Abstract
Two-dimensional (2D) magnets host a wide range of exotic magnetic textures, whose low-energy excitations and finite-temperature properties are typically described by effective spin models based on Heisenberg-like Hamiltonians. A key challenge in this framework is the reliable determination, from ab initio calculations, of exchange parameters and their anisotropic components, crucial for stabilising long-range order. Among the strategies proposed for this task, the energy-mapping method, based on total-energy calculations within Density Functional Theory (DFT), is the most widely adopted, but typically requires laborious, multi-step procedures. To overcome this limitation, we introduce AMaRaNTA (Automating Magnetic paRAmeters iN a Tensorial Approach), a computational package that systematically automates the energy-mapping method, through its “four-state” formulation, to extract exchange and anisotropy parameters in 2D magnets. In its current implementation, AMaRaNTA returns the nearest-neighbour exchange tensor, complemented by scalar parameters for second- and third-nearest-neighbour exchange interactions as well as single-ion anisotropy. Together, these provide a minimal yet sufficient set of parameters to capture magnetic frustration and anisotropies, essential for stabilising several observed magnetic states in 2D materials. Applied to a representative subset of the Materials Cloud 2D Structure database, AMaRaNTA demonstrates robust and reproducible screening of magnetic interactions, with clear potential for high-throughput simulations.
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Data availability
The dataset generated and analysed in the current study is available in the Supplementary Materials.
Code availability
The underlying code for this study is publicly available at https://github.com/AMaRaNTA-code/AMaRaNTA.
References
Tsubokawa, I. On the Magnetic Properties of a CrBr3 Single Crystal. J. Phys. Soc. Jpn. 15, 1664–1668 (1960).
Dillon, J. F. & Olson, C. E. Magnetization, Resonance, and Optical Properties of the Ferromagnet CrI3. J. Appl. Phys. 36, 1259–1260 (1965).
Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270–273 (2017).
Gong, C. et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature 546, 265–269 (2017).
Wang, X. et al. Raman spectroscopy of atomically thin two-dimensional magnetic iron phosphorus trisulfide (FePS3) crystals. 2D Mater. 3, 031009 (2016).
Lee, J.-U. et al. Ising-Type Magnetic Ordering in Atomically Thin FePS3. Nano Lett. 16, 7433–7438 (2016).
Gong, C. & Zhang, X. Two-dimensional magnetic crystals and emergent heterostructure devices. Science363 (2019).
Gibertini, M., Koperski, M., Morpurgo, A. F. & Novoselov, K. S. Magnetic 2D materials and heterostructures. Nat. Nanotechnol. 14, 408–419 (2019).
Jiang, X. et al. Recent progress on 2D magnets: Fundamental mechanism, structural design and modification. Appl. Phys. Rev.8 (2021).
Wang, Q. H. et al. The Magnetic Genome of Two-Dimensional van der Waals Materials. ACS Nano 16, 6960–7079 (2022).
Song, T. et al. Giant tunneling magnetoresistance in spin-filter van der Waals heterostructures. Science 360, 1214–1218 (2018).
Wang, Z. et al. Tunneling Spin Valves Based on Fe3GeTe2/hBN/Fe3GeTe2 van der Waals Heterostructures. Nano Lett. 18, 4303–4308 (2018).
Zhang, B., Lu, P., Tabrizian, R., Feng, P. X.-L. & Wu, Y. 2D Magnetic heterostructures: spintronics and quantum future. npj Spintronics 2, 1–10 (2024).
Deng, Y. et al. Gate-tunable room-temperature ferromagnetism in two-dimensional Fe3GeTe2. Nature 563, 94–99 (2018).
Zhang, G. et al. Above-room-temperature strong intrinsic ferromagnetism in 2D van der Waals Fe3GaTe2 with large perpendicular magnetic anisotropy. Nat. Commun. 13, 1–8 (2022).
Chen, Z., Yang, Y., Ying, T. & Guo, J. -g High-Tc Ferromagnetic Semiconductor in Thinned 3D Ising Ferromagnetic Metal Fe3GaTe2. Nano Lett. 24, 993–1000 (2024).
Mermin, N. D. & Wagner, H. Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models. Phys. Rev. Lett. 17, 1133–1136 (1966).
Irkhin, V. Y., Katanin, A. A. & Katsnelson, M. I. Self-consistent spin-wave theory of layered Heisenberg magnets. Phys. Rev. B 60, 1082–1099 (1999).
Lado, J. L. & Fernández-Rossier, J. On the origin of magnetic anisotropy in two dimensional CrI3. 2D Mater. 4, 035002 (2017).
Sødequist, J. & Olsen, T. Two-dimensional altermagnets from high throughput computational screening: Symmetry requirements, chiral magnons, and spin-orbit effects. Appl. Phys. Lett. 124, 182409 (2024).
Dzyaloshinsky, I. A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255 (1958).
Moriya, T. Anisotropic Superexchange Interaction and Weak Ferromagnetism. Phys. Rev. 120, 91–98 (1960).
Milivojević, M., Orozović, M., Picozzi, S., Gmitra, M. & Stavrić, S. Interplay of altermagnetism and weak ferromagnetism in two-dimensional RuF4. 2D Mater. 11, 035025 (2024).
Rößler, U. K., Bogdanov, A. N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797–801 (2006).
Yi, S. D., Onoda, S., Nagaosa, N. & Han, J. H. Skyrmions and anomalous Hall effect in a Dzyaloshinskii-Moriya spiral magnet. Phys. Rev. B 80, 054416 (2009).
Heinze, S. et al. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat. Phys. 7, 713–718 (2011).
Liu, Y., Yang, B., Guo, X., Picozzi, S. & Yan, Y. Modulation of skyrmion helicity by competition between Dzyaloshinskii-Moriya interaction and magnetic frustration. Phys. Rev. B 109, 094431 (2024).
Zhang, Y. et al. Emergence of skyrmionium in a two-dimensional CrGe(Se, Te)3 Janus monolayer. Phys. Rev. B 102, 241107 (2020).
Xu, C. et al. Topological spin texture in Janus monolayers of the chromium trihalides Cr(I, X)3. Phys. Rev. B 101, 060404 (2020).
Ga, Y. et al. Anisotropic Dzyaloshinskii-Moriya interaction protected by D2d crystal symmetry in two-dimensional ternary compounds. npj Comput. Mater. 8, 1–7 (2022).
Cui, Q. et al. Anisotropic Dzyaloshinskii–Moriya Interaction and Topological Magnetism in Two-Dimensional Magnets Protected by xn–P4m2-hwc Crystal Symmetry. Nano Lett. 22, 2334–2341 (2022).
Liang, J. et al. Very large Dzyaloshinskii-Moriya interaction in two-dimensional Janus manganese dichalcogenides and its application to realize skyrmion states. Phys. Rev. B 101, 184401 (2020).
Moessner, R. & Chalker, J. T. Low-temperature properties of classical geometrically frustrated antiferromagnets. Phys. Rev. B 58, 12049–12062 (1998).
Ramirez, A. P. Strongly Geometrically Frustrated Magnets. Annu. Rev. Mater. Res. 453–480 (1994).
Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010).
McGuire, M. A. Crystal and Magnetic Structures in Layered, Transition Metal Dihalides and Trihalides. Crystals 7, 121 (2017).
Rastelli, E., Tassi, A. & Reatto, L. Non-simple magnetic order for simple Hamiltonians. Physica B+C 97, 1–24 (1979).
Schmidt, B. & Thalmeier, P. Frustrated two dimensional quantum magnets. Phys. Rep. 703, 1–59 (2017).
Chakrabartty, D. et al. Role of Competing Magnetic Exchange on Non-Collinear to Collinear Magnetic Ordering and Skyrmion Stabilization in Centrosymmetric Hexagonal Magnets. ACS Nano 19, 3614–3623 (2025).
Amoroso, D., Barone, P. & Picozzi, S. Spontaneous skyrmionic lattice from anisotropic symmetric exchange in a Ni-halide monolayer. Nat. Commun. 11, 1–9 (2020).
Cheong, S.-W. & Mostovoy, M. Multiferroics: a magnetic twist for ferroelectricity. Nat. Mater. 6, 13–20 (2007).
Tokura, Y. & Seki, S. Multiferroics with Spiral Spin Orders. Adv. Mater. 22, 1554–1565 (2010).
Fumega, A. O. & Lado, J. L. Microscopic origin of multiferroic order in monolayer NiI2. 2D Mater. 9, 025010 (2022).
Song, Q. et al. Evidence for a single-layer van der Waals multiferroic. Nature 602, 601–605 (2022).
Kohn, W. Nobel Lecture: Electronic structure of matter—wave functions and density functionals. Rev. Mod. Phys. 71, 1253–1266 (1999).
Oroszlány, L., Ferrer, J., Deák, A., Udvardi, L. & Szunyogh, L. Exchange interactions from a nonorthogonal basis set: From bulk ferromagnets to the magnetism in low-dimensional graphene systems. Phys. Rev. B 99, 224412 (2019).
Korotin, D.mM., Mazurenko, V. V., Anisimov, V. I. & Streltsov, S. V. Calculation of exchange constants of the Heisenberg model in plane-wave-based methods using the Green’s function approach. Phys. Rev. B 91, 224405 (2015).
He, X., Helbig, N., Verstraete, M. J. & Bousquet, E. TB2J: A python package for computing magnetic interaction parameters. Comput. Phys. Commun. 264, 107938 (2021).
Martínez-Carracedo, G. et al. Relativistic magnetic interactions from nonorthogonal basis sets. Phys. Rev. B 108, 214418 (2023).
Zimmermann, B. et al. Comparison of first-principles methods to extract magnetic parameters in ultrathin films: Co/Pt(111). Phys. Rev. B 99, 214426 (2019).
Noodleman, L. Valence bond description of antiferromagnetic coupling in transition metal dimers. J. Chem. Phys. 74, 5737–5743 (1981).
Liechtenstein, A. I., Katsnelson, M. I., Antropov, V. P. & Gubanov, V. A. Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys. J. Magn. Magn. Mater. 67, 65–74 (1987).
Szilva, A. et al. Quantitative theory of magnetic interactions in solids. Rev. Mod. Phys. 95, 035004 (2023).
Sandratskii, L. M. & Guletskii, P. G. Symmetrised method for the calculation of the band structure of noncollinear magnets. J. Phys. F: Met. Phys. 16, L43 (1986).
Sandratskii, L. M. Symmetry analysis of electronic states for crystals with spiral magnetic order. I. General properties. J. Phys.: Condens. Matter 3, 8565 (1991).
Mounet, N. et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nat. Nanotechnol. 13, 246–252 (2018).
Haastrup, S. et al. The Computational 2D Materials Database: high-throughput modeling and discovery of atomically thin crystals. 2D Mater. 5, 042002 (2018).
Torelli, D., Moustafa, H., Jacobsen, K. W. & Olsen, T. High-throughput computational screening for two-dimensional magnetic materials based on experimental databases of three-dimensional compounds. npj Comput. Mater. 6, 1–12 (2020).
Gjerding, M. N. et al. Recent progress of the Computational 2D Materials Database (C2DB). 2D Mater. 8, 044002 (2021).
Sødequist, J. & Olsen, T. Type II multiferroic order in two-dimensional transition metal halides from first principles spin-spiral calculations. 2D Mater. 10, 035016 (2023).
Xiang, H., Lee, C., Koo, H.-J., Gong, X. & Whangbo, M.-H. Magnetic properties and energy-mapping analysis. Dalton Trans. 42, 823–853 (2012).
Li, X. et al. Spin Hamiltonians in Magnets: Theories and Computations. Molecules 26, 803 (2021).
Xiang, H. J., Kan, E. J., Wei, S.-H., Whangbo, M.-H. & Gong, X. G. Predicting the spin-lattice order of frustrated systems from first principles. Phys. Rev. B 84, 224429 (2011).
Xu, C., Feng, J., Xiang, H. & Bellaiche, L. Interplay between Kitaev interaction and single ion anisotropy in ferromagnetic CrI3 and CrGeTe3 monolayers. npj Comput. Mater. 4, 1–6 (2018).
Xu, C. et al. Possible Kitaev Quantum Spin Liquid State in 2D Materials with S = 3/2. Phys. Rev. Lett. 124, 087205 (2020).
Huber, S. P. et al. AiiDA 1.0, a scalable computational infrastructure for automated reproducible workflows and data provenance. Sci. Data 7, 1–18 (2020).
Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993).
Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).
Campi, D., Mounet, N., Gibertini, M., Pizzi, G. & Marzari, N. Expansion of the Materials Cloud 2D Database. ACS Nano 17, 11268–11278 (2023).
Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).
Rau, J. G., Lee, E. K.-H. & Kee, H.-Y. Generic Spin Model for the Honeycomb Iridates beyond the Kitaev Limit. Phys. Rev. Lett. 112, 077204 (2014).
Menichetti, G., Calandra, M. & Polini, M. Electronic structure and magnetic properties of few-layer Cr2Ge2Te6: the key role of nonlocal electron–electron interaction effects. 2D Mater. 6, 045042 (2019).
Uhrin, M., Huber, S. P., Yu, J., Marzari, N. & Pizzi, G. Workflows in AiiDA: Engineering a high-throughput, event-based engine for robust and modular computational workflows. Comput. Mater. Sci. 187, 110086 (2021).
Larsen, A. H. et al. The atomic simulation environment — a Python library for working with atoms. J. Phys.: Condens. Matter 29, 273002 (2017).
Zhuang, H. L., Xie, Y., Kent, P. R. C. & Ganesh, P. Computational discovery of ferromagnetic semiconducting single-layer CrSnTe3. Phys. Rev. B 92, 035407 (2015).
Chittari, B. L. et al. Electronic and magnetic properties of single-layer MPX3 metal phosphorous trichalcogenides. Phys. Rev. B 94, 184428 (2016).
Yang, K., Ning, Y., Ma, Y., Zhou, Y. & Wu, H. Contrasting magnetism in VPS3 and CrI3 monolayers with the common honeycomb S = 3/2 spin lattice. Phys. Rev. B 111, 134421 (2025).
Liu, C. et al. Probing the Néel-Type Antiferromagnetic Order and Coherent Magnon–Exciton Coupling in Van Der Waals VPS3. Adv. Mater. 35, 2300247 (2023).
Riedl, K. et al. Microscopic origin of magnetism in monolayer 3d transition metal dihalides. Phys. Rev. B 106, 035156 (2022).
Gu, Y. et al. Ni-based transition metal trichalcogenide monolayer: A strongly correlated quadruple-layer graphene. Phys. Rev. B 100, 165405 (2019).
Bazazzadeh, N. et al. Symmetry enhanced spin-Nernst effect in honeycomb antiferromagnetic transition metal trichalcogenide monolayers. Phys. Rev. B 103, 014425 (2021).
Basnet, R. et al. Controlling magnetic exchange and anisotropy by nonmagnetic ligand substitution in layered MPX3 (M = Ni, Mn; X = S, Se). Phys. Rev. Res. 4, 023256 (2022).
Peng, C. et al. Kitaev physics in the two-dimensional magnet NiPSe3. Phys. Rev. Res. 6, 033206 (2024).
Yang, J. et al. Zigzag antiferromagnetic property of two-dimensional NiPX3 (X = S/Se) monolayers in their pristine structure and Janus phase. RSC Adv. 15, 23115–23123 (2025).
Autieri, C. et al. Limited Ferromagnetic Interactions in Monolayers of MPS3 (M = Mn and Ni). J. Phys. Chem. C 126, 6791–6802 (2022).
Olsen, T. Magnetic anisotropy and exchange interactions of two-dimensional FePS3, NiPS3 and MnPS3 from first principles calculations. J. Phys. D: Appl. Phys. 54, 314001 (2021).
Zhang, D. et al. Topological Axion States in the Magnetic Insulator MnBi2Te4 with the Quantized Magnetoelectric Effect. Phys. Rev. Lett. 122, 206401 (2019).
Li, Y., Jiang, Z., Li, J., Xu, S. & Duan, W. Magnetic anisotropy of the two-dimensional ferromagnetic insulator MnBi2Te4. Phys. Rev. B 100, 134438 (2019).
Otrokov, M. M. et al. Prediction and observation of an antiferromagnetic topological insulator. Nature 576, 416–422 (2019).
Li, B. et al. Competing Magnetic Interactions in the Antiferromagnetic Topological Insulator MnBi2Te4. Phys. Rev. Lett. 124, 167204 (2020).
Yang, B., Han, X. & Picozzi, S. Emergence of topological bimerons in monolayer CrSBr. Phys. Rev. Mater. 9, 064003 (2025).
Kruse, M. et al. Two-dimensional ferroelectrics from high throughput computational screening. npj Comput. Mater. 9, 1–11 (2023).
Priessnitz, J. & Legut, D. OstravaJ: a tool for calculating magnetic exchange interactions via DFT. arXiv: 2501.08251 (2025).
Wan, G. et al. Sym4state.jl: An efficient computation package for magnetic materials. Comput. Phys. Commun. 303, 109283 (2024).
Lou, F. et al. PASP: Property analysis and simulation package for materials. J. Chem. Phys. 154, 114103 (2021).
Wang, B. et al. Prediction of a two-dimensional high-TC f-electron ferromagnetic semiconductor. Mater. Horiz. 7, 1623–1630 (2020).
Liu, Q. et al. Surprising pressure-induced magnetic transformations from helimagnetic order to antiferromagnetic state in NiI2. Nat. Commun. 16, 1–8 (2025).
Orozović, M., Šoškić, B. N., Picozzi, S., Šljivančanin, Ž & Stavrić, S. Hole doping as an efficient route to increase the Curie temperature in monolayer CrI3. 2D Mater. 12, 045025 (2025).
Abuawwad, N., Dias, M.dS., Abusara, H. & Lounis, S. CrTe2 as a two-dimensional material for topological magnetism in complex heterobilayers. Phys. Rev. B 108, 094409 (2023).
Ni, J. Y. et al. Giant Biquadratic Exchange in 2D Magnets and Its Role in Stabilizing Ferromagnetism of NiCl2 Monolayers. Phys. Rev. Lett. 127, 247204 (2021).
Li, X. et al. Realistic Spin Model for Multiferroic NiI2. Phys. Rev. Lett. 131, 036701 (2023).
Xiang, H. J., Kan, E. J., Zhang, Y., Whangbo, M.-H. & Gong, X. G. General Theory for the Ferroelectric Polarization Induced by Spin-Spiral Order. Phys. Rev. Lett. 107, 157202 (2011).
Edström, A., Barone, P., Picozzi, S. & Stengel, M. Magnetoelectricity of topological solitons in 2D magnets. npj Comput. Mater. 11, 295 (2025).
Cococcioni, M. & de Gironcoli, S. Linear response approach to the calculation of the effective interaction parameters in the LDA+U method. Phys. Rev. B 71, 035105 (2005).
Aryasetiawan, F., Karlsson, K., Jepsen, O. & Schönberger, U. Calculations of Hubbard U from first-principles. Phys. Rev. B 74, 125106 (2006).
Archer, T. et al. Exchange interactions and magnetic phases of transition metal oxides: Benchmarking advanced ab initio methods. Phys. Rev. B 84, 115114 (2011).
Desmarais, J. K., Flament, J.-P. & Erba, A. Spin-orbit coupling from a two-component self-consistent approach. II. Non-collinear density functional theories. J. Chem. Phys. 151, 074108 (2019).
Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).
Liechtenstein, A. I., Anisimov, V. I. & Zaanen, J. Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators. Phys. Rev. B 52, R5467–R5470 (1995).
Lançon, D., Ewings, R. A., Guidi, T., Formisano, F. & Wildes, A. R. Magnetic exchange parameters and anisotropy of the quasi-two-dimensional antiferromagnet NiPS3. Phys. Rev. B 98, 134414 (2018).
Musari, A. A. & Kratzer, P. Lattice dynamics, elastic, magnetic, thermodynamic and thermoelectric properties of the two-dimensional semiconductors MPSe3 (M = Cd, Fe and NI): a first-principles study. Mater. Res. Express 9, 106302 (2022).
Sun, H. et al. Coexistence of zigzag antiferromagnetic order and superconductivity in compressed NiPSe3. Materials Today Physics 36, 101188 (2023).
Acknowledgements
The authors acknowledge (in alphabetical order) Jakob Baumsteiger, Guido Menichetti, Lei Qiao, Alessandro Stroppa, and Cesare Tresca for useful discussions. The necessary structure files for the dataset generation were provided as a courtesy by Davide Campi. The work was funded by the European Union—NextGenerationEU, through the ICSC-Centro Nazionale di Ricerca in High-Performance Computing, Big Data and Quantum Computing (Grant No. CN00000013, CUP J93C22000540006, PNRR Investimento M4.C2.1.4). A.M. and M.G. acknowledge partial support from the PRIN Project “Simultaneous electrical control of spin and valley polarisation in van der Waals magnetic materials” (SECSY–CUP Grant Nos. E53D23001700006 and J53D23001400001, PNRR Investimento M4.C2.1.1), which is funded by the European Union—NextGenerationEU. S.P. acknowledges partial support from the PRIN Project “SORBET—Spin-orbit effects in two-dimensional magnets” (IT-MIUR Grant No. 2022ZY8HJY) within NextGenerationEU. S.P., A.D. and G.C. acknowledge partial support from PNRR Partenariato PE4 “National Quantum Science and Technology Institute” (NQSTI) project PE0000023 (CUP B53C22004180005), the CANVAS project (CUP B53C22005670005), funded by the Italian Ministry of the Environment and the Energy Security and the National Innovation Ecosystem VITALITY (Grant No. ECS00000041, CUP B43C22000470005). The views and opinions expressed are solely those of the authors and do not necessarily reflect those of the European Union, nor can the European Union be held responsible for them. S.S. acknowledges financial support from the Vinča Institute, provided by the Ministry of Science, Technological Development, and Innovation of the Republic of Serbia. S.S., P.B., A.D., G.C. and S.P. acknowledge additional funding from the Ministry of Foreign Affairs of Italy and the Ministry of Science, Technological Development, and Innovation of Serbia through the bilateral project “Van der Waals Heterostructures for Altermagnetic Spintronic”, realised under the executive programme for scientific and technological cooperation between the two countries.We acknowledge the CINECA award under the ISCRA initiative (project ISCRA-B HP10BA00W3), for the availability of high-performance computing resources and support.
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F.O. software preparation, execution, supervision, data analysis, writing—original draft; A.D. execution, supervision, writing—original draft; L.V., C.F. software preparation; G.C. execution; P.B. supervision; A.M., M.G. conceptualisation, supervision; S.S. conceptualisation, software preparation; S.P. conceptualisation, supervision. All authors participated in the revision and editing of the manuscript and approved the final version.
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Orlando, F., Droghetti, A., Varrassi, L. et al. AMaRaNTA: automated first-principles exchange parameters in 2D magnets. npj Comput Mater (2026). https://doi.org/10.1038/s41524-026-01968-4
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DOI: https://doi.org/10.1038/s41524-026-01968-4
