0.01 eV per atom lower than the spin-paired structure, the structure
was concluded to be magnetically more stable than its non-magnetic
counterpart. The atomic structures of calculated self-intercalated TMDs
(33.3% and 66.7% intercalation concentration) are presented in Supple-
mentary Fig. 29, in which the polymorphism of single-layer MoX 2 , WX 2 ,
NbX 2 and TaX 2 (X = S, Se and Te) reveals an H-phase, whereas the rest of
the TMDs are T-phase, adopting an AA stacking polytype. MoX 2 and WX 2
adopt the AA′ stacking order whereas NbX 2 and TaX 2 adopt AB′ stack-
ing. All intercalants occupy the octahedral vacancies in the vdW gap.
Data availability
The main data supporting the findings of this study are available within
the paper and its Supplementary Information. Additional data are
available from the corresponding authors upon reasonable request.
Code availability
The Python code is available in the Supplementary Information.
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Acknowledgements K.P.L. thanks A*STAR Project ‘Scalable Growth of Ultrathin Ferroelectric
Materials for Memory Technologies’ (grant number A1983c0035) and support from the Centre
for Advanced 2D Materials, National University of Singapore. W.Z. acknowledges support from
the National Key R&D Program of China (2018YFA0305800) and the Natural Science
Foundation of China (51622211). S.J.P. is grateful to the National University of Singapore for
funding and the Ministry of Education (MOE) for a Tier 2 grant ‘Atomic scale understanding and
optimization of defects in 2D materials’ (MOE2017-T2-2-139). Z.L. thanks the MOE for a Tier 2
grant (2017-T2-2-136) and a Tier 3 grant (2018-T3-1-002), and the A*STAR QTE programme. X.L.
acknowledges support from the National Natural Science Foundation of China (grant number
11804286) and the Fundamental Research Funds for the Central Universities (grant number
19lgpy263). DFT calculations were performed using resources of the National Supercomputer
Center in Guangzhou supported by the Special Program for Applied Research on Super
Computation of the NSFC Guangdong Joint Fund (second phase). K.S.T. acknowledges funding
from the European Research Council under the European Union’s Horizon 2020 research and
innovation programme (grant number 773122, LIMA). The Center for Nanostructured Graphene
is sponsored by the Danish National Research Foundation, project DNRF103. We thank J. P. Shi,
F. F. Cui and Y. F. Zhang for providing high-quality CVD samples.Author contributions X.Z., S.J.P. and K.P.L. conceived the idea. S.J.P. and K.P.L. supervised the
execution of the whole work. X.Z. and W.Z. performed the electron microscopy experiments
and data analysis. X.L., A.C.R.-J. and C.W. performed the DFT calculations and data analysis.
A.C.R.-J. and K.S.T. performed the high-throughput DFT calculations. W.F., Y.D., L.K. and Z.L.
grew the samples. D.W. and T.V. measured the magnetism. P.S. performed device fabrication
and measurement. J.D. and S.N. developed the Python scripts for data analysis. All authors
discussed the results and participated in writing the manuscript.Competing interests The authors declare no competing interests.
Additional information
Supplementary information is available for this paper at https://doi.org/10.1038/s41586-020-
2241-9.
Correspondence and requests for materials should be addressed to X.L., S.J.P. or K.P.L.
Peer review information Nature thanks Thomas Heine and the other, anonymous, reviewer(s)
for their contribution to the peer review of this work.
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