Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Nuclear spin polarization and control in hexagonal boron nitride

Abstract

Electron spins in van der Waals materials are playing a crucial role in recent advances in condensed-matter physics and spintronics. However, nuclear spins in van der Waals materials remain an unexplored quantum resource. Here we report optical polarization and coherent control of nuclear spins in a van der Waals material at room temperature. We use negatively charged boron vacancy ($${V}_{\mathrm{B}}^{-}$$) spin defects in hexagonal boron nitride to polarize nearby nitrogen nuclear spins. We observe the Rabi frequency of nuclear spins at the excited-state level anti-crossing of $${V}_{\mathrm{B}}^{-}$$ defects to be 350 times larger than that of an isolated nucleus, and demonstrate fast coherent control of nuclear spins. Further, we detect strong electron-mediated nuclear–nuclear spin coupling that is five orders of magnitude larger than the direct nuclear-spin dipolar coupling, enabling multi-qubit operations. Our work opens new avenues for the manipulation of nuclear spins in van der Waals materials for quantum information science and technology.

This is a preview of subscription content, access via your institution

Access options

\$32.00

All prices are NET prices.

Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The custom codes that support the findings of this study are available from the corresponding author upon reasonable request.

References

1. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).

2. Zhang, Y., Tan, Y.-W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).

3. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

4. Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419–425 (2013).

5. Novoselov, K., Mishchenko, A., Carvalho, A. & Castro Neto, A. 2D materials and van der Waals heterostructures. Science 353, aac9439 (2016).

6. Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005).

7. Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).

8. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

9. Gong, C. et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature 546, 265–269 (2017).

10. Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270–273 (2017).

11. Banerjee, A. et al. Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet. Nat. Mater. 15, 733–740 (2016).

12. Chen, Y. et al. Strong correlations and orbital texture in single-layer 1T-TaSe2. Nat. Phys. 16, 218–224 (2020).

13. Liu, X. & Hersam, M. C. 2D materials for quantum information science. Nat. Rev. Mater. 4, 669–684 (2019).

14. Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).

15. Cai, J., Retzker, A., Jelezko, F. & Plenio, M. B. A large-scale quantum simulator on a diamond surface at room temperature. Nat. Phys. 9, 168–173 (2013).

16. Gershenfeld, N. A. & Chuang, I. L. Bulk spin-resonance quantum computation. Science 275, 350–356 (1997).

17. Lovchinsky, I. et al. Magnetic resonance spectroscopy of an atomically thin material using a single-spin qubit. Science 355, 503–507 (2017).

18. Gottscholl, A. et al. Initialization and read-out of intrinsic spin defects in a van der Waals crystal at room temperature. Nat. Mater. 19, 540–545 (2020).

19. Gottscholl, A. et al. Room temperature coherent control of spin defects in hexagonal boron nitride. Sci. Adv. 7, eabf3630 (2021).

20. Abdi, M., Chou, J.-P., Gali, A. & Plenio, M. B. Color centers in hexagonal boron nitride monolayers: a group theory and ab initio analysis. ACS Photonics 5, 1967–1976 (2018).

21. Ivády, V. et al. Ab initio theory of the negatively charged boron vacancy qubit in hexagonal boron nitride. npj Comput. Mater. 6, 41 (2020).

22. Reimers, J. R. et al. Photoluminescence, photophysics, and photochemistry of the $${V}_{\mathrm{B}}^{-}$$ defect in hexagonal boron nitride. Phys. Rev. B 102, 144105 (2020).

23. Chejanovsky, N. et al. Single-spin resonance in a van der Waals embedded paramagnetic defect. Nat. Mater. 20, 1079–1084 (2021).

24. Stern, H. L. et al. Room-temperature optically detected magnetic resonance of single defects in hexagonal boron nitride. Nat. Commun. 13, 618 (2022).

25. Pakdel, A., Bando, Y. & Golberg, D. Nano boron nitride flatland. Chem. Soc. Rev. 43, 934–959 (2014).

26. Kianinia, M., White, S., Froch, J. E., Bradac, C. & Aharonovich, I. Generation of spin defects in hexagonal boron nitride. ACS Photonics 7, 2147–2152 (2020).

27. Gao, X. et al. High-contrast plasmonic-enhanced shallow spin defects in hexagonal boron nitride for quantum sensing. Nano Lett. 21, 7708–7714 (2021).

28. Guo, N.-J. et al. Generation of spin defects by ion implantation in hexagonal boron nitride. ACS Omega 7, 1733–1739 (2022).

29. Gao, X. et al. Femtosecond laser writing of spin defects in hexagonal boron nitride. ACS Photonics 8, 994–1000 (2021).

30. Gottscholl, A. et al. Spin defects in hBN as promising temperature, pressure and magnetic field quantum sensors. Nat. Commun. 12, 4480 (2021).

31. Healey, A. et al. Quantum microscopy with van der Waals heterostructures. Preprint at https://arxiv.org/abs/2112.03488 (2021).

32. Huang, M. et al. Wide field imaging of van der Waals ferromagnet Fe3GeTe2 by spin defects in hexagonal boron nitride. Preprint at https://arxiv.org/abs/2112.13570 (2021).

33. Dutt, M. G. et al. Quantum register based on individual electronic and nuclear spin qubits in diamond. Science 316, 1312–1316 (2007).

34. Gangloff, D. et al. Quantum interface of an electron and a nuclear ensemble. Science 364, 62–66 (2019).

35. Ruskuc, A., Wu, C.-J., Rochman, J., Choi, J. & Faraon, A. Nuclear spin-wave quantum register for a solid-state qubit. Nature 602, 408–413 (2022).

36. Bermudez, A., Jelezko, F., Plenio, M. B. & Retzker, A. Electron-mediated nuclear-spin interactions between distant nitrogen-vacancy centers. Phys. Rev. Lett. 107, 150503 (2011).

37. Ping, Y. & Smart, T. J. Computational design of quantum defects in two-dimensional materials. Nat. Comput. Sci. 1, 646–654 (2021).

38. Smart, T. J., Li, K., Xu, J. & Ping, Y. Intersystem crossing and exciton–defect coupling of spin defects in hexagonal boron nitride. npj Comput. Mater. 7, 59 (2021).

39. Wu, F., Galatas, A., Sundararaman, R., Rocca, D. & Ping, Y. First-principles engineering of charged defects for two-dimensional quantum technologies. Phys. Rev. Mater. 1, 071001 (2017).

40. Mathur, N. et al. Excited-state spin-resonance spectroscopy of $${V}_{\mathrm{B}}^{-}$$ defect centers in hexagonal boron nitride. Nat. Commun. 13, 3233 (2022).

41. Baber, S. et al. Excited state spectroscopy of boron vacancy defects in hexagonal boron nitride using time-resolved optically detected magnetic resonance. Nano Lett. 22, 461 (2022).

42. Yu, P. et al. Excited-state spectroscopy of spin defects in hexagonal boron nitride. Nano Lett. 22, 3545–3549 (2022).

43. Mu, Z. et al. Excited-state optically detected magnetic resonance of spin defects in hexagonal boron nitride. Phys. Rev. Lett. 128, 216402 (2022).

44. Jacques, V. et al. Dynamic polarization of single nuclear spins by optical pumping of nitrogen-vacancy color centers in diamond at room temperature. Phys. Rev. Lett. 102, 057403 (2009).

45. Murzakhanov, F. F. Electron–nuclear coherent coupling and nuclear spin readout through optically polarized $${V}_{\mathrm{B}}^{-}$$ spin states in hBN. Nano Lett. 22, 2718–2724 (2022).

46. Chen, M., Hirose, M. & Cappellaro, P. et al. Measurement of transverse hyperfine interaction by forbidden transitions. Phys. Rev. B 92, 020101 (2015).

47. Sangtawesin, S. et al. Hyperfine-enhanced gyromagnetic ratio of a nuclear spin in diamond. New J. Phys. 18, 083016 (2016).

48. Lee, J., Park, H. & Seo, H. First-principles theory of extending the spin qubit coherence time in hexagonal boron nitride. Preprint at https://arxiv.org/abs/2202.04346 (2022).

49. Haykal, A. et al. Decoherence of $${V}_{\mathrm{B}}^{-}$$ spin defects in monoisotopic hexagonal boron nitride. Nat. Commun. 13, 4347 (2022).

50. Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 21, 395502 (2009).

51. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).

Acknowledgements

T.L. thanks the Purdue Quantum Science and Engineering Institute (PQSEI) for support through the seed grant, the DARPA NLM program, the DARPA QUEST program and the National Science Foundation under grant no. PHY-2110591. Y.P. is supported by the National Science Foundation under grant no. DMR-1760260. A.E.L.A and Y.P.C. acknowledge support by the Quantum Science Center, a US Department of Energy, Office of Science, National Quantum Information Science Research Center. Y.P.C. also thanks the hospitality of NIMS and support of Tohoku AIMR and FriDUO program. B.J. and S.A.B. are supported by the Office of Naval Research (ONR) grant award no. N00014-20-1-2806. K.W. and T.T. acknowledge support from JSPS KAKENHI (grant nos. 19H05790, 20H00354 and 21H05233). The ab initio calculations used resources of the lux supercomputer at the University of California, Santa Cruz, funded by the National Science Foundation MRI grant no. AST 1828315; the Center for Functional Nanomaterials, which is a US Department of Energy, Office of Science, facility; and the Scientific Data and Computing center, a component of the Computational Science Initiative, at Brookhaven National Laboratory under contract no. DE-SC0012704.

Author information

Authors

Contributions

T.L. and X.G. conceived and designed the project. X.G., Z.X., S.V., P.J. and K.S. built the setup. K.L., X.G. and S.V. performed the calculations. B.J. fabricated the MW waveguides. T.T. and K.W. grew the hBN crystals. X.G., S.V. and A.E.L.A. created the hBN nanosheets with spin defects. X.G. performed the measurements. X.G., T.L., S.V., K.L. and Y.P. analysed the results. T.L., Y.P., Y.P.C. and S.A.B supervised the project. All the authors contributed to the writing of the manuscript.

Corresponding author

Correspondence to Tongcang Li.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Materials thanks Weibo Gao, Fedor Jelezko and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–12, Table 1 and discussion.

Source data

Source Data Fig. 1

Source data for Fig. 1.

Source Data Fig. 2

Source data for Fig. 2.

Source Data Fig. 3

Source data for Fig. 3.

Source Data Fig. 4

Source data for Fig. 4.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

Gao, X., Vaidya, S., Li, K. et al. Nuclear spin polarization and control in hexagonal boron nitride. Nat. Mater. 21, 1024–1028 (2022). https://doi.org/10.1038/s41563-022-01329-8

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41563-022-01329-8