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arxiv: 2502.00551 · v4 · pith:SAKAAY3Nnew · submitted 2025-02-01 · ❄️ cond-mat.mtrl-sci

Deep Spin Defects in Zinc Oxide for High-Fidelity Single-Shot Readout

Shimin Zhang , Taejoon Park , Erik Perez , Kejun Li , Xingyi Wang , Masoud Mansouri , Yanyong Wang , Jorge D Vega Bazantes
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Ruiqi Zhang Jianwei Sun Kai-Mei C. Fu Hosung Seo Yuan Ping
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Pith reviewed 2026-05-23 03:35 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords zinc oxidespin defectsmolybdenum vacancyoptically addressable qubitsHuang-Rhys factorspin coherencefirst-principles calculationssingle-shot readout
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The pith

The molybdenum-vacancy complex in zinc oxide forms an optically addressable spin qubit with millisecond coherence and high-fidelity readout.

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

The paper uses first-principles calculations to predict that a specific defect in zinc oxide meets the requirements for a usable spin qubit. It identifies the molybdenum-vacancy complex as having a spin-triplet ground state, visible optical transitions, and unusually weak coupling to vibrations. These features are shown to support long spin coherence times and reliable optical readout even at higher temperatures. If accurate, the result expands the set of host materials available for solid-state quantum devices beyond established options like diamond or silicon carbide.

Core claim

First-principles calculations establish that the molybdenum-vacancy complex Mo_Zn-V_O in ZnO possesses a spin-triplet ground state, visible-range optical transitions with high quantum yield, a Huang-Rhys factor of approximately 5, and spin coherence times of about 4 ms when nuclear and impurity baths are included. Strong spin-orbit coupling combined with the lack of Jahn-Teller distortion enables spin-selective intersystem crossing, which in turn supports high-fidelity single-shot readout across wide magnetic field ranges and at elevated temperatures.

What carries the argument

The molybdenum-vacancy complex (Mo_Zn-V_O), whose formation energy, optical transitions, Huang-Rhys factor, and spin dynamics are computed from first-principles to demonstrate qubit suitability.

If this is right

  • Spin coherence remains near 4 ms provided paramagnetic impurity levels stay below 0.035 ppm.
  • High-fidelity single-shot readout becomes feasible at room temperature and over broad magnetic fields due to spin-selective intersystem crossing.
  • Zinc oxide joins the list of viable hosts for deep-level defect qubits, enabling integration with existing oxide electronics and photonics.
  • The combination of dilute nuclear spins in ZnO and the defect's small Huang-Rhys factor reduces decoherence channels compared with other known ZnO defects.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Device fabrication could leverage mature ZnO growth techniques to place the defect at controlled depths for scalable qubit arrays.
  • Similar vacancy-complex motifs in other wide-bandgap oxides may warrant first-principles screening for comparable optical and spin properties.
  • Temperature-dependent readout fidelity measurements would directly test the predicted absence of Jahn-Teller distortion effects.

Load-bearing premise

The first-principles calculations correctly predict the defect's formation, optical properties, electron-phonon coupling strength, and spin coherence without large errors from the exchange-correlation functional or finite supercell size.

What would settle it

Experimental measurement of the Huang-Rhys factor for the Mo_Zn-V_O defect in real ZnO crystals yielding a value well above 10 would indicate the computed optical properties do not hold.

Figures

Figures reproduced from arXiv: 2502.00551 by Erik Perez, Hosung Seo, Jianwei Sun, Jorge D Vega Bazantes, Kai-Mei C. Fu, Kejun Li, Masoud Mansouri, Ruiqi Zhang, Shimin Zhang, Taejoon Park, Xingyi Wang, Yanyong Wang, Yuan Ping.

Figure 1
Figure 1. Figure 1: FIG. 1: The computational workflow of defect candi [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Defect formation energies of complex vacancy [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Single-particle levels and wavefunctions. Single-particle defect levels (horizontal black (majority spin) and [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Electron-phonon properties of (Mo [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Spin decoherence of transition metal-vacancy [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Electronic spin-induced decoherence time T [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Spin properties and optical read-out of [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
read the original abstract

Wide-bandgap oxides such as ZnO are favorable hosts for spin defect qubits due to their dilute nuclear spin background and potential for ultra-high purity. Yet, a deep-level defect qubit with robust optical and spin properties has not been identified in this material. Here, using first-principles calculations, we predict that the molybdenum-vacancy complex, Mo_Zn-V_O, exhibits the essential characteristics of an optically addressable spin qubit: a spin-triplet ground state, visible-range optical transitions with high quantum yield, and an unusually small Huang-Rhys factor (~5, compared to 10-30 in known ZnO defects). We further find long spin coherence times (T_2 ~ 4 ms) when both nuclear and impurity spin baths are considered, with paramagnetic impurities setting a threshold concentration of 0.035 ppm. Importantly, the combination of strong spin-orbit coupling and the absence of Jahn-Teller distortion supports spin-selective intersystem crossing and high-fidelity single-shot readout at elevated temperatures and across wide magnetic field ranges. By identifying ZnO as a host for deep-level defect qubits, our work points toward a pathway to scalable, integrable oxide-based quantum technologies and broadens the material foundation for solid-state quantum information science.

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

2 major / 2 minor

Summary. The manuscript uses first-principles calculations to predict that the molybdenum-vacancy complex (Mo_Zn-V_O) in ZnO exhibits the properties of an optically addressable spin qubit, including a spin-triplet ground state, visible-range optical transitions with high quantum yield, an unusually small Huang-Rhys factor of ~5 (versus 10-30 for known ZnO defects), long spin coherence times T_2 ~4 ms (limited by paramagnetic impurities at 0.035 ppm threshold), and high-fidelity single-shot readout enabled by strong spin-orbit coupling and lack of Jahn-Teller distortion.

Significance. If the predictions hold, the work would be significant by establishing ZnO as a viable host for deep-level defect qubits, leveraging its dilute nuclear-spin background and high-purity potential for scalable, integrable quantum technologies. The reported combination of small HR factor, long T_2, and robust readout would broaden the material platform for solid-state quantum information science beyond conventional hosts.

major comments (2)
  1. [Abstract and Computational Methods] Abstract and Computational Methods: The central quantitative claims (HR factor ~5, T_2 ~4 ms, high-fidelity readout) rest on the accuracy of the first-principles results, yet no details are provided on the exchange-correlation functional, supercell size, k-point sampling, or convergence tests for the configuration-coordinate diagrams, electron-phonon coupling, or spin-bath calculations. This is load-bearing because semi-local functionals commonly used for ZnO defects can misplace levels by 0.3-1 eV and alter relaxation energies, potentially changing the reported HR factor and coherence time by tens of percent and undermining the 'unusually small' and 'long' descriptors.
  2. [Results section on spin coherence] Results section on spin coherence: The T_2 ~4 ms value and 0.035 ppm impurity threshold are presented as key for elevated-temperature operation, but without explicit description of the spin-bath model (e.g., how nuclear and impurity baths are treated or any cluster-correlation expansion parameters), it is impossible to assess whether the long coherence survives realistic variations in the computational setup.
minor comments (2)
  1. [Abstract] The comparison of HR factors to 'known ZnO defects' (10-30) should include explicit citations to the specific prior calculations or experiments being referenced.
  2. Figure captions and text should clarify whether the optical transitions are computed including or excluding zero-phonon-line shifts and whether quantum-yield estimates include non-radiative pathways beyond the HR factor.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which highlight the need for greater methodological transparency. We address each major comment below and have revised the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: [Abstract and Computational Methods] Abstract and Computational Methods: The central quantitative claims (HR factor ~5, T_2 ~4 ms, high-fidelity readout) rest on the accuracy of the first-principles results, yet no details are provided on the exchange-correlation functional, supercell size, k-point sampling, or convergence tests for the configuration-coordinate diagrams, electron-phonon coupling, or spin-bath calculations. This is load-bearing because semi-local functionals commonly used for ZnO defects can misplace levels by 0.3-1 eV and alter relaxation energies, potentially changing the reported HR factor and coherence time by tens of percent and undermining the 'unusually small' and 'long' descriptors.

    Authors: We agree that these computational details are essential for assessing the robustness of the quantitative predictions. In the revised manuscript we have expanded the Computational Methods section to specify the exchange-correlation functional (including Hubbard U values), supercell sizes, k-point sampling, and convergence tests performed for the configuration-coordinate diagrams and electron-phonon coupling. These additions directly address the concern regarding possible shifts in defect levels and relaxation energies. revision: yes

  2. Referee: [Results section on spin coherence] Results section on spin coherence: The T_2 ~4 ms value and 0.035 ppm impurity threshold are presented as key for elevated-temperature operation, but without explicit description of the spin-bath model (e.g., how nuclear and impurity baths are treated or any cluster-correlation expansion parameters), it is impossible to assess whether the long coherence survives realistic variations in the computational setup.

    Authors: We acknowledge that an explicit description of the spin-bath model is required. In the revised manuscript we have added a dedicated paragraph in the spin-coherence Results section that details the treatment of nuclear and impurity baths, the cluster-correlation expansion parameters, and the assumptions underlying the 0.035 ppm threshold. This will enable evaluation of the coherence time under variations in the computational setup. revision: yes

Circularity Check

0 steps flagged

No circularity: all listed properties derived from first-principles DFT calculations with no fitted inputs or self-referential definitions.

full rationale

The paper's central claims rest on first-principles calculations of defect properties (spin-triplet ground state, optical transitions, Huang-Rhys factor, spin coherence times). No equations or steps reduce by construction to fitted parameters renamed as predictions, self-citations that bear the load of uniqueness, or ansatzes smuggled in. The derivation chain is external to the paper's own outputs and can be independently reproduced or falsified with different functionals or supercell sizes. This is the standard non-circular case for ab initio defect papers.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the accuracy of standard DFT approximations for defect electronic structure and spin dynamics in ZnO; no free parameters are explicitly fitted in the abstract, but the defect itself is a new postulated entity whose properties are computed rather than measured.

axioms (1)
  • domain assumption Density functional theory with standard approximations is sufficiently accurate to predict defect formation energies, optical transitions, Huang-Rhys factors, and spin coherence times in ZnO.
    Invoked throughout the computational prediction described in the abstract.
invented entities (1)
  • Mo_Zn-V_O complex no independent evidence
    purpose: Optically addressable spin qubit host
    New defect complex introduced and characterized computationally; no experimental confirmation provided.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Rationalizing defect formation energies in metals and semiconductors with semilocal density functionals

    cond-mat.mtrl-sci 2026-04 unverdicted novelty 5.0

    LDA outperforms other functionals for monovacancy formation energies in fcc metals, while the LAK meta-GGA yields the highest accuracy for interstitials in diamond silicon, approaching QMC benchmarks.

Reference graph

Works this paper leans on

143 extracted references · 143 canonical work pages · cited by 1 Pith paper

  1. [1]

    of 0.40µsand 0.37µsfor (Mo ZnvO)2+ and (Nb ZnvO)+, respectively. Both exhibit strong non- Gaussian features with stretched exponents of 0.51 and 0.56 for (Mo ZnvO)2+ and (Nb ZnvO)+, respectively, due to a strong anisotropic hyperfine coupling [68]. We re- mark that the T ∗ 2 times of these qubit candidates are an order of magnitude smaller than that of di...

    work page

  2. [2]

    𝑒)|−⟩ |+⟩ 1𝐸 (𝑒𝑒) 1𝐴

    of (Nb ZnvO)+ (a) and (Mo ZnvO)2+ (b) in ZnO under various external magnetic field strengths (B0). (c, d) Hahn-echo coherence decay (T 2 ) of (Nb ZnvO)+ (c) and (Mo ZnvO)2+ (d) in ZnO under various external magnetic field strengths. FIG. 6: Electronic spin-induced decoherence time T 2 as a function of electron spin concentrations. The black dashed line sh...

    work page

  3. [3]

    M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. L. Hollenberg, Phys. Rep.528, 1 (2013)

    work page 2013

  4. [4]

    Orphal-Kobin, C

    L. Orphal-Kobin, C. G. Torun, J. M. Bopp, G. Pieplow, and T. Schr¨ oder, Adv. Quantum Technol.n/a, 2300432 (2024)

    work page 2024

  5. [5]

    I. B. W. Harris and D. Englund, Phys. Rev. B109, 085414 (2024)

    work page 2024

  6. [6]

    Karapatzakis, J

    I. Karapatzakis, J. Resch, M. Schrodin, P. Fuchs, M. Ki- eschnick, J. Heupel, L. Kussi, C. S¨ urgers, C. Popov, J. Meijer, C. Becher, W. Wernsdorfer, and D. Hunger, Phys. Rev. X14, 031036 (2024)

    work page 2024

  7. [7]

    S. A. Tarasenko, A. V. Poshakinskiy, D. Simin, V. A. Soltamov, E. N. Mokhov, P. G. Baranov, V. Dyakonov, and G. V. Astakhov, Phys. Status Solidi B255, 1700258 (2018)

    work page 2018

  8. [8]

    Castelletto and A

    S. Castelletto and A. Boretti, J. Phys. Photonics2, 022001 (2020)

    work page 2020

  9. [9]

    Gottscholl, M

    A. Gottscholl, M. Kianinia, V. Soltamov, S. Orlin- skii, G. Mamin, C. Bradac, C. Kasper, K. Krambrock, A. Sperlich, M. Toth, I. Aharonovich, and V. Dyakonov, Nat. Mater.19, 540 (2020)

    work page 2020

  10. [10]

    Gottscholl, M

    A. Gottscholl, M. Diez, V. Soltamov, C. Kasper, A. Sperlich, M. Kianinia, C. Bradac, I. Aharonovich, and V. Dyakonov, Sci. Adv7, eabf3630 (2021)

    work page 2021

  11. [11]

    R. Gong, G. He, X. Gao, P. Ju, Z. Liu, B. Ye, E. A. Henriksen, T. Li, and C. Zu, Nat. Commun14, 3299 (2023)

    work page 2023

  12. [12]

    Kanai, F

    S. Kanai, F. J. Heremans, H. Seo, G. Wolfowicz, C. P. Anderson, S. E. Sullivan, M. Onizhuk, G. Galli, D. D. Awschalom, and H. Ohno, Proc. Natl. Acad. Sci. U.S.A. 119, e2121808119 (2022)

    work page 2022

  13. [13]

    Ping and T

    Y. Ping and T. J. Smart, Nat. Comput. Sci.1, 646 (2021)

    work page 2021

  14. [14]

    D. D. Awschalom, R. Hanson, J. Wrachtrup, and B. B. Zhou, Nat. Photon12, 516 (2018)

    work page 2018

  15. [15]

    J. R. Weber, W. F. Koehl, J. B. Varley, A. Janotti, B. B. Buckley, C. G. Van De Walle, and D. D. Awschalom, Proc. Natl. Acad. Sci. U.S.A.107, 8513 (2010)

    work page 2010

  16. [16]

    Falson, D

    J. Falson, D. Maryenko, Y. Kozuka, A. Tsukazaki, and M. Kawasaki, Appl. Phys. Express4, 091101 (2011)

    work page 2011

  17. [17]

    Q. Li, J. Zhang, J. Chong, and X. Hou, Appl. Phys. Express6, 121102 (2013)

    work page 2013

  18. [18]

    Falson, Y

    J. Falson, Y. Kozuka, M. Uchida, J. H. Smet, T.-h. Arima, A. Tsukazaki, and M. Kawasaki, Scientific Re- ports6, 26598 (2016)

    work page 2016

  19. [19]

    Haynes,CRC Handbook of Chemistry and Physics, 91st Edition(Taylor & Francis Group, 2010)

    W. Haynes,CRC Handbook of Chemistry and Physics, 91st Edition(Taylor & Francis Group, 2010)

    work page 2010

  20. [20]

    Niaouris, M

    V. Niaouris, M. V. Durnev, X. Linpeng, M. L. K. Viitaniemi, C. Zimmermann, A. Vishnuradhan, 17 Y. Kozuka, M. Kawasaki, and K.-M. C. Fu, Phys. Rev. B105, 195202 (2022)

    work page 2022

  21. [21]

    Linpeng, M

    X. Linpeng, M. L. Viitaniemi, A. Vishnuradhan, Y. Kozuka, C. Johnson, M. Kawasaki, and K.-M. C. Fu, Phys. Rev. Applied10, 064061

    work page

  22. [22]

    X. Wang, C. Zimmermann, M. Titze, V. Niaouris, E. R. Hansen, S. H. D’Ambrosia, L. Vines, E. S. Bielejec, and K.-M. C. Fu, Phys. Rev. Applied19, 054090

    work page

  23. [23]

    M. L. K. Viitaniemi, C. Zimmermann, V. Niaouris, S. H. D’Ambrosia, X. Wang, E. S. Kumar, F. Mohammad- beigi, S. P. Watkins, and K.-M. C. Fu, Nano Lett.22, 2134

    work page

  24. [24]

    Linpeng, M

    X. Linpeng, M. L. Viitaniemi, A. Vishnuradhan, Y. Kozuka, C. Johnson, M. Kawasaki, and K.-M. C. Fu, Phys. Rev. Applied10, 064061 (2018)

    work page 2018

  25. [25]

    Niaouris, S

    V. Niaouris, S. H. D’Ambrosia, C. Zimmermann, X. Wang, E. R. Hansen, M. Titze, E. S. Bielejec, and K.-M. C. Fu, Opt. Quantum2, 7 (2024)

    work page 2024

  26. [26]

    C. Gray, L. Trefflich, R. R¨ oder, C. Ronning, M. O. Henry, and E. McGlynn, J. Phys. D: Appl. Phys.50, 145105 (2017)

    work page 2017

  27. [27]

    Hao, S.-Y

    Y.-M. Hao, S.-Y. Lou, S.-M. Zhou, R.-J. Yuan, G.-Y. Zhu, and N. Li, Nanoscale Res Lett7, 100 (2012)

    work page 2012

  28. [28]

    Liao, H.-F

    S.-C. Liao, H.-F. Lin, S.-W. Hung, and C.-T. Hu, JVST B24, 1322 (2006)

    work page 2006

  29. [29]

    Shahroosvand and M

    H. Shahroosvand and M. Ghorbani-asl, J. Lumin.144, 223 (2013)

    work page 2013

  30. [30]

    Singh, D

    S. Singh, D. Nakamura, K. Sakai, T. Okada, and M. S. Ramachandra Rao, New J. Phys.12, 023007 (2010)

    work page 2010

  31. [31]

    D. M. Irber, F. Poggiali, F. Kong, M. Kieschnick, T. L¨ uhmann, D. Kwiatkowski, J. Meijer, J. Du, F. Shi, and F. Reinhard, Nat Commun12, 532 (2021)

    work page 2021

  32. [32]

    D. J. Christle, P. V. Klimov, C. F. De Las Casas, K. Sz´ asz, V. Iv´ ady, V. Jokubavicius, J. Ul Hassan, M. Syv¨ aj¨ arvi, W. F. Koehl, T. Ohshima, N. T. Son, E. Janz´ en,´A. Gali, and D. D. Awschalom, Phys. Rev. X7, 021046 (2017)

    work page 2017

  33. [33]

    Hopper, H

    D. Hopper, H. Shulevitz, and L. Bassett, Microma- chines9, 437 (2018)

    work page 2018

  34. [34]

    Robledo, L

    L. Robledo, L. Childress, H. Bernien, B. Hensen, P. F. A. Alkemade, and R. Hanson, Nature477, 574 (2011)

    work page 2011

  35. [35]

    E. I. Rosenthal, S. Biswas, G. Scuri, H. Lee, A. J. Stein, H. C. Kleidermacher, J. Grzesik, A. E. Rugar, S. Aghaeimeibodi, D. Riedel, M. Titze, E. S. Bielejec, J. Choi, C. P. Anderson, and J. Vuˇ ckovi´ c, Phys. Rev. X14, 041008 (2024)

    work page 2024

  36. [36]

    C. P. Anderson, E. O. Glen, C. Zeledon, A. Bourassa, Y. Jin, Y. Zhu, C. Vorwerk, A. L. Crook, H. Abe, J. Ul- Hassan, T. Ohshima, N. T. Son, G. Galli, and D. D. Awschalom, Science Advances8, eabm5912 (2022)

    work page 2022

  37. [37]

    W. F. Koehl, B. B. Buckley, F. J. Heremans, G. Calu- sine, and D. D. Awschalom, Nature479, 84 (2011)

    work page 2011

  38. [38]

    D. D. Sukachev, A. Sipahigil, C. T. Nguyen, M. K. Bhaskar, R. E. Evans, F. Jelezko, and M. D. Lukin, Phys. Rev. Lett.119(2017)

    work page 2017

  39. [39]

    H. Seo, H. Ma, M. Govoni, and G. Galli, Phys. Rev. Mater.1, 075002 (2017)

    work page 2017

  40. [40]

    F. Oba, M. Choi, A. Togo, and I. Tanaka, STAM12, 034302 (2011)

    work page 2011

  41. [41]

    Y. K. Frodason, K. M. Johansen, T. S. Bjørheim, B. G. Svensson, and A. Alkauskas, Phys. Rev. B95, 094105 (2017)

    work page 2017

  42. [42]

    S. J. Clark, J. Robertson, S. Lany, and A. Zunger, Phys. Rev. B81, 115311 (2010)

    work page 2010

  43. [43]

    Janotti and C

    A. Janotti and C. G. Van De Walle, Phys. Rev. B76, 165202 (2007)

    work page 2007

  44. [44]

    Govoni and G

    M. Govoni and G. Galli, J. Chem. Theory Comput.11, 2680 (2015)

    work page 2015

  45. [45]

    Y. Ma, M. Rohlfing, and A. Gali, Phys. Rev. B81, 041204 (2010)

    work page 2010

  46. [46]

    Iv´ ady, G

    V. Iv´ ady, G. Barcza, G. Thiering, S. Li, H. Hamdi, J.-P. Chou, ¨O. Legeza, and A. Gali, npj Comput Mater6, 1 (2020)

    work page 2020

  47. [47]

    K. Li, V. D. Dergachev, I. D. Dergachev, S. Zhang, S. A. Varganov, and Y. Ping, Phys. Rev. B110, 184302 (2024)

    work page 2024

  48. [48]

    J. R. Reimers, J. Shen, M. Kianinia, C. Bradac, I. Aharonovich, M. J. Ford, and P. Piecuch, Phys. Rev. B102, 144105 (2020)

    work page 2020

  49. [49]

    H. Ma, N. Sheng, M. Govoni, and G. Galli, Phys. Chem. Chem. Phys.22, 25522 (2020)

    work page 2020

  50. [50]

    H. Ma, M. Govoni, and G. Galli, npj Comput Mater6, 1 (2020)

    work page 2020

  51. [51]

    Sheng, C

    N. Sheng, C. Vorwerk, M. Govoni, and G. Galli, J. Chem. Theory Comput.18, 3512 (2022)

    work page 2022

  52. [52]

    Vorwerk, N

    C. Vorwerk, N. Sheng, M. Govoni, B. Huang, and G. Galli, Nat Comput Sci2, 424 (2022)

    work page 2022

  53. [53]

    Rocca, Y

    D. Rocca, Y. Ping, R. Gebauer, and G. Galli, Phys. Rev. B85, 045116 (2012)

    work page 2012

  54. [54]

    V. W.-z. Yu, Y. Jin, G. Galli, and M. Govoni, J. Chem. Theory Comput.20, 10899 (2024)

    work page 2024

  55. [55]

    Czelej, M

    K. Czelej, M. R. Lambert, M. E. Turiansky, A. Koshe- varnikov, S. Mu, and C. G. Van de Walle, ACS Nano 18, 28724 (2024)

    work page 2024

  56. [56]

    J. L. Lyons, J. B. Varley, D. Steiauf, A. Janotti, and C. G. Van de Walle, J. Appl. Phys122, 035704 (2017)

    work page 2017

  57. [57]

    J. J. Markham, Rev. Mod. Phys.31, 956 (1959)

    work page 1959

  58. [58]

    Walker, Rep

    J. Walker, Rep. Prog. Phys.42, 1605 (1979)

    work page 1979

  59. [59]

    F. Wu, T. J. Smart, J. Xu, and Y. Ping, Phys. Rev. B 100, 081407 (2019)

    work page 2019

  60. [60]

    Alkauskas, Q

    A. Alkauskas, Q. Yan, and C. G. Van de Walle, Phys. Rev. B90, 075202 (2014)

    work page 2014

  61. [61]

    Alkauskas, J

    A. Alkauskas, J. L. Lyons, D. Steiauf, and C. G. Van De Walle, Phys. Rev. Lett.109, 267401 (2012)

    work page 2012

  62. [62]

    J. L. Lyons, A. Alkauskas, A. Janotti, and C. G. Van De Walle, Appl. Phys. Lett.111, 042101 (2017)

    work page 2017

  63. [63]

    Y. K. Frodason, K. M. Johansen, T. S. Bjørheim, B. G. Svensson, and A. Alkauskas, Phys. Rev. B97, 104109 (2018)

    work page 2018

  64. [64]

    Alkauskas, B

    A. Alkauskas, B. B. Buckley, D. D. Awschalom, and C. G. V. de Walle, New J. Phys.16, 073026 (2014)

    work page 2014

  65. [65]

    Bulancea-Lindvall, J

    O. Bulancea-Lindvall, J. Davidsson, R. Armiento, and I. A. Abrikosov, Phys. Rev. B108, 224106 (2023)

    work page 2023

  66. [66]

    Mackoit-Sinkeviˇ cien˙ e, M

    M. Mackoit-Sinkeviˇ cien˙ e, M. Maciaszek, C. G. Van de Walle, and A. Alkauskas, Appl. Phys. Lett.115, 212101 (2019)

    work page 2019

  67. [67]

    S. A. Tawfik, S. Ali, M. Fronzi, M. Kianinia, T. T. Tran, C. Stampfl, I. Aharonovich, M. Toth, and M. J. Ford, Nanoscale9, 13575 (2017)

    work page 2017

  68. [68]

    R. D. Shannon, Acta Cryst A32, 751 (1976)

    work page 1976

  69. [69]

    K. Li, T. J. Smart, and Y. Ping, Phys. Rev. Mater.6, L042201 (2022)

    work page 2022

  70. [70]

    Zhao, S.-W

    N. Zhao, S.-W. Ho, and R.-B. Liu, Phys. Rev. B85, 115303 (2012)

    work page 2012

  71. [71]

    J. R. Maze, A. Dr´ eau, V. Waselowski, H. Duarte, J.-F. Roch, and V. Jacques, New J. Phys.14, 103041 (2012). 18

    work page 2012

  72. [72]

    R. Nagy, M. Niethammer, M. Widmann, Y.-C. Chen, P. Udvarhelyi, C. Bonato, J. U. Hassan, R. Karhu, I. G. Ivanov, N. T. Son, J. R. Maze, T. Ohshima, ¨O. O. Soykal, ´A. Gali, S.-Y. Lee, F. Kaiser, and J. Wrachtrup, Nat Commun10, 1954 (2019)

    work page 1954

  73. [73]

    B. C. Rose, C. D. Weis, A. M. Tyryshkin, T. Schenkel, and S. A. Lyon, Diam. Relat. Mater72, 32 (2017)

    work page 2017

  74. [74]

    W. B. Mims, Phys. Rev. B5, 2409 (1972)

    work page 1972

  75. [75]

    L.-P. Yang, C. Burk, M. Widmann, S.-Y. Lee, J. Wrachtrup, and N. Zhao, Phys. Rev. B90, 241203 (2014)

    work page 2014

  76. [76]

    Bulancea-Lindvall, M

    O. Bulancea-Lindvall, M. T. Eiles, N. T. Son, I. A. Abrikosov, and V. Iv´ ady, Phys. Rev. Applied19, 064046 (2023)

    work page 2023

  77. [77]

    L. S. Vlasenko and G. D. Watkins, Phys. Rev. B71, 125210 (2005)

    work page 2005

  78. [78]

    Zuo, S.-D

    X. Zuo, S.-D. Yoon, A. Yang, W.-H. Duan, C. Vittoria, and V. G. Harris, J. Appl. Phys105, 07C508 (2009)

    work page 2009

  79. [79]

    Fedorov, M

    A. Fedorov, M. Visotin, A. Kholtobina, A. Kuzubov, N. Mikhaleva, and H. S. Hsu, J. Magn. Magn. Mater 440, 5 (2017)

    work page 2017

  80. [80]

    Q. L. Lin, G. P. Li, N. N. Xu, H. Liu, D. J. E, and C. L. Wang, J. Chem. Phys150, 094704 (2019)

    work page 2019

Showing first 80 references.