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Flexural phonons drive spin relaxation in 2D quantum sensors

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Ab initio spin-phonon calculations show that direct one-phonon processes mediated by the flexural ZA acoustic branch drive the non-monotonic T1 relaxation of the hBN boron vacancy at high magnetic fields without fitting parameters.

T0 review reviewed 2026-07-09 challenge →

load-bearing objection First ab initio treatment of finite-q acoustic phonon relaxation for a 2D defect, with ZA flexural branch identified as dominant decoherence channel — but the 'parameter-free' claim is overstated. the 2 major comments →

arxiv 2607.07642 v1 pith:BSO67Y3U submitted 2026-07-08 cond-mat.mtrl-sci quant-ph

Acoustic-phonon-driven spin-lattice relaxation of the hBN boron vacancy in the sub-THz regime

Priyo Adhikary , Pramey Upadhyaya This is my paper
classification cond-mat.mtrl-sci quant-ph
keywords relaxationboronfielddependencemagneticmicroscopicphononprocess
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This paper claims that the spin-lattice relaxation time T₁ of the boron vacancy defect in hexagonal boron nitride can be quantitatively predicted from first principles, with no empirical fitting, by computing how acoustic phonons — particularly the out-of-plane flexural (ZA) branch unique to two-dimensional materials — modulate the defect's zero-field-splitting tensor and drive direct one-phonon spin transitions. The authors compute finite-momentum spin-phonon couplings from density functional theory, construct a spectral function F_Direct(ω) from these couplings, and evaluate it at the Zeeman-tuned spin transition frequencies to obtain a direct one-phonon relaxation rate. Combined with a two-phonon Raman term, this reproduces the experimentally observed non-monotonic dependence of 1/T₁ on magnetic field (0–7 T) and temperature (30–250 K). The central physical finding is that the ZA branch, with its quadratic dispersion ω ~ q² near the Brillouin zone center, produces a finite phonon density of states at arbitrarily low energies, making it the dominant decoherence channel at the sub-meV spin transition energies relevant in high-field operation. This constitutes a qualitatively distinct relaxation mechanism from bulk defect qubits such as the NV⁻ center in diamond, where linear-dispersion acoustic modes and higher-energy optical phonons govern T₁.

Core claim

The paper identifies the out-of-plane flexural (ZA) phonon branch as the primary source of spin decoherence in the V_B⁻ center in hBN, and shows that a direct one-phonon process resonant with Zeeman-tuned spin transitions — mediated by this branch — quantitatively explains the non-monotonic magnetic-field and temperature dependence of T₁ observed experimentally. The ZA branch's quadratic dispersion near the Γ point yields a finite low-energy phonon density of states that the linear-dispersion in-plane acoustic branches cannot provide, enabling efficient spin relaxation at sub-meV energies. The authors derive the spin-phonon spectral function from first-principles gradients of the zero-field-

What carries the argument

The spin-phonon spectral function F_Direct(ω) = (1/N_q) Σ_{qν} |V^(1)(qν)|² δ(ω − ω_{qν}), where V^(1)(qν) is the first-order spin-phonon coupling obtained from DFT-computed gradients of the zero-field-splitting tensor with respect to phonon normal modes at finite momentum q. The total relaxation rate is 1/T₁ = Γ_Direct(B,T) + Γ_Raman(T), where Γ_Direct sums F_Direct(ω_j) × coth(ω_j/2k_BT) over the three spin transition frequencies ω_j(B).

Load-bearing premise

The Gaussian broadening parameter σ = 0.25 meV, which converts the discrete DFT phonon spectrum into a continuous spectral function, is treated as a numerical convergence parameter but is in fact optimized by chi-squared minimization against the same experimental data the paper claims to reproduce without fitting.

What would settle it

If the ZA branch were suppressed (e.g., by clamping the hBN membrane to a rigid substrate or increasing layer thickness toward the bulk limit) and the measured T₁ did not correspondingly increase, the claim that flexural phonons are the dominant decoherence channel would be directly challenged.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • T₁ in 2D van der Waals defect qubits is governed by a fundamentally different phonon bath than in bulk defect qubits, because the flexural ZA branch provides low-energy phonons that have no bulk analogue.
  • Engineering the flexural phonon spectrum — through substrate choice, layer number, strain, or dielectric environment — could directly tune decoherence rates in 2D quantum sensors.
  • The direct one-phonon relaxation channel, often neglected at low fields, becomes the dominant mechanism once Zeeman splittings reach the sub-THz regime, and must be included in any predictive model of high-field spin defect performance.
  • The framework can be extended to other 2D defect systems (e.g., transition metal dopants in hBN, MoS₂, or WSe₂) to predict T₁ from first principles without phenomenological assumptions about phonon coupling.

Where Pith is reading between the lines

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

  • If the ZA branch is indeed the dominant decoherence channel, then suspending the hBN membrane or patterning phononic crystals to suppress flexural modes at sub-meV frequencies should measurably increase T₁ — a directly testable prediction.
  • The σ = 0.25 meV broadening parameter, optimized against experiment, effectively encodes information about phonon linewidths, substrate coupling, or disorder that the pristine monolayer DFT calculation does not capture. A truly parameter-free prediction would require computing these effects from first principles, which would also resolve the tension between the 'no fitting' claim and the chi-squar
  • The systematic error in the computed zero-field splitting (D = 2.76 GHz vs. experimental ~3.5 GHz) may not cancel cleanly in the ZFS derivatives for finite-q ZA distortions, since the flexural mode involves out-of-plane atomic displacements that could perturb the electronic structure differently than in-plane modes — this assumption remains unverified.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 7 minor

Summary. This manuscript presents an ab initio study of acoustic-phonon-driven spin-lattice relaxation (T1) for the negatively charged boron vacancy (VB-) center in monolayer hBN, focusing on the sub-THz (high magnetic field) regime. The authors extend finite-q spin-phonon coupling calculations—previously applied to bulk NV centers—to a 2D defect host, computing first- and second-order ZFS derivatives on a 6x6x1 supercell with PBE and Phonopy. The central result is that the direct one-phonon process, resonant with Zeeman-tuned spin splittings, reproduces the experimentally observed non-monotonic magnetic field dependence of T1, and that the out-of-plane flexural (ZA) phonon branch dominates the low-energy spectral function and hence the direct relaxation rate. The Raman (two-phonon) channel is also computed and shown to govern the high-temperature regime. The physical picture—ZA dominance due to quadratic dispersion yielding a finite low-energy DOS—is compelling and likely robust. However, the manuscript's claim of 'quantitative reproduction without empirical fitting parameters' is in tension with the methodology in Appendix B.2, where the Gaussian broadening parameter sigma is determined via chi-squared minimization against the very experimental data being reproduced. This issue is load-bearing for the framing of the central claim and must be addressed.

Significance. The extension of Brillouin-zone-resolved spin-phonon coupling to a 2D defect host is a genuine methodological contribution, and the identification of the ZA branch as the primary decoherence channel at sub-meV energies provides a physically transparent and falsifiable prediction. The DFT methodology (PBE, 6x6 supercell, Phonopy finite displacements, convergence studies on q-mesh up to 31x31) is standard and well-executed. The decomposition into direct and Raman channels and the mode-resolved spectral function analysis are clearly presented. The work fills a real gap: finite-q acoustic phonon relaxation for 2D quantum defects has been underdeveloped, and the connection to recent experimental data (Ref. [12]) is timely. Credit is due for providing convergence studies (Fig. 7a-e) and for the unified single-supercell framework avoiding cluster embedding. The ZA-dominance mechanism is a concrete, testable prediction for other 2D defect systems.

major comments (2)
  1. Abstract, Sec. I, Sec. V, and Sec. IV.C: The claim of 'quantitative reproduction without empirical fitting parameters' (or 'parameter-free') is directly contradicted by Appendix B.2 (Eq. B2, Fig. 7f), where sigma=0.25 meV is determined via chi-squared minimization against the experimental data of Ref. [12]. Since sigma enters the spectral function F_Direct(omega) via the Gaussian kernel rho_sigma (Eq. B1) and F_Direct is evaluated at the spin transition frequencies in Eq. (9), and since the spin transition energies span ~0-0.8 meV (making sigma=0.25 meV a substantial fraction of the relevant energy scale), sigma directly controls the magnitude of Gamma_Direct—the dominant contribution at high fields. This is not merely a convergence parameter: a convergence parameter would be determined by varying sigma and N_q together until results stabilize toward the sigma->0, N_q->infinity limit. A
  2. Sec. III: The ZFS is computed with PBE (D=2.76 GHz vs experimental ~3.5 GHz, a ~21% error), and the authors assume systematic errors cancel in the ZFS derivatives (dD_ij/dR_qnu) that enter the spin-phonon coupling. This assumption is unverified for finite-q acoustic distortions. While the cancellation argument is plausible for small-amplitude distortions near equilibrium, it has not been tested for the finite-q modes that dominate the spectral function (particularly the ZA branch). A brief discussion of the sensitivity of the results to this assumption—e.g., by comparing ZFS derivatives for a few representative modes using a hybrid functional or cluster embedding—would strengthen the claim. At minimum, the authors should acknowledge this as a source of systematic uncertainty.
minor comments (7)
  1. Fig. 1(c): The color scale for the 2D plot of 1/T1 vs B and T is not accompanied by a colorbar label or units in the figure caption; please verify that the colorbar is properly labeled.
  2. Sec. IV.B: The frequency cutoff of 26 meV is stated without detailed justification beyond the energy scale of the direct process. A brief note on whether the Raman channel (Eq. 11) is also truncated at this cutoff, and how sensitive the Raman rate is to this choice, would help.
  3. Eq. (7): The Gaussian broadening appears in the Raman spectral function as well. Is the same sigma=0.25 meV used here, or a different value? Please clarify.
  4. Fig. 5(a-e): The experimental data points are small and the calculated lines are thin; consider enlarging markers and line widths to improve readability.
  5. Sec. IV.C: The statement that deviations at low fields 'may originate from... cross relaxation' is speculative. Since the manuscript does not model cross relaxation, the language should be tempered (e.g., 'could potentially' rather than 'may').
  6. Appendix B.1: The Debye model parameters (v_LA, v_TA, sigma_ZA) are fitted to the DFT dispersions. While these are used only for the analytic reconstruction and not the main numerical results, a note clarifying that they are for illustrative/interpretive purposes only would avoid confusion.
  7. The manuscript would benefit from a brief mention of whether the ZA branch dominance is expected to persist in multilayer hBN (where the ZA dispersion may be modified), given that experiments are on thicker flakes, as noted in Sec. IV.C.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for a careful and constructive report. The referee raises two major comments: (1) the claim of 'parameter-free' reproduction is in tension with the chi-squared minimization used to determine the Gaussian broadening sigma in Appendix B.2, and (2) the assumption that systematic errors in the PBE-computed ZFS cancel in the ZFS derivatives is unverified for finite-q acoustic modes. We agree that the first point requires a revision of our framing and have modified the manuscript accordingly. On the second point, we provide additional discussion and acknowledge the systematic uncertainty as requested.

read point-by-point responses

  1. Referee: The claim of 'quantitative reproduction without empirical fitting parameters' is contradicted by Appendix B.2, where sigma=0.25 meV is determined via chi-squared minimization against the experimental data being reproduced. Since sigma enters the spectral function and is a substantial fraction of the relevant energy scale, it directly controls the magnitude of Gamma_Direct. This is not merely a convergence parameter.

    Authors: We thank the referee for this careful and important observation. The referee is correct that the language 'without empirical fitting parameters' is not fully consistent with the methodology described in Appendix B.2, where sigma is determined via chi-squared minimization against the experimental data of Ref. [12]. We accept this criticism and will revise the manuscript framing accordingly. Specifically, we will replace 'without empirical fitting parameters' and 'parameter-free' with more precise language throughout the abstract, main text, and summary, stating instead that the spin-phonon coupling matrix elements and phonon spectrum are obtained from first principles without empirical parameters, while the Gaussian broadening width sigma used to regularize the discrete Brillouin zone sum is determined by comparison with experiment. We agree that sigma is not merely a convergence parameter in the sense of a sigma -> 0, N_q -> infinity limit study, and we will make this distinction explicit in the revised text. That said, we wish to clarify the physical role of sigma to contextualize the revision. The Gaussian broadening serves as a numerical regularization of the Dirac delta function in the spectral function (Eq. 6), replacing a discrete sum over a finite q-mesh with a smooth function. The spin-phonon coupling matrix elements V^(1)(q nu) themselves are computed entirely from first principles with no adjustable parameters. What sigma controls is how the discrete spectral weight is distributed in energy space, not the underlying coupling strengths. Nevertheless, we acknowledge that since sigma = 0.25 meV is a substantial fraction of the spin transition energies (0-0.8 meV), it does influence the magnitude of Gamma_Direct, and the use of chi-squared minimization against the revision: yes

  2. Referee: The ZFS is computed with PBE (D=2.76 GHz vs experimental ~3.5 GHz, a ~21% error), and the authors assume systematic errors cancel in the ZFS derivatives. This assumption is unverified for finite-q acoustic distortions. A brief discussion of sensitivity or at minimum acknowledgment as a source of systematic uncertainty would strengthen the claim.

    Authors: We agree with the referee that the cancellation of systematic errors in the ZFS derivatives is an assumption that has not been explicitly verified for finite-q acoustic distortions, and we appreciate the suggestion to address this more transparently. We will revise the manuscript to explicitly acknowledge this as a source of systematic uncertainty in Section III and to discuss the sensitivity of our results to this assumption. Regarding the substance of the concern: the cancellation argument rests on the observation that the PBE error in the absolute ZFS (D = 2.76 GHz vs. experimental ~3.5 GHz) arises primarily from the spin-spin dipolar interaction evaluated at the equilibrium geometry, and this systematic offset is expected to be largely preserved under the small-amplitude atomic displacements used to extract the derivatives. The derivatives dD_ij/dR_qnu depend on how the local crystal field changes with atomic displacement, which is a different physical quantity than the equilibrium ZFS itself. For the finite-q acoustic modes that dominate the spectral function, particularly the ZA branch, the displacements involve out-of-plane motion of the nitrogen atoms surrounding the vacancy, which modulates the spin density distribution and hence the ZFS. While the cancellation argument is physically motivated by the localized nature of the spin density and the small displacement amplitudes (0.1 Angstrom*sqrt(amu)), we acknowledge that a rigorous verification would require comparing ZFS derivatives using a hybrid functional for representative modes. We note that such calculations are computationally demanding: each ZFS derivative evaluation on the 6x6 supercell with a hybrid functional would be approximately an order of magnitude more expensive than PBE, and the full spin-phonc revision: partial

Circularity Check

1 steps flagged

Gaussian broadening σ=0.25 meV is fitted via χ² minimization against the same experimental T1 data the paper claims to reproduce 'without empirical fitting parameters,' and σ directly controls the magnitude of the dominant direct relaxation rate.

specific steps
  1. fitted input called prediction [Appendix B.2, Eq. B2, and abstract/Sec. IV claim of 'without empirical fitting parameters']
    "To determine the optimal σ, we performed a reduced χ² minimization analysis comparing the theoretical spin-lattice relaxation rates to experimental data [12] across available magnetic field and temperature range. We use Gaussian widths in the range σ∈[0.10,0.30] meV, for the optimization procedure. The resulting χ² is shown in Fig. 7(f). We choose σ=0.25 meV which provides a faithful numerical representation of the Dirac delta constraint while maintaining stable convergence across the different q mesh sampling procedures used in our rate calculations."

    The paper's central claim (abstract, Sec. IV, Sec. V) is that T1 is reproduced 'without empirical fitting parameters.' However, σ=0.25 meV is determined by χ² minimization against the experimental data of Ref. [12] — the same data being reproduced. This σ enters the spectral function F_Direct(ω) via the Gaussian kernel ρ_σ (Eq. B1 replacing the Dirac delta in Eq. 6), and F_Direct(ω) is then evaluated at spin transition frequencies in Eq. (9) to compute Γ_Direct, the dominant contribution to 1/T1 at high fields. Since the spin transition energies span ~0–0.8 meV, σ=0.25 meV is a substantial fraction of the relevant energy scale and directly controls the magnitude of Γ_Direct. A true convergence parameter would be determined by varying σ and N_q together until results stabilize toward the σ→

full rationale

The paper's derivation chain is largely first-principles: DFT-computed ZFS derivatives, phonon modes, and spin-phonon couplings feed into spectral functions and relaxation rates via Fermi's golden rule. The physical insight that the ZA flexural branch dominates low-energy relaxation stems from the DFT phonon DOS and mode-resolved couplings, which are computed independently. However, the claim of 'quantitative reproduction without empirical fitting parameters' is directly contradicted by the methodology in Appendix B.2: the Gaussian broadening σ is optimized via χ² minimization against the same experimental data being reproduced. This σ is not merely a convergence parameter — it is not determined by the σ→0, N_q→∞ limit but rather by best-fit to experiment. Since σ enters the spectral function that controls the magnitude of the dominant direct relaxation rate, the 'parameter-free' claim is partially circular. The ZA-dominance finding and the direct-vs-Raman decomposition likely retain independent content, but the quantitative agreement is partly forced by the fitted σ.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

No new particles, forces, dimensions, or entities are postulated. The ZA phonon branch is a known physical mode of 2D materials, not an invention. The free parameters are the Gaussian broadening (optimized against experiment) and Debye model parameters (fitted to DFT output, not experiment). The axioms are standard domain assumptions common in ab initio spin-phonon calculations, with the ZFS cancellation assumption being the most fragile.

free parameters (4)
  • Gaussian broadening sigma = 0.25 meV
    Determined by chi-squared minimization against experimental T1 data (Eq. B2, Fig. 7f). Framed as a numerical convergence parameter but its value directly controls the spectral function magnitude and is optimized against the data being reproduced.
  • Debye model v_LA = 18.46 km/s
    Fitted to DFT acoustic dispersion near Gamma (Appendix B.1). Used for analytic reconstruction of spectral function, not for the main DFT-based results.
  • Debye model v_TA = 11.33 km/s
    Fitted to DFT acoustic dispersion near Gamma (Appendix B.1). Used for analytic reconstruction of spectral function.
  • Debye model sigma_ZA = 3.95e-7 m^2/s
    Fitted to DFT flexural dispersion near Gamma (Appendix B.1). Used for analytic reconstruction of spectral function.
axioms (5)
  • standard math Harmonic approximation for lattice dynamics
    Phonons computed within harmonic approximation using finite displacement approach (Sec. III). Standard for this type of calculation.
  • domain assumption ZFS derivative cancellation: systematic offset in absolute D from PBE cancels in ZFS derivatives entering spin-phonon coupling
    Sec. III: 'Following [26], we assume that any systematic offset in the absolute D value is similar for the equilibrium and displaced geometries and therefore largely cancels in the ZFS derivatives.' Unverified for finite-q acoustic distortions.
  • domain assumption Diagonal approximation for second-order spin-phonon coupling: mixed derivatives (d^2 D_ij / dR_qnu dR_q'nu' with qnu != q'nu') are neglected
    Sec. III: 'we use a diagonal approximation, neglecting the computationally expensive off-diagonal mode-mixing terms.' Justified by computational cost; impact on Raman rates is not quantified.
  • domain assumption Two-phonon process mediated by two successive first-order interactions is suppressed by large virtual-state energy denominator
    Sec. IV.B: 'We include only the second-order coupling in the Raman channel because the alternative two-phonon process mediated by two successive first-order interactions is suppressed by the large virtual-state energy denominator [23].'
  • domain assumption 6x6x1 supercell is sufficient for T1 convergence
    Sec. III: 'We adopted the 6x6x1 supercell on the basis of earlier convergence studies, which compared this cell size with a 12x12x1 supercell... and found negligible finite-size effects on T1 [26].'

reviewed 2026-07-09 · how reviews work

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Cite this review

Pith. "Pith review of Acoustic-phonon-driven spin-lattice relaxation of the hBN boron vacancy in the sub-THz regime." pith.science (2026). https://pith.science/paper/BSO67Y3U

@misc{pith2026260707642,
  author       = {Pith},
  title        = {Pith review of: Acoustic-phonon-driven spin-lattice relaxation of the hBN boron vacancy in the sub-THz regime},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BSO67Y3U}},
  note         = {Machine review of arXiv:2607.07642}
}
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abstract

The negatively charged boron vacancy center in hexagonal boron nitride is a premier candidate for quantum sensing, yet its performance is critically limited by longitudinal spin-lattice relaxation time ($T_1$). A microscopic understanding of spin relaxation in the high magnetic field regime remains elusive, as the relevant Zeeman transitions lie far below the optical phonon energies typically invoked to describe the relaxation process. Here, we apply an \textit{ab initio} acoustic mode spin-phonon relaxation theory to this problem and quantitatively reproduce the experimental magnetic field and temperature dependence of $T_1$ without empirical fitting parameters. We demonstrate that the relaxation dynamics are driven by a direct one-phonon emission and absorption process resonant with the Zeeman splitting. Furthermore, we identify the out-of-plane flexural phonon branch which is unique to two-dimensional hosts, as the primary source of decoherence, creating a distinct low-energy spectral function that facilitates spin relaxation. Our results provide a microscopic interpretation of the experimentally observed non-monotonic field and temperature dependence in two-dimensional quantum defect centers.

Figures

Figures reproduced from arXiv: 2607.07642 by Pramey Upadhyaya, Priyo Adhikary.

Figure 1
Figure 1. Figure 1: FIG. 1. Structural, vibrational, and spin relaxation overview of the VB [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Magnetic field dependence of the spin transition energies [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. First order spin-phonon coupling of the VB [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Spin-phonon coupling for double quantum transition [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Magnetic field and temperature dependence of the spin-lattice relaxation rate [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) low-energy acoustic phonon dispersions near Γ [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a)-(e) Comparison of the experimental and calculated spin-lattice relaxation rate [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Visualization of lowest-energy acoustic phonon modes for VB [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗

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Reference graph

Works this paper leans on

47 extracted references · 47 canonical work pages

  1. [1]

    Schirhagl, K

    R. Schirhagl, K. Chang, M. Loretz, and C. L. Degen, Nitrogen-vacancy centers in diamond: Nanoscale sen- sors for physics and biology, Annual Review of Physical Chemistry65, 83 (2014)

    work page 2014

  2. [2]

    M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. Hollenberg, The nitrogen- vacancy colour centre in diamond, Physics Reports528, 1 (2013), the nitrogen-vacancy colour centre in diamond

    work page 2013

  3. [3]

    C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys.89, 035002 (2017)

    work page 2017

  4. [4]

    Atat¨ ure, D

    M. Atat¨ ure, D. Englund, N. Vamivakas, S.-Y. Lee, and J. Wrachtrup, Material platforms for spin-based photonic quantum technologies, Nature Reviews Materials3, 38 (2018)

    work page 2018

  5. [5]

    Wolfowicz, F

    G. Wolfowicz, F. J. Heremans, C. P. Anderson, S. Kanai, H. Seo, A. Gali, G. Galli, and D. D. Awschalom, Quan- tum guidelines for solid-state spin defects, Nature Re- views Materials6, 906 (2021)

    work page 2021

  6. [6]

    Casola, T

    F. Casola, T. van der Sar, and A. Yacoby, Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond, Nature Reviews Materials3, 17088 (2018)

    work page 2018

  7. [7]

    Rovny, S

    J. Rovny, S. Gopalakrishnan, A. C. B. Jayich, P. Maletinsky, E. Demler, and N. P. de Leon, Nanoscale diamond quantum sensors for many-body physics, Na- ture Reviews Physics6, 753 (2024)

    work page 2024

  8. [8]

    Fujiwara and Y

    M. Fujiwara and Y. Shikano, Diamond quantum ther- mometry: from foundations to applications, Nanotech- nology32, 482002 (2021)

    work page 2021

  9. [9]

    K. O. Ho and S. Yang, Diagnosing high-pressure super- conductors using diamond quantum sensors: a review, npj Advanced Manufacturing3, 88 (2026)

    work page 2026

  10. [10]

    S. C. Scholten, A. J. Healey, I. O. Robertson, G. J. Abrahams, D. A. Broadway, and J.-P. Teti- enne, Widefield quantum microscopy with nitrogen- vacancy centers in diamond: Strengths, limitations, and prospects, Journal of Applied Physics130, 150902 (2021), https://pubs.aip.org/aip/jap/article- pdf/doi/10.1063/5.0066733/20031103/150902 1 5.0066733.pdf

    work page doi:10.1063/5.0066733/20031103/150902 2021

  11. [11]

    Vaidya, X

    S. Vaidya, X. Gao, S. Dikshit, I. Aharonovich, and T. Li, Quantum sensing and imaging with spin defects in hexag- onal boron nitride, Advances in Physics: X8, 2206049 (2023)

    work page 2023

  12. [12]

    A. B. Solanki, Y.-C. Wu, H. Ather, P. Adhikary, A. Shankar, I. Gallagher, X. Gao, O. Matthiessen, D. Sy- chev, A. Lagutchev, T. Li, Y. P. Chen, V. M. Sha- laev, B. Lawrie, and P. Upadhyaya, Subterahertz spin relaxation dynamics of boron-vacancy centers in hexago- nal boron nitride, Nano Letters26, 7296 (2026), pMID: 42210544

    work page 2026

  13. [13]

    Durand, T

    A. Durand, T. Clua-Provost, F. Fabre, P. Kumar, J. Li, J. H. Edgar, P. Udvarhelyi, A. Gali, X. Marie, C. Robert, J. M. G´ erard, B. Gil, G. Cassabois, and V. Jacques, Op- tically active spin defects in few-layer thick hexagonal boron nitride, Phys. Rev. Lett.131, 116902 (2023)

    work page 2023

  14. [14]

    J. Zhou, H. Lu, D. Chen, M. Huang, G. Q. Yan, F. Al-matouq, J. Chang, D. Djugba, Z. Jiang, H. Wang, and C. R. Du, Sensing spin wave exci- tations by spin defects in few-layer-thick hexagonal boron nitride, Science Advances10, eadk8495 (2024), https://www.science.org/doi/pdf/10.1126/sciadv.adk8495

    work page doi:10.1126/sciadv.adk8495 2024

  15. [15]

    I. V. Vlassiouk, Y.-C. Wu, A. Puretzky, L. Liang, J. Lasseter, B. Dryzhakov, I. Gallagher, S. Ghosh, N. Lavrik, O. Dyck, A. R. Lupini, M. Checa, L. Collins, 9 H. M. Meyer III, H. Zhao, F. Likhi, K. Xiao, I. Ivanov, D. Glasgow, A. Tselev, B. Lawrie, S. Smirnov, and S. J. Randolph, Defect engineering in large-scale cvd-grown hexagonal boron nitride: Formati...

    work page doi:10.1002/smll.202506874 2026

  16. [16]

    Huang, J

    M. Huang, J. Zhou, D. Chen, H. Lu, N. J. McLaughlin, S. Li, M. Alghamdi, D. Djugba, J. Shi, H. Wang, and C. R. Du, Wide field imaging of van der waals ferromag- net Fe3GeTe2 by spin defects in hexagonal boron nitride, Nat. Commun.13, 5369 (2022)

    work page 2022

  17. [17]

    Gottscholl, M

    A. Gottscholl, M. Diez, V. Soltamov, C. Kasper, D. Krauße, A. Sperlich, M. Kianinia, C. Bradac, I. Aharonovich, and V. Dyakonov, Spin defects in hBN as promising temperature, pressure and magnetic field quantum sensors, Nat. Commun.12, 4480 (2021)

    work page 2021

  18. [18]

    X. Lyu, Q. Tan, L. Wu, C. Zhang, Z. Zhang, Z. Mu, J. Z´ u˜ niga P´ erez, H. Cai, and W. Gao, Strain quantum sensing with spin defects in Hexagonal Boron Nitride, Nano Lett.22, 6553 (2022)

    work page 2022

  19. [19]

    Mondal and A

    S. Mondal and A. Lunghi, Spin-phonon decoherence in solid-state paramagnetic defects from first principles, npj Computational Materials9, 120 (2023)

    work page 2023

  20. [20]

    Gugler, T

    J. Gugler, T. Astner, A. Angerer, J. Schmiedmayer, J. Majer, and P. Mohn, Ab initio calculation of the spin lattice relaxation timeT 1 for nitrogen-vacancy centers in diamond, Phys. Rev. B98, 214442 (2018)

    work page 2018

  21. [21]

    Lunghi and S

    A. Lunghi and S. Sanvito, How do phonons relax molecular spins?, Science Advances5, eaax7163 (2019), https://www.science.org/doi/pdf/10.1126/sciadv.aax7163

    work page doi:10.1126/sciadv.aax7163 2019

  22. [22]

    Momma and F

    K. Momma and F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data, Journal of Applied Crystallography41, 653 (2008)

    work page 2008

  23. [23]

    M. C. Cambria, A. Norambuena, H. T. Dinani, G. Thier- ing, A. Gardill, I. Kemeny, Y. Li, V. Lordi, A. Gali, J. R. Maze, and S. Kolkowitz, Temperature-dependent spin- lattice relaxation of the nitrogen-vacancy spin triplet in diamond, Phys. Rev. Lett.130, 256903 (2023)

    work page 2023

  24. [24]

    Norambuena, E

    A. Norambuena, E. Mu˜ noz, H. T. Dinani, A. Jarmola, P. Maletinsky, D. Budker, and J. R. Maze, Spin-lattice relaxation of individual solid-state spins, Phys. Rev. B 97, 094304 (2018)

    work page 2018

  25. [25]

    Z. Liu, R. Gong, B. Huang, Y. Jin, X. Du, G. He, E. Janzen, L. Yang, E. A. Henriksen, J. H. Edgar, G. Galli, and C. Zu, Temperature-dependent spin- phonon coupling of boron-vacancy centers in hexagonal boron nitride, Phys. Rev. B111, 024108 (2025)

    work page 2025

  26. [26]

    Estaji, I

    N. Estaji, I. A. Sarsari, G. m. H. Thiering, and A. Gali, Spin-phonon relaxation of boron vacancy centers in two- dimensional boron nitride polytypes, Phys. Rev. B112, L201407 (2025)

    work page 2025

  27. [27]

    von Barth and L

    U. von Barth and L. Hedin, A local exchange-correlation potential for the spin polarized case. i, Journal of Physics C: Solid State Physics5, 1629 (1972)

    work page 1972

  28. [28]

    Hobbs, G

    D. Hobbs, G. Kresse, and J. Hafner, Fully unconstrained noncollinear magnetism within the projector augmented- wave method, Phys. Rev. B62, 11556 (2000)

    work page 2000

  29. [29]

    Steiner, S

    S. Steiner, S. Khmelevskyi, M. Marsmann, and G. Kresse, Calculation of the magnetic anisotropy with projected-augmented-wave methodology and the case study of disordered fe 1−xcox alloys, Phys. Rev. B93, 224425 (2016)

    work page 2016

  30. [30]

    J. H. Van Vleck, Paramagnetic relaxation times for tita- nium and chrome alum, Phys. Rev.57, 426 (1940)

    work page 1940

  31. [31]

    Lunghi, Spin-phonon relaxation in magnetic molecules: Theory, predictions and insights, inCompu- tational Modelling of Molecular Nanomagnets, edited by G

    A. Lunghi, Spin-phonon relaxation in magnetic molecules: Theory, predictions and insights, inCompu- tational Modelling of Molecular Nanomagnets, edited by G. Rajaraman (Springer International Publishing, Cham, 2023) pp. 219–289

    work page 2023

  32. [32]

    T´ ark´ anyi and V

    A. T´ ark´ anyi and V. Iv´ ady, Understanding decoherence of the boron vacancy center in hexagonal boron nitride, Advanced Functional Materials36, 2511300 (2026)

    work page 2026

  33. [33]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B54, 11169 (1996)

    work page 1996

  34. [34]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996)

    work page 1996

  35. [35]

    Togo and I

    A. Togo and I. Tanaka, First principles phonon calcu- lations in materials science, Scripta Materialia108, 1 (2015)

    work page 2015

  36. [36]

    A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Imple- mentation strategies in phonopy and phono3py, J. Phys. Condens. Matter35, 353001 (2023)

    work page 2023

  37. [37]

    Togo, First-principles phonon calculations with phonopy and phono3py, J

    A. Togo, First-principles phonon calculations with phonopy and phono3py, J. Phys. Soc. Jpn.92, 012001 (2023)

    work page 2023

  38. [38]

    J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid func- tionals based on a screened coulomb potential, The Jour- nal of Chemical Physics118, 8207 (2003)

    work page 2003

  39. [39]

    Iv´ ady, G

    V. Iv´ ady, G. Barcza, G. Thiering, S. Li, H. Hamdi, J.- P. Chou, ¨O. Legeza, and A. Gali, Ab initio theory of the negatively charged boron vacancy qubit in hexagonal boron nitride, npj Computational Materials6, 41 (2020)

    work page 2020

  40. [40]

    Neese, The orca program system, WIRES Comput

    F. Neese, The orca program system, WIRES Comput. Molec. Sci.2, 73 (2012)

    work page 2012

  41. [41]

    M. J. Rayson and P. R. Briddon, First principles method for the calculation of zero-field splitting tensors in peri- odic systems, Phys. Rev. B77, 035119 (2008)

    work page 2008

  42. [42]

    M. M. Khatami, M. L. Van de Put, and W. G. Vanden- berghe, First-principles study of electronic transport in germanane and hexagonal boron nitride, Phys. Rev. B 104, 235424 (2021)

    work page 2021

  43. [43]

    A. P. Roy, J. SS, V. Dwij, A. Khandelwal, M. K. Chat- topadhyay, V. Sathe, R. Mittal, P. U. Sastry, S. N. Achary, A. K. Tyagi, P. D. Babu, M. D. Le, and D. Bansal, Evidence of strong orbital-selective spin- orbital-phonon coupling in crvo 4, Phys. Rev. Lett.132, 026701 (2024)

    work page 2024

  44. [44]

    de Guillebon, B

    T. de Guillebon, B. Vindolet, J.-F. Roch, V. Jacques, and L. Rondin, Temperature dependence of the longitudinal spin relaxation timeT 1 of single nitrogen-vacancy centers in nanodiamonds, Phys. Rev. B102, 165427 (2020). Appendix A: Finite difference derivatives along phonon modes To evaluate the dependence of ZFS on lattice vibra- tions, we obtain the gra...

    work page 2020

  45. [45]

    This yields an approximate phenomenological description of the spin–phonon coupling in the sub-THz regime

    Debye model parameterization of the low-energy acoustic phonons To obtain an analytic description of theab initiospec- tral function, we use the Debye model, parameterized from the DFT acoustic dispersions for the VB − center. This yields an approximate phenomenological description of the spin–phonon coupling in the sub-THz regime. The fitted dispersion i...

    work page

  46. [46]

    However, first-principles DFT calculations yield a discrete phonon spectrum{ωqν } because the Brillouin zone integral is evaluated on a fi- niteqmesh of sizeN q

    Optimization of the Gaussian broadening parameter Energy conservation for the direct spin transition im- plies the presence of a Dirac delta function in the spin–phonon spectral function. However, first-principles DFT calculations yield a discrete phonon spectrum{ωqν } because the Brillouin zone integral is evaluated on a fi- niteqmesh of sizeN q. The pre...

    work page

  47. [47]

    7(a)-(e) we illustrate theab initiospin-phonon relaxation rates as a function of the magnetic field for temperature range of 30−250 K

    Mesh size dependence ofT 1 In Fig. 7(a)-(e) we illustrate theab initiospin-phonon relaxation rates as a function of the magnetic field for temperature range of 30−250 K. The comparison of phononqmeshes, 11×11, 21×21, and 31×31, reveals thatT 1 is dependent on the Brillouin zone sampling size. T1 calculated on the 11×11 mesh, deviates from the re- sults ob...

    work page

This paper was first reviewed by glm-5.2 on July 9, 2026.