Skip to main content

Thank you for visiting 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


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

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Optical polarization of nuclear spins in hBN with \({V}_{\mathrm{B}}^{-}\) spin defects.
Fig. 2: Polarization of the three nearest nitrogen nuclear spins.
Fig. 3: ODNMR spectroscopy of the three nearest nitrogen nuclear spins.
Fig. 4: Coherent control of nuclear spins in hBN.

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.


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

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  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).

    Article  CAS  Google Scholar 

  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).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

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

    Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  31. Healey, A. et al. Quantum microscopy with van der Waals heterostructures. Preprint at (2021).

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

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

    Article  CAS  Google Scholar 

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

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

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

    CAS  Article  Google Scholar 

  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).

    Google Scholar 

  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).

    CAS  Article  Google Scholar 

Download references


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 and Affiliations



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.

Additional information

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.

Reporting Summary

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

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gao, X., Vaidya, S., Li, K. et al. Nuclear spin polarization and control in hexagonal boron nitride. Nat. Mater. 21, 1024–1028 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing