pith. sign in

arxiv: 2604.09794 · v1 · submitted 2026-04-10 · ❄️ cond-mat.mtrl-sci · cond-mat.mes-hall

Ferromagnetic interlayer exchange coupling in a few layers of CrSBr on a gold thin film

Pith reviewed 2026-05-10 17:25 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.mes-hall
keywords CrSBrferromagnetic orderinginterlayer exchange couplinggold thin filmvan der Waals magnetselectron transferdensity functional theoryspin-polarized low energy electron microscopy
0
0 comments X

The pith

Electron transfer from gold stabilizes ferromagnetic ordering in CrSBr layers thinner than 11 nm.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that thin layers of the van der Waals magnet CrSBr placed on a gold film exhibit a ferromagnetic ground state rather than the antiferromagnetic ordering found in thicker samples or bulk. This change occurs for thicknesses below 11 nanometers. The authors attribute the stabilization to electrons transferring from the gold into the CrSBr, which alters the interlayer exchange coupling. This is supported by direct imaging with spin-polarized low energy electron microscopy and by density functional theory calculations. Reflected-electron spectroscopy further reveals modifications to the unoccupied electronic states in the thin layers on gold.

Core claim

Using spin-polarized low energy electron microscopy, we directly image the magnetic texture of thin CrSBr on a Au film and uncover a ferromagnetic ground state for CrSBr thicknesses smaller than 11 nm. We argue that the stabilization of the ferromagnetic ordering is obtained via electron transfer from the Au film to the CrSBr flakes, in agreement with ab-initio density functional theory calculations. Reflected-electron spectroscopy shows clear differences in the unoccupied density of states between a few layers of CrSBr on Au and bulk CrSBr, pointing towards electronic band structure modification in thin CrSBr.

What carries the argument

Electron transfer from the gold film to the CrSBr layers, which modifies the interlayer exchange coupling to favor ferromagnetic alignment over the conventional antiferromagnetic state.

Load-bearing premise

The ferromagnetic state observed below 11 nm thickness results specifically from electron transfer from the gold rather than from strain, hybridization, or other interface effects not captured in the model.

What would settle it

If spin-polarized low energy electron microscopy images show antiferromagnetic ordering in CrSBr on gold below 11 nm thickness, or if density functional theory calculations that block charge transfer from gold still predict a ferromagnetic ground state.

read the original abstract

The two-dimensional character of van der Waals magnets allows for efficient control of their properties via proximity effects and electrical stimuli, making them promising candidates for application in spin-electronics. We use spin-polarized low energy electron microscopy to directly image the magnetic texture of thin CrSBr on top of a Au film, uncovering a ferromagnetic ground state for CrSBr thicknesses smaller than 11 nm. We argue that the stabilization of the ferromagnetic ordering - as compared to the conventional antiferromagnetic one - is obtained via electron transfer from the Au film to the CrSBr flakes, in agreement with ab-initio density functional theory calculations. Reflected-electron spectroscopy shows clear differences in the unoccupied density of states between a few layers of CrSBr on Au and bulk CrSBr, pointing towards electronic band structure modification in thin CrSBr. This work sheds light on the possibility to tune magnetic properties of two-dimensional magnets via substrate engineering.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript reports direct imaging via spin-polarized low-energy electron microscopy (SPLEEM) of a ferromagnetic ground state in CrSBr flakes thinner than 11 nm deposited on a gold thin film, contrasting with the antiferromagnetic ordering typical of thicker or bulk CrSBr. The authors attribute the stabilization of ferromagnetic interlayer exchange coupling to electron transfer from the Au substrate into the CrSBr layers. This interpretation is supported by ab-initio DFT calculations showing that electron doping favors the ferromagnetic state, and by reflected-electron spectroscopy indicating modifications to the unoccupied density of states in the thin layers on Au relative to bulk CrSBr. The work highlights substrate engineering as a route to tune magnetic properties in 2D van der Waals magnets.

Significance. If the causal mechanism is confirmed, the result would be significant for the field of 2D magnetism and spintronics, demonstrating a practical proximity effect that converts the native antiferromagnetic interlayer coupling to ferromagnetic in a thickness range relevant for devices. The direct SPLEEM imaging of the magnetic texture and the consistency check provided by DFT calculations are clear strengths; the spectroscopy data further supports electronic-structure modification at the interface.

major comments (3)
  1. [Abstract and discussion of mechanism] The central claim (abstract and discussion) that the observed ferromagnetic state for thicknesses below 11 nm arises specifically from electron transfer from Au is load-bearing for the interpretation but rests on DFT agreement without direct experimental quantification of transferred charge density or Fermi-level position in the CrSBr. No core-level XPS shifts, transport measurements, or ARPES data are presented to establish the doping level, leaving strain, vdW hybridization, or other interface perturbations as viable alternatives not experimentally excluded.
  2. [Reflected-electron spectroscopy section] In the reflected-electron spectroscopy results, the reported differences in unoccupied DOS between thin CrSBr on Au and bulk CrSBr are consistent with band-structure changes but do not isolate doping as the cause; the data lack comparison to control models (e.g., strained CrSBr without charge transfer or hybrid interface calculations) that would be needed to rule out competing interface effects.
  3. [DFT calculations] The DFT calculations (supporting the electron-transfer scenario) assume a specific charge redistribution at the interface that propagates through ~10–15 monolayers to stabilize FM order up to 11 nm; however, the manuscript provides no sensitivity analysis on the transferred charge amount nor cross-check against any estimated experimental doping, weakening the link between the model and the observed thickness threshold.
minor comments (2)
  1. [Figures] Figure captions and axis labels in the SPLEEM and spectroscopy panels could more explicitly state the CrSBr thicknesses and reference the bulk comparison sample for clarity.
  2. [Experimental methods] A brief statement on the uncertainty in the exact number of monolayers corresponding to the 11 nm threshold would help readers assess how far the interface effect extends.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which highlight important aspects of our interpretation. We address each major comment point by point below. We have revised the manuscript to clarify limitations and strengthen the presentation of our evidence where possible, while maintaining the core findings from SPLEEM imaging, DFT, and spectroscopy.

read point-by-point responses
  1. Referee: [Abstract and discussion of mechanism] The central claim (abstract and discussion) that the observed ferromagnetic state for thicknesses below 11 nm arises specifically from electron transfer from Au is load-bearing for the interpretation but rests on DFT agreement without direct experimental quantification of transferred charge density or Fermi-level position in the CrSBr. No core-level XPS shifts, transport measurements, or ARPES data are presented to establish the doping level, leaving strain, vdW hybridization, or other interface perturbations as viable alternatives not experimentally excluded.

    Authors: We agree that direct quantification of charge transfer (e.g., via XPS, ARPES, or transport) would provide stronger causal evidence and that alternatives such as strain or vdW hybridization are not fully excluded by experiment. Our interpretation integrates the thickness-dependent FM imaging, DFT results showing FM stabilization with electron doping, and spectroscopic DOS changes. In the revised manuscript, we will tone down the abstract and discussion to describe electron transfer as a supported mechanism rather than the sole confirmed cause, and add explicit discussion of alternative interface effects and the indirect nature of the evidence. revision: partial

  2. Referee: [Reflected-electron spectroscopy section] In the reflected-electron spectroscopy results, the reported differences in unoccupied DOS between thin CrSBr on Au and bulk CrSBr are consistent with band-structure changes but do not isolate doping as the cause; the data lack comparison to control models (e.g., strained CrSBr without charge transfer or hybrid interface calculations) that would be needed to rule out competing interface effects.

    Authors: The spectroscopy data demonstrate clear modifications to the unoccupied DOS in thin CrSBr on Au relative to bulk, consistent with interface-induced electronic changes. We acknowledge that without control calculations for strain or hybridization effects, doping cannot be isolated as the unique cause. Such additional modeling is computationally demanding and outside the present scope. We will revise the spectroscopy section to state that the results indicate band-structure modification at the interface but do not exclusively establish doping as the mechanism, while retaining the data as supporting evidence aligned with the DFT scenario. revision: partial

  3. Referee: [DFT calculations] The DFT calculations (supporting the electron-transfer scenario) assume a specific charge redistribution at the interface that propagates through ~10–15 monolayers to stabilize FM order up to 11 nm; however, the manuscript provides no sensitivity analysis on the transferred charge amount nor cross-check against any estimated experimental doping, weakening the link between the model and the observed thickness threshold.

    Authors: The DFT calculations model charge redistribution at the Au/CrSBr interface and show how it can stabilize FM order over multiple layers, matching the experimental thickness range. We did not include a sensitivity analysis on charge amount or direct comparison to experimental doping estimates, since no independent doping measurement was performed. In the revised manuscript, we will add a discussion of the model's assumptions, including how different charge-transfer values affect the FM thickness threshold, to better connect the calculations to the observed 11 nm limit. revision: partial

Circularity Check

0 steps flagged

No circularity: experimental imaging and DFT consistency check are independent

full rationale

The paper's core result is the direct experimental observation via SPLEEM of a ferromagnetic ground state in CrSBr flakes thinner than 11 nm on Au, which stands on its own as an imaging measurement. The interpretation that this arises specifically from electron transfer is presented as an argument supported by separate ab-initio DFT calculations (showing FM stabilization under doping) and reflected-electron spectroscopy (showing DOS modifications). No load-bearing step reduces a claimed prediction or uniqueness result to a fitted parameter, self-defined quantity, or prior self-citation by construction. DFT functions as an external consistency check rather than a derivation whose output is forced by the experimental inputs. No equations or ansatze in the provided chain exhibit self-definitional or renaming circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The work is primarily experimental with supporting standard DFT; no new free parameters are introduced to fit the magnetic transition, no ad-hoc axioms are stated beyond routine assumptions of DFT, and no new particles or entities are postulated.

pith-pipeline@v0.9.0 · 5516 in / 1099 out tokens · 60665 ms · 2026-05-10T17:25:18.586837+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

40 extracted references · 40 canonical work pages

  1. [1]

    Nature , year =

    Burch, K.S., Mandrus, D., Park, J.-G.: Magnetism in two-dimensional van der Waals materials. Nature563, 47–52 (2018). https://doi.org/10.1038/s41586-018-0631-z

  2. [2]

    Nature Nanotechnology14, 408–419 (2019)

    Gibertini, M., Koperski, M., Morpurgo, A.F., Novoselov, K.S.: Magnetic 2D materials and heterostructures. Nature Nanotechnology14, 408–419 (2019). https://doi.org/10.1038/ s41565-019-0438-6

  3. [3]

    Gate-tunable room-temperature ferromagnetism in two-dimensional Fe3GeTe2,

    Deng, Y., Yu, Y., Song, Y., Zhang, J., Wang, N.Z., Sun, Z., Yi, Y., Wu, Y.Z., Wu, S., Zhu, J., Wang, J., Chen, X.H., Zhang, Y.: Gate-tunable room-temperature ferromagnetism in two-dimensional Fe3GeTe2. Nature563, 94–99 (2018). https://doi.org/10.1038/s41586-018-0626-9

  4. [4]

    and Fox, Eli J

    Sharpe, A.L., Fox, E.J., Barnard, A.W., Finney, J., Watanabe, K., Taniguchi, T., Kastner, M.A., Goldhaber-Gordon, D.: Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science365, 605–608 (2019). https://doi.org/10.1126/science.aaw3780

  5. [5]

    Nature Communications15, 4735 (2024)

    Tabataba-Vakili, F., Nguyen, H.P.G., Rupp, A., Mosina, K., Papavasileiou, A., Watanabe, K., Taniguchi, T., Maletinsky, P., Glazov, M.M., Sofer, Z., Baimuratov, A.S., H¨ ogele, A.: Doping- control of excitons and magnetism in few-layer crsbr. Nature Communications15, 4735 (2024). https://doi.org/10.1038/s41467-024-49048-9

  6. [6]

    Nature Commu- nications15, 1298 (2024)

    Hendriks, F., Rojas-Lopez, R.R., Koopmans, B., Guimar˜ aes, M.H.D.: Electric control of optically- induced magnetization dynamics in a van der waals ferromagnetic semiconductor. Nature Commu- nications15, 1298 (2024). https://doi.org/10.1038/s41467-024-45623-2

  7. [7]

    Nature Nanotechnology20, 609–616 (2025)

    Yao, F., Liao, M., Gibertini, M., Cheon, C.-Y., Lin, X., Wu, F., Watanabe, K., Taniguchi, T., Guti´ errez-Lezama, I., Morpurgo, A.F.: Switching on and off the spin polarization of the conduction band in antiferromagnetic bilayer transistors. Nature Nanotechnology20, 609–616 (2025). https: //doi.org/10.1038/s41565-025-01872-w

  8. [8]

    npj Computational Materials7, 162 (2021)

    Soriano, D., Rudenko, A.N., Katsnelson, M.I., R¨ osner, M.: Environmental screening and ligand- field effects to magnetism in CrI3 monolayer. npj Computational Materials7, 162 (2021). https: //doi.org/10.1038/s41524-021-00631-4

  9. [9]

    Physical Review B107, 235107 (2023)

    Bianchi, M., Acharya, S., Dirnberger, F., Klein, J., Pashov, D., Mosina, K., Sofer, Z., Rudenko, A.N., Katsnelson, M.I., van Schilfgaarde, M., R¨ osner, M., Hofmann, P.: Paramagnetic electronic structure of CrSBr: Comparison between ab initio G W theory and angle-resolved photoemission spectroscopy. Physical Review B107, 235107 (2023). https://doi.org/10....

  10. [10]

    npj Computational Materials9(1), 83 (2023)

    Rudenko, A.N., R¨ osner, M., Katsnelson, M.I.: Dielectric tunability of magnetic properties in orthorhombic ferromagnetic monolayer crsbr. npj Computational Materials9(1), 83 (2023). https: //doi.org/10.1038/s41524-023-01050-3

  11. [11]

    ACS Nano17, 22684–22690 (2023)

    Xie, K., Zhang, X.-W., Xiao, D., Cao, T.: Engineering Magnetic Phases of Layered Antiferromag- nets by Interfacial Charge Transfer. ACS Nano17, 22684–22690 (2023). https://doi.org/10.1021/ acsnano.3c07125

  12. [12]

    npj 2D Materials and Applications8, 54 (2024)

    Watson, M.D., Acharya, S., Nunn, J.E., Nagireddy, L., Pashov, D., R¨ osner, M., van Schilfgaarde, M., Wilson, N.R., Cacho, C.: Giant exchange splitting in the electronic structure of A-type 2D antiferromagnet CrSBr. npj 2D Materials and Applications8, 54 (2024). https://doi.org/10.1038/ s41699-024-00492-7

  13. [13]

    Advanced Materials32(2020)

    Telford, E.J., Dismukes, A.H., Lee, K., Cheng, M., Wieteska, A., Bartholomew, A.K., Chen, Y., Xu, X., Pasupathy, A.N., Zhu, X., Dean, C.R., Roy, X.: Layered antiferromagnetism induces large negative magnetoresistance in the van der waals semiconductor crsbr. Advanced Materials32(2020). https://doi.org/10.1002/adma.202003240

  14. [14]

    ISBN 979-8-89176-335-7

    Zhai, Z., Liu, W., Guo, X., Schulze, D.J., Kuo, T.-W., Agarwal, N., Stangel, A., Joshi, P., Liu, J.P., Deng, L., Hovden, R., Zhao, L., Chu, C.-W., Lv, B.: Emergent ferromagnetism and 11 unusual irreversible magnetoresistance in an intercalated van der Waals antiferromagnet. Proceed- ings of the National Academy of Sciences123(4), 2527293123 (2026). https:...

  15. [15]

    npj 2D Materials and Applications10, 26 (2026)

    Ghimirey, Y.P., Nagireddy, L., Cacho, C., Wilson, N.R., Watson, M.D.: The two conduction bands of monolayer CrSBr on Au. npj 2D Materials and Applications10, 26 (2026). https://doi.org/10. 1038/s41699-026-00662-9

  16. [16]

    Tschudin, M.A., Broadway, D.A., Siegwolf, P., Schrader, C., Telford, E.J., Gross, B., Cox, J., Dubois, A.E.E., Chica, D.G., Rama-Eiroa, R., J. G. Santos, E., Poggio, M., Ziebel, M.E., Dean, C.R., Roy, X., Maletinsky, P.: Imaging nanomagnetism and magnetic phase transitions in atomically thin CrSBr. Nature Communications15, 6005 (2024). https://doi.org/10....

  17. [17]

    npj 2D Materials and Applications7, 62 (2023)

    Ghiasi, T.S., Borst, M., Kurdi, S., Simon, B.G., Bertelli, I., Boix-Constant, C., Ma˜ nas-Valero, S., van der Zant, H.S.J., van der Sar, T.: Nitrogen-vacancy magnetometry of CrSBr by diamond membrane transfer. npj 2D Materials and Applications7, 62 (2023). https://doi.org/10.1038/ s41699-023-00423-y

  18. [18]

    Advanced Materials34, 2201000 (2022)

    Rizzo, D.J., McLeod, A.S., Carnahan, C., Telford, E.J., Dismukes, A.H., Wiscons, R.A., Dong, Y., Nuckolls, C., Dean, C.R., Pasupathy, A.N., Roy, X., Xiao, D., Basov, D.N.: Visualizing Atomically Layered Magnetism in CrSBr. Advanced Materials34, 2201000 (2022). https://doi.org/10.1002/ adma.202201000

  19. [19]

    Advanced Materials29, 1702354 (2017) https://doi.org/10.1002/adma

    Zur, Y., Noah, A., Boix-Constant, C., Ma˜ nas-Valero, S., Fridman, N., Rama-Eiroa, R., Huber, M.E., Santos, E.J.G., Coronado, E., Anahory, Y.: Magnetic Imaging and Domain Nucleation in CrSBr Down to the 2D Limit. Advanced Materials35, 2307195 (2023). https://doi.org/10.1002/adma. 202307195

  20. [20]

    Nano Letters24, 4319–4329 (2024)

    Ziebel, M.E., Feuer, M.L., Cox, J., Zhu, X., Dean, C.R., Roy, X.: CrSBr: An Air-Stable, Two- Dimensional Magnetic Semiconductor. Nano Letters24, 4319–4329 (2024). https://doi.org/10.1021/ acs.nanolett.4c00624

  21. [21]

    Identification of crystalline materials with ultra-low thermal conductivity based on machine learning study

    Song, S.W., Klein, J., Mosina, K., Sofer, Z., Sedmidubsk´ y, D., Dong, J., Chen, K., Ross, F.M., Jaramillo, R.: Magnetic Secondary Phases in the Annealed van der Waals Antiferromagnet CrSBr. The Journal of Physical Chemistry C129, 19002–19011 (2025). https://doi.org/10.1021/acs.jpcc. 5c04211

  22. [22]

    Rougemaille, A

    Rougemaille, N., Schmid, A.K.: Magnetic imaging with spin-polarized low-energy electron microscopy. The European Physical Journal Applied Physics50, 20101 (2010). https://doi.org/10. 1051/epjap/2010048

  23. [23]

    Nature Materials21(7), 754–760 (2022)

    Telford, E.J., Dismukes, A.H., Dudley, R.L., Wiscons, R.A., Lee, K., Chica, D.G., Ziebel, M.E., Han, M.-G., Yu, J., Shabani, S., Scheie, A., Watanabe, K., Taniguchi, T., Xiao, D., Zhu, Y., Pasupathy, A.N., Nuckolls, C., Zhu, X., Dean, C.R., Roy, X.: Coupling between magnetic order and charge transport in a two-dimensional magnetic semiconductor. Nature Ma...

  24. [24]

    In: Kaufmann, E.N

    Flege, J.I., Tang, W.X., Altman, M.S.: Low-Energy Electron Microscopy. In: Kaufmann, E.N. (ed.) Characterization of Materials, pp. 1–22. Wiley, Hoboken, NJ, USA (2012). https://doi.org/10.1002/ 0471266965.com157

  25. [25]

    arXiv:2411.18761 (2024)

    Dale, N., Ashour, O.A., Vila, M., Regmi, R.B., Fox, J., Johnson, C.W., Fedorov, A., Stibor, A., Ghimire, N.J., Griffin, S.M.: Non-relativistic spin splitting above and below the Fermi level in a g-wave altermagnet. arXiv:2411.18761 (2024)

  26. [26]

    Nature Communications14, 5966 (2023)

    Wang, T., Zhang, D., Yang, S., Lin, Z., Chen, Q., Yang, J., Gong, Q., Chen, Z., Ye, Y., Liu, W.: Magnetically-dressed crsbr exciton-polaritons in ultrastrong coupling regime. Nature Communications14, 5966 (2023). https://doi.org/10.1038/s41467-023-41688-7

  27. [27]

    Physical Review B108, 195410 (2023)

    Bianchi, M., Hsieh, K., Porat, E.J., Dirnberger, F., Klein, J., Mosina, K., Sofer, Z., Rudenko, A.N., 12 Katsnelson, M.I., Chen, Y.P., R¨ osner, M., Hofmann, P.: Charge transfer induced Lifshitz transition and magnetic symmetry breaking in ultrathin CrSBr crystals. Physical Review B108, 195410 (2023). https://doi.org/10.1103/PhysRevB.108.195410

  28. [28]

    ACS Nano17(6), 5316–5328 (2023)

    Klein, J., Pingault, B., Florian, M., Heißenb¨ uttel, M.-C., Steinhoff, A., Song, Z., Torres, K., Dirn- berger, F., Curtis, J.B., Weile, M., Penn, A., Deilmann, T., Dana, R., Bushati, R., Quan, J., Luxa, J., Sofer, Z., Al` u, A., Menon, V.M., Wurstbauer, U., Rohlfing, M., Narang, P., Lonˇ car, M., Ross, F.M.: The Bulk van der Waals Layered Magnet CrSBr is...

  29. [29]

    Advanced Functional Materials34(2), 2307259 (2024)

    Yu, J., Liu, D., Ding, Z., Yuan, Y., Zhou, J., Pei, F., Pan, H., Ma, T., Jin, F., Wang, L., Zhu, W., Wang, S., Wu, Y., Liu, X., Hou, D., Gao, Y., Qiu, Z., Yang, M., Li, Q.: Direct Imaging of Antiferromagnet-Ferromagnet Phase Transition in van der Waals Antiferromagnet CrSBr. Advanced Functional Materials34(2), 2307259 (2024). https://doi.org/10.1002/adfm....

  30. [30]

    Nature Communications17, 853 (2025)

    Zhao, G., Zhao, Y., Zhang, Y., Yang, K., Guo, Z., Liu, J., Zhao, T., Yan, K., Chen, X., Li, Q., Cheng, Y., Zhang, C., Wang, Z., Liu, Y., Ye, J., Mei, J.-W., Yuan, Z., Shi, W.: Doping-induced magnetic phase transition enables all-electrical spin control in CrSBr. Nature Communications17, 853 (2025). https://doi.org/10.1038/s41467-025-67561-3

  31. [31]

    Physical Review B112, 144442 (2025)

    den Teuling, R., Das, R., Bondarenko, A.V., Tartakovskaya, E.V., Bauer, G.E.W., Blanter, Y.M.: Spin waves in the bilayer van der Waals magnet CrSBr. Physical Review B112, 144442 (2025). https://doi.org/10.1103/w4xn-2yff

  32. [32]

    Nature Communications16, 9498 (2025)

    Hong, C., Sun, Z., Sheng, Z., Wu, S., Chen, Y., Tian, M., Wan, N., Mi, Q., Liu, Z., Chu, W., Wu, S.: Charge transfer governed interlayer magnetic coupling and symmetry breaking in a van der Waals magnet. Nature Communications16, 9498 (2025). https://doi.org/10.1038/s41467-025-64555-z

  33. [33]

    arXiv:2510.08018 (2025)

    Mondal, P., Verma, S., Lan, W., Krelle, L., Tan, R., von Klitzing, R., Watanabe, K., Taniguchi, T., Mosina, K., Sofer, Z., Kamra, A., Urbaszek, B.: Twist-tuned exchange and hysteresis in a bilayer van der Waals magnet. arXiv:2510.08018 (2025)

  34. [34]

    Nature Nanotechnology , year=

    Cenker, J., Sivakumar, S., Xie, K., Miller, A., Thijssen, P., Liu, Z., Dismukes, A., Fonseca, J., Anderson, E., Zhu, X., Roy, X., Xiao, D., Chu, J.-H., Cao, T., Xu, X.: Reversible strain-induced magnetic phase transition in a van der Waals magnet. Nature Nanotechnology17, 256–261 (2022). https://doi.org/10.1038/s41565-021-01052-6

  35. [35]

    Kresse, G., Joubert, D.: From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B59, 1758–1775 (1999)

  36. [36]

    Kresse and J

    Kresse, G., Hafner, J.: Ab initio molecular dynamics for liquid metals. Physical Review B47, 558–561 (1993). https://doi.org/10.1103/PhysRevB.47.558

  37. [37]

    Physical Review B54, 11169–11186 (1996)

    Kresse, G., Furthm¨ uller, J.: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review B54, 11169–11186 (1996). https://doi.org/10.1103/ PhysRevB.54.11169

  38. [38]

    Perdew, J.P., Burke, K., Ernzerhof, M.: Generalized Gradient Approximation Made Simple. Phys. Rev. Lett.77, 3865–3868 (1996). https://doi.org/10.1103/PhysRevLett.77.3865

  39. [39]

    Liechtenstein, A.I., Anisimov, V.I., Zaanen, J.: Density-functional theory and strong interactions: Orbital ordering in mott-hubbard insulators. Phys. Rev. B52, 5467–5470 (1995). https://doi.org/ 10.1103/PhysRevB.52.R5467

  40. [40]

    Effect of the damping function in disper- sion corrected density functional theory,

    Grimme, S., Ehrlich, S., Goerigk, L.: Effect of the damping function in dispersion corrected density functional theory. Journal of Computational Chemistry32(7), 1456–1465 (2011). https://doi.org/ 10.1002/jcc.21759 13