Na in diamond: high spin defects revealed by the ADAQ high-throughput computational database.pdf
npj | computational materials Article Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences https://doi.org/10.1038/s41524-024-01292-9 Na in diamond: high spin defects revealed by the ADAQ high-throughput computational database Check for updates Joel Davidsson , William Stenlund, Abhijith S. Parackal, Rickard Armiento & Igor A. Abrikosov Color centers in diamond are at the forefront of the second quantum revolution. A handful of defects are in use, and ﬁnding ones with all the desired properties for quantum applications is arduous. By using high-throughput calculations, we screen 21,607 defects in diamond and collect the results in the ADAQ database. Upon exploring this database, we ﬁnd not only the known defects but also several unexplored defects. Speciﬁcally, defects containing sodium stand out as particularly relevant because of their high spins and predicted improved optical properties compared to the NV center. Hence, we studied these in detail, employing high-accuracy theoretical calculations. The single sodium substitutional (NaC) has various charge states with spin ranging from 0.5 to 1.5, ZPL in the near- infrared, and a high Debye-Waller factor, making it ideal for biological quantum applications. The sodium vacancy (NaV) has a ZPL in the visible region and a potential rare spin-2 ground state. Our results show sodium implantation yields many interesting spin defects that are valuable additions to the arsenal of point defects in diamond studied for quantum applications. Of all point defects in diamond, the NV center1–3 stands out as the most studied and used in quantum applications with many ongoing parallel efforts. It fulﬁlls many of the defect properties listed for various quantum applications4. The NV center is the main defect considered as a computa- tional qubit5,6 with recent advancements in fault-tolerant operation7. While more work is needed before it can be realized at large scale8, it has already demonstrated promise as a ﬂying qubit by transmitting quantum infor- mation over long distance9 and multinode network capabilities10,11, which goes towards the quantum internet12,13. It has also been demonstrated as memoryforquantuminformation14,15.Recentadvancesinquantumsensing with NV centers include magnetrometry16 at extreme conditions17, nano- scale nuclear magnetic resonance18–20, relaxometry21, and biological applications22–24. These are just some of the explored and proposed appli- cations for the NV center. It is a genuinely versatile defect that is also well understoodfromthetheoreticalside25,26withknownpropertiessuchasspin- 1, many-body structure etc. However, the NV center does have some drawbacks. It has a Zero Phonon Line (ZPL) in the visible range (outside the ﬁrst and second biological window27,28 as well as the telecom region29) with a low Debye-Waller factor (~3.2%30) and is affected by spectral diffusion31–33. Other defects in diamond improve on these aspects. The group 14 (Si34–37, Ge38,39, Sn40,41, and Pb42,43) vacancy centers44 have a wide range of ZPLs from near-infrared to visible with higher Debye-Waller factors, from about 20% to 70%45. Since the dopant sits between two vacancy positions, known as a split-vacancy conﬁguration, these defects have D3d symmetry, speciﬁcally inversion, that suppresses spectral diffusion. This property, combined with the high Debye-Waller factor, makes these defects ideal for photonics46–48. They are also considered spin qubits, and as the ion size increases, the ground state splitting becomes larger, providing coherent spin control as demonstrated for the SnV49,50. However, the group 14 vacancy centers also have some drawbacks. They are spin-1/2, one of the defect states are below or just above to the valence band edge, and the ZPLs are in the visible range. There are a handful of other less studied defects in diamond, mainly other vacancy complexes in a split-vacancy conﬁguration. Theoretically suggesteddefects include the group 13 (Al, Ga,In, and Tl) vacancycenters51. These centers have spin-1 and ZPLs in the visible region with Debye-Waller factors from about 15% to 43%. Another vacancy defect is the MgV center with spin-1/2 in the negative charge state with a Debye-Waller factor of 54%52. This defect is found along with single substitutional Mg during Mg implantation53. Yet another vacancy complex is the NiV with spin-1/2, ZPL in the near-infrared range, and predicted Debye-Waller factor between28% and 74%54. Recent experimental study announced the Debye-Waller factor for this defect is 51%55. The NiC (W8) is a related defect with notably spin-3/2 56,57. This defect is one of the few with spin-3/2 reported in diamond. Themoststudiedspin-3/2defectisthesiliconvacancyinSiC58.Thehighspin gives unique sensing opportunities for strain and temperature which are Department of Physics, Chemistry and Biology, Linköping University, Linköping, Sweden. e-mail: joel.davidsson@liu.se npj Computational Materials |  (2024) 10:109  1 1234567890():,; 1234567890():,; universal for defects with spin larger or equal to spin-3/2 59. So far, no spin-2 defectindiamondhasbeenreported.Morediamonddefectscanbefoundin Refs. 60,61. High-throughput experimental search has studied known defects in diamond62. Apart from the known defects in diamonds, there are many unknown defects63. Notable examples include: ST1 (spin-0, ZPL in the visible range, oxygenrelated)64–66; TR12(spin0,ZPLinthe visiblerange,staticJahn-Teller distortion)67,68; implanted defects with F (ZPL in the visible range, possibly FV center with spin-1/2 or spin-1)69, and Xe (ZPL in the ultraviolet range with high Debye Waller around 74%, possibly XeV center with spin-1/2 or spin-1)70. Given all these defects, has the best defect in diamond been found? To answer this, we turn to theoretical high-throughput methods. Previous such studies systematically looked at vacancy center complexes71. However, this study limits the dopants to p-elements and the defects to vacancy centers. The large space of point defects in diamond remains unexplored. In this paper, we screen defects in diamond using the high-throughput framework ADAQ (Automatic Defect Analysis and Qualiﬁcation)72,73, whichinturnusesthehigh-throughputtoolkit(httk)74.TheADAQsoftware package is a culmination of a series of publications related to SiC58,75–77 that focus on accurately calculating magneto-optical propertiesfor point defects, such as ZPL. ADAQ has been successfully applied to SiC and CaO, where modiﬁed silicon vacancy78 and XCaVO defects with X = Sb, Bi, and I79 were found. In this paper, we turn our attention to diamond to investigate single and double defects consisting of vacancies as well as substitutional and interstitial s- and p-elements, however, we do exclude interstitial-interstitial clusters (due to sheer size of them, about 90000 defects). We include defects that are separated up to 2.6 Å, which roughly corresponds to second nearest neighbors and we only make double defects with one external dopant. The result is a total of 21,607 defects to consider. These defects were screened at the PBE DFT level (see “Discussion” for more on the workﬂow and cal- culational details), and the results were stored to the ADAQ database. The stored properties include: formation energy, charge transition levels, defect levels, defect spin, zero phonon line with radiative lifetime and transition dipole moment (including polarization), ΔQ (relaxation between ground and excited state), and more. This paper is organized as follows: “Results” is divided into two main parts, database searches and spin defects with sodium. “Database Search: Intro”describeshowthemoststabledefectsarefoundonthedefecthull,and discusses ZPL accuracy for the previously known defects in diamond. Here, we also narrow down the number of relevant defects for quantum appli- cations by multiple searches that ﬁlter out defects with NV-like properties (spin-1 and a bright ZPL, “Database Search: NV-like Spin-1 Defects”), higher spin states (spin-3/2 “Database Search: Spin-3/2 Defects” and spin-2 “DatabaseSearch:Spin-2Defects”),orhighDebye-Wallerfactors(Database Search: Spin Defects With a High Debye-Waller Factor). Whenconsidering all these properties, the sodium substitutional and vacancy center stand out. Hence, in “Sodium Substitutional NaC” and “Sodium Vacancy (NaV)”, we studied these defects further with higher-order methods (such as HSE DFT calculation) to conﬁrm their properties. Results This section is divided into two main parts: several sections exploring dif- ferent point defects in diamonds and two more sections examining spin defects with sodium in more detail. Database search: intro The most stable defects are located on the defect hull—the lowest formation energy per stoichiometry and per Fermi energy78,80. In the ADAQ database, all known defects, consisting of s- and p-elements, mentioned in the introduction are found on the defect hull. In this section, we discuss these defects and their optical properties compared with experiments and other theoretical calculations. ADAQ predicts the ZPL of defects with at least one occupied and unoccupied defect state within the band gap. However, due to the use of the PBE functional, they are systematically underestimated. For the NV center, ADAQ predicts a ZPL of 1.700 eV (see Table 1), whereas the experimental value is 1.945 eV1 (a difference of 0.245 eV). For the group 14 vacancy defects;SiV, GeV,and SnV do not have a ZPL inthedatabasebecause one of the defect states involved in the transition is below the valence band edge45. However, as the dopant gets larger, the defect state enters the band gap45. Hence, the PbV center does have a state in the band gap, which ADAQ ﬁnds and predicts a ZPL of 2.122 eV, which is close to the measured 2.384 eV (520 nm)42 (a difference of 0.263 eV). In general, we ﬁnd from comparing the ADAQ ZPL predictions from the screening workﬂow to experimentally measured defects that the ZPLs are underestimated by around 0.25 eV (mean difference). Similar mean difference and variation are observed for defects in SiC72,75,78. One can also compare the ADAQ ZPL predictions with other theo- retical results. For the group 13 vacancy defects, the ADAQ ZPLs are AlV 1.00 eV, GaV 1.72 eV, InV 1.87 eV, and TlV 2.31 eV (see Table 1). When comparing with the HSE calculations done in ref. 51, the ZPLs are for GaV 1.82 eV (difference 0.1 eV), InV 2.12 eV (difference 0.25 eV), and TlV 2.84 eV (0.53 eV). The ZPL for the AlV center is not reported due to numerical convergence issues51. Finally, the MgV center is on the defect hull, and ADAQ reports a ZPL of 0.31 eV.In the screeningworkﬂow,ADAQcalculates onlyone excitation. This excitation for the MgV defect matches with the theoretical results in ref. 52, where the lowest excitation (2Eg −2Eu in the doublet state without Jahn–Teller effect) has an adsorption value of 0.7 eV. Database search: NV-like Spin-1 defects To look for NV-like defects, we search for spin-1 defects on the defect hull with a ZPL larger than 0.5 eV and a transition dipole moment (TDM) larger than 3 debye. We ﬁnd 15 unique defects, seeTable 1. Apart from the already discussed substitutional vacancy complexes (the NV center and group 13 vacancies), there are also vacancy centers consisting of Li and Ba. Both of these show similar properties as the NV center, but with lower ZPL and ΔQ for both, and higher brightness for the Ba defect. The Ba defect has a large formation energy, about 20 eV, which is similar to the XeCVacC. Large formation energy is not necessarily a problem since XeV is suggested to be the most probable defect after Xe implantation70. ADAQ supports this conclusion since the single Xe sub- stitutional has a higher formation energy of around 29 eV. Table 1 | Spin-1 defects on defect hull with ZPL larger than 0.5 eV and TDM larger than 3 debye Defect Defect Charge ZPL TDM ΔQ Type [eV] [debye] [amu1/2Å] XV (known) NCVacC −1 1.70 6.66 0.56 AlCVacC −1 1.0 5.92 0.51 GaCVacC −1 1.72 5.33 0.48 InCVacC −1 1.88 6.31 0.33 TlCVacC −1 2.31 3.61 0.46 XV LiCVacC 1 0.64 4.38 0.41 BaCVacC 0 1.29 11.17 0.42 XCIntC ICIntC −1 0.57 3.34 0.80 BrCIntC −1 0.63 7.91 0.51 XCIntX KCIntK 0 0.82 7.62 0.78 XCXC MgCMgC 0 0.63 3.55 0.58 XC KC −1 0.6 3.77 0.96 KC 1 0.78 5.74 0.24 XeC 0 0.73 5.78 0.49 FC −1 1.20 9.83 0.42 HC −1 1.29 6.86 0.60 https://doi.org/10.1038/s41524-024-01292-9 Article npj Computational Materials |  (2024) 10:109  2 2.4. The isosurface level used in Fig. 2 c) is 0.025 Å−3, same as ref. 89, while the isolevel in b) is ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 0:025 p Å−3/2 = 0.1581 Å−3/2, meaning the a1 orbital in b) has the exact same shape as ∣a1∣2. Data availability FormoreinformationabouttheADAQdatabase,seehttps://httk.org/adaq/. Code availability For more information about the ADAQ source code, see https://httk.org/ adaq/. Received: 22 June 2023; Accepted: 11 May 2024; References 1. Davies, G., Hamer, M. F. & Price, W. C. Optical studies of the 1.945 eV vibronic band in diamond. Proc. R. Soc. A Math. Phys. Sci. 348, 285–298 (1976). 2. Gruber,A. etal. Scanningconfocal opticalmicroscopyandmagnetic resonance on single defect centers. Science 276, 2012–2014 (1997). 3. Jelezko, F. et al. Single spin states in a defect center resolved by optical spectroscopy. Appl. Phys. Lett. 81, 2160–2162 (2002). 4. Wolfowicz, G. et al. Quantum guidelines for solid-state spin defects. Nat. Rev. Mater. 6, 906–925 (2021). 5. Nizovtsev, A. P. et al. 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Support from the Swedish Government Strategic Research Area Swedish e-science Research Centre (SeRC) and the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971) are gratefully acknowledged. This work was partially sup- portedby the KnutandAlice Wallenberg Foundationthrough the Wallenberg Centre for Quantum Technology (WACQT). J.D. and R.A. acknowledge support from the Swedish Research Council (VR) Grant no. 2022-00276 and 2020-05402, respectively. The computations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) and the Swedish National Infrastructure for Computing (SNIC) at NSC, partially funded by the Swedish Research Council through grant agreement nos. 2022-06725 and no. 2018-05973. Author contributions J.D. conceptualized the project in discussion with R.A., analyzed the data, and wrote the manuscript. W.S. performed the sodium defects calculations and made the ﬁgures. A.P. performedthe high-throughputcalculations. R.A. and I.A.A. supervised the project and reviewed the manuscript. Funding Open access funding provided by Linköping University. Competing interests The authors declare no competing interests. Additional information Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41524-024-01292-9. Correspondence and requests for materials should be addressed to Joel Davidsson. Reprints and permissions information is available at http://www.nature.com/reprints Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional afﬁliations. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. © The Author(s) 2024 https://doi.org/10.1038/s41524-024-01292-9 Article npj Computational Materials |  (2024) 10:109  9
Title: Na in diamond: high spin defects revealed by the ADAQ high-throughput computational database ​

Authors: Joel Davidsson, William Stenlund, Abhijith S. Parackal, Rickard Armiento, Igor A. Abrikosov ​
Publisher: Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences ​
Date: 2024-05-11 00:00:00
Abstract: Color centers in diamond are at the forefront of the second quantum revolution. ​ A handful of defects are in use, and finding ones with all the desired properties for quantum applications is arduous. ​ By using high-throughput calculations, we screen 21,607 defects in diamond and collect the results in the ADAQ database. ​ Upon exploring this database, we find not only the known defects but also several unexplored defects. ​ Specifically, defects containing sodium stand out as particularly relevant because of their high spins and predicted improved optical properties compared to the NV center. ​ Hence, we studied these in detail, employing high-accuracy theoretical calculations. ​ The single sodium substitutional (NaC) has various charge states with spin ranging from 0.5 to 1.5, ZPL in the near-infrared, and a high Debye-Waller factor, making it ideal for biological quantum applications. ​ The sodium vacancy (NaV) has a ZPL in the visible region and a potential rare spin-2 ground state. ​ Our results show sodium implantation yields many interesting spin defects that are valuable additions to the arsenal of point defects in diamond studied for quantum applications. ​