003c/em\u003e \u003cstrong\u003e4\u003c/strong\u003e, 3382-3386 (2013).\u003c/li\u003e\n\u003cli\u003eHeyd, J., Scuseria, G. E. \u0026amp; Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. \u003cem\u003eThe Journal of Chemical Physics\u003c/em\u003e \u003cstrong\u003e118\u003c/strong\u003e, 8207-8215 (2003).\u003c/li\u003e\n\u003cli\u003eTogo, A., Oba, F. \u0026amp; Tanaka, I. First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures. \u003cem\u003ePhysical Review B\u003c/em\u003e \u003cstrong\u003e78\u003c/strong\u003e, 134106 (2008).\u003c/li\u003e\n\u003cli\u003eTogo, A. \u0026amp; Tanaka, I. First principles phonon calculations in materials science. \u003cem\u003eScripta Materialia\u003c/em\u003e \u003cstrong\u003e108\u003c/strong\u003e, 1-5 (2015).\u003c/li\u003e\n\u003cli\u003eTaylor, J., Guo, H. \u0026amp; Wang, J. Ab initio modeling of quantum transport properties of molecular electronic devices. \u003cem\u003ePhysical Review B\u003c/em\u003e \u003cstrong\u003e63\u003c/strong\u003e, 245407 (2001).\u003c/li\u003e\n\u003cli\u003eStradi, D., Martinez, U., Blom, A., Brandbyge, M. \u0026amp; Stokbro, K. General atomistic approach for modeling metal-semiconductor interfaces using density functional theory and nonequilibrium Green\u0026apos;s function. \u003cem\u003ePhysical Review B\u003c/em\u003e\u003cstrong\u003e93\u003c/strong\u003e, 155302 (2016). \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-computational-materials","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjcompumats","sideBox":"Learn more about [npj Computational Materials](http://www.nature.com/npjcompumats/)","snPcode":"41524","submissionUrl":"https://mts-npjcompumats.nature.com/","title":"npj Computational Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5980980/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5980980/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Two-dimensional (2D) transition metal oxyhalides and nitrogen-halides (TMBXs, where TM = transition metal, B = O-group and N-group elements, X = halogen) have emerged as promising candidates for exploring multiferroic orders and spintronic applications. In this study, we conduct a systematic first-principles high-throughput screening combined with machine learning to identify novel 2D ferromagnetic and multiferroic materials within TMBX family. From a comprehensive dataset comprising 672 TMBX monolayers, we identify 78 ferromagnetic systems, of which 38 exhibit high Curie temperatures (TC ≥ 200 K), significantly expanding the known library of 2D magnetic materials. A machine learning model is developed to elucidate the key factors governing ferromagnetism, revealing that the second-nearest neighbor exchange interaction (J2) plays a dominant role in determining TC. Furthermore, we discover seven ferromagnetic-ferroelectric multiferroic systems, revealing unique polarization switching pathways. Notably, spin transport simulations using the nonequilibrium Green's function formalism demonstrate exceptional spin filtering capabilities (~ 100 %) and giant bias-dependent tunneling magnetoresistance (\u003e 105 %). These findings deepen the fundamental understanding of 2D multiferroics and establish a solid platform for future experimental exploration and the development of next-generation spintronic devices.","manuscriptTitle":"High Throughput Discovery of 2D Ferromagnetic and Multiferroic Transition Metal Oxyhalides and Nitrogen Halides ","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-11 06:06:24","doi":"10.21203/rs.3.rs-5980980/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accepted","date":"2025-04-22T17:40:54+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-15T10:48:32+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-11T07:21:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"28423964170090209548168018167311492794","date":"2025-04-11T01:27:24+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-10T10:35:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"17339865619003156297283700569311279580","date":"2025-04-10T10:25:50+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"292313732354801563426973193048024133261","date":"2025-04-10T10:15:15+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-04-10T10:08:05+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-04-04T06:08:00+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Computational Materials","date":"2025-03-19T03:16:04+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-computational-materials","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjcompumats","sideBox":"Learn more about [npj Computational Materials](http://www.nature.com/npjcompumats/)","snPcode":"41524","submissionUrl":"https://mts-npjcompumats.nature.com/","title":"npj Computational Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"57051ecf-a674-4bf3-8d93-77ac0a35c599","owner":[],"postedDate":"April 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":47001207,"name":"Physical sciences/Physics/Condensed matter physics/Electronic properties and materials"},{"id":47001208,"name":"Physical sciences/Physics/Condensed matter physics/Ferroelectrics and multiferroics"},{"id":47001209,"name":"Physical sciences/Physics/Condensed matter physics/Ferromagnetism"},{"id":47001210,"name":"Physical sciences/Physics/Condensed matter physics/Magnetic properties and materials"},{"id":47001211,"name":"Physical sciences/Physics/Condensed matter physics/Spintronics"}],"tags":[],"updatedAt":"2025-10-13T16:01:25+00:00","versionOfRecord":{"articleIdentity":"rs-5980980","link":"https://doi.org/10.1038/s41524-025-01620-7","journal":{"identity":"npj-computational-materials","isVorOnly":false,"title":"npj Computational Materials"},"publishedOn":"2025-10-10 15:57:05","publishedOnDateReadable":"October 10th, 2025"},"versionCreatedAt":"2025-04-11 06:06:24","video":"","vorDoi":"10.1038/s41524-025-01620-7","vorDoiUrl":"https://doi.org/10.1038/s41524-025-01620-7","workflowStages":[]},"version":"v1","identity":"rs-5980980","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5980980","identity":"rs-5980980","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}