Magnetic-field dependence of spin-phonon relaxation and dephasing due to g-factor fluctuations from first principles

Adela Habib; Joshua Quinton; Junqing Xu; Mani Chandra; Mayada Fadel; Ravishankar Sundararaman; Yuan Ping

REVIEW 2 major objections 5 minor 32 references

Magnetic-field dependence of spin-phonon relaxation and dephasing due to g-factor fluctuations from first principles

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Off-diagonal g-tensor fluctuations, not just spin-flip scattering, determine how electron spin lifetimes T1, T2, and T2* depend on magnetic field in silicon and CsPbBr3.

desk verdict A first-principles Hahn-echo route to T2 with a new off-diagonal g-tensor mechanism for B-dependent T1 in silicon; solid and novel, but the missing convergence tests need addressing. read the letter →

arxiv 2411.18608 v2 pith:BD57EDTK submitted 2024-11-27 cond-mat.mtrl-sci physics.comp-ph

Joshua Quinton , Mayada Fadel , Junqing Xu , Adela Habib , Mani Chandra , Yuan Ping , Ravishankar Sundararaman This is my paper · ORCID

classification cond-mat.mtrl-sciphysics.comp-ph

keywords g-tensorfluctuationsspin-phononrelaxationspindephasingHahnechodensitymatrixdynamicselectron-phononscatteringsiliconCsPbBr3

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Spin lifetimes are usually analyzed with the Elliott-Yafet and Dyakonov-Perel pictures, which tie magnetic-field dependence to spin flips and to precession-frequency spread from diagonal g-factor variation. This paper shows that the off-diagonal components of the g-tensor—how the precession axis tilts from one electron state to the next—drive a random-walk dephasing that controls the field dependence of all three lifetimes, T1, T2, and T2*, in inversion-symmetric silicon and CsPbBr3 with only intrinsic spin-phonon scattering. By simulating Hahn echo measurements in real time from first principles, the authors extract T2 directly and find that, in silicon, even the longitudinal T1 changes strongly with magnetic field because of these off-diagonal fluctuations. If correct, this gives a first-principles route to predicting spin coherence times for quantum information and spintronics, without ad hoc dephasing models.

What carries the argument

The load-bearing object is the state-resolved Landé g-tensor, extracted from DFT by expanding -L + g0 S in a Pauli basis; its diagonal fluctuations (σ∥) and off-diagonal fluctuations (σ⊥) over thermally occupied band-edge states set the Larmor precession frequency spread and precession-axis tilt. The mechanism is a Bloch-sphere random walk: after each electron-phonon scattering event, the spin's precession axis and frequency change because the g-tensor of the new state differs, so even a spin initially parallel to the applied field gradually tilts away. The analytical model, Eqs. (5)-(7), expresses T1, T2, and T2* in terms of the zero-field Elliott-Yafet spin-flip time τs0, the momentum scattering time τp, and the two fluctuation widths σ⊥ and σ∥, with functions F⊥(x) and F∥(x) that interpolate between an x2 low-field regime and saturation.

What would settle it

Measure the longitudinal spin lifetime T1 of conduction electrons in high-purity silicon at 100 K as a function of magnetic field from 0 to 10 T; the paper predicts T1 drops from about 195 ns at zero field to a field-independent value near 70 ns beyond roughly 3 T, so observing no such drop would falsify the off-diagonal g-fluctuation mechanism.

Watch

Extended reading notes

Core claim

The central claim is that the tensorial g-factor, specifically its off-diagonal state-to-state fluctuations, produces magnetic-field-dependent spin relaxation that standard pictures miss. In silicon and CsPbBr3—both inversion-symmetric—the authors show that intrinsic electron-phonon scattering combined with g-tensor fluctuations yields a field-dependent T1, a distinct T2 obtained from simulated Hahn echoes, and a T2* that falls roughly as 1/B. The physical mechanism is a Bloch-sphere random walk: after each phonon scattering event, the spin precesses about a slightly different axis because the g-tensor changes, so even spins initially parallel to the field wander away from it. The analytical model, Eqs. (5)-(7), reproduces the first-principles field dependence with fitted parameters close to the DFT values and identifies regimes where T1, T2, and T2* are ordered differently in the two materials.

Load-bearing premise

The predictions rely on the Born-Markov approximation that phonons act as a memoryless bath, which may fail at low temperatures or strong electron-phonon coupling and would shift all lifetimes.

Editorial extensions

If this is right

In inversion-symmetric crystals, intrinsic spin-phonon scattering alone produces a magnetic-field-dependent T1 whenever off-diagonal g-tensor fluctuations are non-zero, with the zero-field limit recovering the Elliott-Yafet spin-flip time τs0.
T2 can be extracted from first-principles simulation of a Hahn echo sequence, separating irreversible decoherence from reversible dephasing without introducing any ad hoc dephasing model.
The ordering of lifetimes differs by material: CsPbBr3 shows T1 ≫ T2 > T2* at a few tesla, while silicon shows T2 ≈ T2* over the same range because its diagonal g-fluctuations are much smaller than its off-diagonal ones.
The analytical model predicts distinct saturation regimes: T1 saturates once B ≫ ℏ/(|ḡ|τpμB), T2 saturates at a larger field set by σ∥, and T2* enters a free-induction-decay regime where it falls as 1/B.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the off-diagonal g-fluctuation mechanism is right, it should also operate for localized electron spins such as donors or defects in silicon, where the g-tensor varies from site to site; measuring T1(B) in such ensembles could validate the mechanism outside the band-transport regime studied here.
The same random-walk picture suggests that strain or alloying, which alter the g-tensor anisotropy, could tune the magnetic-field dependence of spin lifetimes, turning σ⊥ and σ∥ into design parameters for spin qubits.
The distinction between T2* and T2 is often overlooked in ensemble measurements; this work implies that comparing measured T2* and Hahn-echo T2 as a function of field could directly bound the diagonal and off-diagonal g-fluctuation widths in a material.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this is a legitimately new result—first-principles Hahn-echo simulation to extract T2, plus a mechanism where off-diagonal g-tensor fluctuations make T1 field-dependent even in low-SOC Si. The central mechanism survives reading; the soft spots are about reproducibility, not concept.

What's new: they directly simulate the π/2–π echo sequence from the Lindblad dynamics and separate T2 from T2*. That is a step beyond their earlier perovskite work (Ref 16), which only had T1 and T2*. The Si result—T1 dropping by roughly a factor of 2.8 between 0 and 20 T from intrinsic spin-phonon scattering alone—is surprising and physically plausible once you see the off-diagonal g components in Fig 1a. The analytic model (Eqs. 5–7) ties the effect to σ⊥, and the fitted parameters are close to the DFT-extracted ones (Table II), which is a good consistency check.

Where it's soft: first, convergence. There are no error bars on any lifetime, no k-grid density for the g-factor path, and the paper itself reports finite-k artifacts in the CsPbBr3 echo map (Fig 2c). For Si, σ⊥ ≈ 0.006 is small, and the predicted T1 reduction is large; without a convergence test in k or in the δG broadening, the quantitative prefactor is not pinned down. That doesn't kill the mechanism, but it means the numbers in Fig 5 could shift. Second, the analytic model fits τp, σ⊥, and σ∥ to the same curves it explains (Tables I and II). That's circular in a mild sense, but the direct simulations stand alone, so it's not load-bearing. Third, the Born-Markov/Lindblad approximation is standard for this group and defended by prior benchmarks; it's a reasonable starting assumption, not a hidden flaw. I'd note the absence of code/data artifacts as a practical barrier to checking convergence yourself.

The stress-test worry about a sampling artifact is overstated. The B-dependent T1 shows up in the direct simulation, and the fitted σ⊥ tracks the DFT value. The real issue is lack of convergence evidence, not evidence of error.

Bottom line: this deserves a serious referee. The right outcome is conditional acceptance with a request for convergence tests, k-grid details, and code/data release. I'd bring it to reading group and would cite it for the T2 methodology.

Referee Report

2 major / 5 minor

Summary. The manuscript presents real-time first-principles density-matrix dynamics simulations with electron-phonon Lindblad scattering to compute spin relaxation (T1), irreversible decoherence (T2), and reversible dephasing (T2*) in CsPbBr3 and silicon as functions of magnetic field. By explicitly simulating Hahn echo sequences, the authors separate dephasing from decoherence and identify g-tensor fluctuations—particularly off-diagonal components—as the source of a magnetic-field-dependent T1 in inversion-symmetric silicon. An analytical random-walk model (Eqs. 5–7) is introduced, and its parameters are compared with DFT-derived values in Tables I and II.

Significance. If the results hold, this is an important step: it provides a first-principles route to T2 via direct Hahn echo simulation without ad hoc dephasing models, and it predicts a new intrinsic mechanism by which off-diagonal g-tensor fluctuations make T1 field-dependent even in low-spin-orbit, inversion-symmetric Si. The analytical model with closed-form field-dependence functions is an interpretative strength, and the authors' explicit acknowledgment of finite-k artifacts is honest. The main limitation is the absence of convergence evidence for the computed fluctuations and lifetimes, which is essential because the predicted effect scales with σ⊥².

major comments (2)

[III.C, Fig. 5, and Eq. (5)] The central claim—that off-diagonal g-tensor fluctuations with σ⊥≈0.006 produce the strong B-dependence of T1 in silicon—is not backed by convergence tests. The manuscript does not report the k-grid density or thermal-weighting details used to compute σ⊥, gives no error bars on σ⊥ or on the lifetimes, and acknowledges finite-k artifacts in the Hahn echo simulations (Fig. 2c). Because the T1 rate in Eq. (5) scales as σ⊥², a modest error in σ⊥ translates into a large error in the predicted reduction. Please provide convergence of σ⊥ and of T1, T2, and T2* with respect to k sampling, and error estimates for the fit parameters in Tables I and II.
[II.A, Eq. (1)] The entire calculation inherits the Born-Markov/Lindblad approximation, but the paper does not test its validity for the long-time, low-temperature regimes considered (4 K for CsPbBr3, 100 K for Si). The predicted lifetimes all shift if the Markovian assumption fails, and no comparison with experimental T1 or T2 for silicon is offered. Please provide a quantitative argument for Markovianity (for example, phonon correlation time versus momentum scattering time τp) or a benchmark against an exact or measured case, since the predicted effects rely on accumulated phase over many scattering events.

minor comments (5)

[II.C, III.A, Fig. 4 caption, Table I caption, III.C] There are several typos that should be corrected: 'elctronic' (II.C), 'dicsussed' (III.A), 'functon' (Fig. 4 caption), 'paramters' (Table I caption), 'contributs' (III.C), 'occuring' (III.B), and the reference 'Table III C' after Fig. 5 should be 'Table II'.
[II.D] The Hahn echo protocol would benefit from explicit numerical details: the number of τ delays used, pulse durations and B1 magnitudes, and the fitting windows used to extract Secho(techo). This would help readers assess the quality of the T2 extraction.
[III.B, Tables I–II] The agreement between fitted and DFT parameters is presented as confirmation of the mechanism, but because τp, σ⊥, and σ∥ are fitted to the same lifetime curves, it is a consistency check rather than an independent test. Please state this explicitly or, ideally, overlay the model curves using only DFT-derived parameters.
[Fig. 2(c)] The color scale and the exact meaning of the horizontal and vertical axes are not defined in the caption; please add a legend or explicit axis labels.
[I and II.D] The phrase 'reversible decoherence processes' is unusual; since dephasing is a reversible loss of ensemble coherence rather than irreversible single-spin decoherence, consider rewording to 'reversible dephasing' throughout.

Circularity Check

1 steps flagged · score 2.0 of 10

The central first-principles spin-lifetime predictions are self-contained; the only mild circularity is the analytical model's fitted 'predictions' being compared with the same lifetime curves they were fit to, though the DFT-derived parameter comparison provides independent support.

fitted input called prediction [Section III.B, Eqs. (5)-(7), Figs. 4-5 and Tables I-II]
"Figure 4 compares the predictions of this model to the first-principles spin relaxation times for CsPbBr3, with the corresponding paramters of the model compared to the DFT predictions in Table I. Note that the model captures all the features of the field dependence ofT1, T2 and T2*, with parameters quite close to the values extracted from DFT, confirming the proposed mechanism for the field dependence."

The analytical model (Eqs. 5-7) is fit to the first-principles T1, T2, and T2* curves by adjusting tau_p, sigma_perp, and sigma_parallel, as shown by the Fit Value columns in Tables I and II. The plotted 'model predictions' in Figs. 4-5 are therefore not independent of the data they are compared against; some agreement is built in by construction. The circularity is limited because the fitted values are checked against independently computed DFT values, and the central field-dependence claim comes from the real-time first-principles simulations rather than from the fitted model.

full rationale

The first-principles density-matrix evolution (Eq. 1) does not use the analytical model; T1, T2, and T2* are extracted by exponential fits to simulated spin dynamics and Hahn echo sequences. The g-tensor is extracted from the same S and L matrix elements that enter the Zeeman Hamiltonian, so attributing the field dependence to g-factor fluctuations is a consistency interpretation, not a circular derivation. The analytical model is an interpretive reduction fitted to the computed lifetimes; the close agreement of its fitted parameters with DFT-derived values provides some independent support, so the circularity is minor. The main scientific claim, that off-diagonal g-tensor fluctuations produce a magnetic-field-dependent T1 in silicon, is a result of the ab initio simulations rather than an input to them. No load-bearing self-citation or ansatz-smuggling is present.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The predictions rely on DFT-plus-Lindblad dynamics as the physical engine, with no new particles or forces. The analytic interpretation adds fitted relaxation parameters, but the central mechanism is present in the direct simulations.

free parameters (4)

tau_p (momentum scattering time) = 0.200 ns (CsPbBr3), 0.00150 ns (Si)
Fit parameter in the analytic random-walk model, Tables I and II; close to the DFT-derived values.
sigma_perp (off-diagonal g-tensor fluctuation) = 0.0551 (CsPbBr3), 0.00652 (Si)
Fit parameter in the analytic model; DFT values are 0.0571 and 0.00614 respectively.
sigma_parallel (diagonal g-tensor fluctuation) = 0.0788 (CsPbBr3), 0.00224 (Si)
Fit parameter in the analytic model; DFT values are 0.101 and 0.00119 respectively.
c0 (dephasing prefactor) = not stated in main text
Numerical constant in Eq. 7, derived from a parabolic g-factor model in the SI; its value is not tabulated.

assumptions (4)

domain assumption Electron-phonon scattering can be described by a Lindblad master equation derived under the Born-Markov approximation.
Invoked in Section II.A to obtain Eq. 1; if bath memory or non-Markovian effects matter, the predicted lifetimes change.
domain assumption DFT with PBE and fully relativistic normconserving pseudopotentials gives accurate band structures, g-tensors, and electron-phonon matrix elements.
Used in Section II.A for all electronic inputs; errors in g-tensor fluctuations would directly affect the proposed mechanism.
domain assumption Wannier interpolation, patched with explicit DFT for selected k, preserves the sharp orbital angular momentum features needed for g-tensors.
Described in Section II.B; the paper acknowledges sharp L features cause interpolation errors and uses explicit DFT replacement.
ad hoc to paper The analytical model represents spin dynamics as a random walk with a single momentum scattering time and Gaussian g-factor fluctuations.
Equations 5-7 and Section III.B; tau_p and sigma parameters are fitted to the simulation data.

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Cite this review

Pith. "Pith review of Magnetic-field dependence of spin-phonon relaxation and dephasing due to g-factor fluctuations from first principles." pith.science (2026). https://pith.science/paper/BD57EDTK

@misc{pith2026241118608,
  author       = {Pith},
  title        = {Pith review of: Magnetic-field dependence of spin-phonon relaxation and dephasing due to g-factor fluctuations from first principles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BD57EDTK}},
  note         = {Machine review of arXiv:2411.18608}
}

read the original abstract

The electron spin decay lifetime in materials can be characterized by relaxation (T1) and irreversible (T2) and reversible (T2*) decoherence processes. Their interplay leads to a complex dependence of spin relaxation times on the direction and magnitude of magnetic fields, relevant for spintronics and quantum information applications. Here, we use real-time first-principles density matrix dynamics simulations to directly simulate Hahn echo measurements, disentangle dephasing from decoherence, and predict T1, T2 and T2* spin lifetimes. We show that g-factor fluctuations lead to non-trivial magnetic field dependence of each of these lifetimes in inversion-symmetric crystals of CsPbBr3 and silicon, even when only intrinsic spin-phonon scattering is present. Most importantly, fluctuations in the off-diagonal components of the g-tensor lead to a strong magnetic field dependence of even the T1 lifetime in silicon. Our calculations elucidate the detailed role of anisotropic g-factors in determining the spin dynamics even in simple, low spin-orbit coupling materials such as silicon.

Figures

Figures reproduced from arXiv: 2411.18608 by the authors.

**Figure 2.** FIG. 2. Predictions of spin relaxation for CsPbBr [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. Impact of tensorial [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. First-principles predictions of spin relaxation times [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5. Same as Figure 4, but for silicon. In this case, [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

ˇZuti´ c, J

I. ˇZuti´ c, J. Fabian, and S. Das Sarma, Spintronics: Fun- damentals and applications, Rev. Mod. Phys. 76, 323 (2004)

2004

[2] [2]

D. D. Awschalom, R. Hanson, J. Wrachtrup, and B. B. Zhou, Quantum technologies with optically interfaced solid-state spins, Nature Photonics 12, 516 (2018)

2018

[3] [3]

Hirohata, K

A. Hirohata, K. Yamada, Y. Nakatani, I.-L. Prejbeanu, B. Di´ eny, P. Pirro, and B. Hillebrands, Review on spin- tronics: Principles and device applications, Journal of Magnetism and Magnetic Materials 509, 166711 (2020)

work page 2020

[4] [4]

Z. Chen, G. Dong, and J. Qiu, Ultrafast pump-probe spectroscopy—a powerful tool for tracking spin-quantum dynamics in metal halide perovskites, Advanced Quan- tum Technologies 4, 10.1002/qute.202100052 (2021)

work page doi:10.1002/qute.202100052 2021

[5] [5]

Giovanni, H

D. Giovanni, H. Ma, J. Chua, M. Gr¨ atzel, R. Ramesh, S. Mhaisalkar, N. Mathews, and T. C. Sum, Highly spin-polarized carrier dynamics and ultralarge photoin- duced magnetization in CH 3NH3PbI3 perovskite thin films, Nano Letters 15, 1553 (2015)

work page 2015

[6] [6]

R. J. Elliott, Theory of the effect of spin-orbit coupling on magnetic resonance in some semiconductors, Phys. Rev. 96, 266 (1954)

1954

[7] [7]

Dyakonov and V

M. Dyakonov and V. Perel, Spin relaxation of con- duction electrons in noncentrosymetric semiconductors, Solid State Physics 13, 3023 (1972)

work page 1972

[8] [8]

M. M. Glazov, Magnetic field effects on spin relaxation in heterostructures, Phys. Rev. B 70, 195314 (2004)

work page 2004