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6CCVD Research

Spin-phonon relaxation times in centrosymmetric materials from first principles

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2020-01-13
JournalPhysical review. B./Physical review. B
AuthorsJinsoo Park, Jin-Jian Zhou, Marco Bernardi
InstitutionsCalifornia Institute of Technology
Citations29
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This research presents a novel, fully-relativistic first-principles approach for accurately calculating the phonon-limited T1 spin relaxation time (SRT) in centrosymmetric semiconductors, a critical parameter for spintronic and quantum technologies.

  • Methodological Breakthrough: A new workflow was developed combining Density Functional Theory (DFT), Density Functional Perturbation Theory (DFPT), and Wannier interpolation to compute the elusive spin-flip electron-phonon (e-ph) coupling matrix elements.
  • Validation in Silicon (Si): The calculated SRTs for Si show excellent quantitative agreement with experimental data across the 50 K to 300 K temperature range, validating the accuracy of the first-principles method.
  • Intrinsic Diamond Limit Predicted: The study provides the first prediction of intrinsic, phonon-limited SRTs in diamond, a key material for quantum technologies, predicting a long coherence time of 540 ”s at 77 K.
  • Debunking Simplification: The analysis definitively shows that spin-flip e-ph interactions and momentum-scattering e-ph interactions are not directly proportional, contradicting a widely used simplifying assumption in previous theoretical models.
  • Microscopic Insight: The method allows for detailed analysis of spin relaxation contributions from specific phonon modes (e.g., LA, LO, TA, TO) and valley scattering processes (intravalley, g, and f intervalley).
  • General Applicability: The proposed workflow is general and can be adapted to study spin relaxation mediated by other perturbations, such as defects, or applied to complex materials like topological insulators.

Technical Specifications

Section titled “Technical Specifications”
ParameterValueUnitContext
Silicon (Si) SRT (300 K)4.9nsCalculated intrinsic limit (compared favorably to 6.0 ns experimental value).
Diamond (C) SRT (300 K)2.3”sPredicted intrinsic, phonon-limited T1 relaxation time.
Diamond (C) SRT (77 K)540”sPredicted intrinsic T1 relaxation time at cryogenic temperature.
Si SRT Temperature TrendT-3N/AObserved temperature dependence (50-300 K).
Diamond SRT Temperature TrendT-2 to T-5.5N/ASharp transition in dependence occurs around 170 K.
Si Momentum Relaxation TrendT-2N/ADiffers significantly from the T-3 SRT trend.
Diamond Momentum Relaxation TrendT-1.5 to T-2.5N/AWeaker temperature dependence than the SRT.
Si Lattice Constant5.43AInput parameter for DFT calculations.
DFT Kinetic Energy Cutoff60 / 120RyUsed for Si / Diamond calculations, respectively.
BZ Interpolation Grid SizeUp to 2003k-pointsRequired for convergence of the Spin Relaxation Times (SRTs).

Key Methodologies

Section titled “Key Methodologies”

The calculation of the Elliott-Yafet Spin-Phonon Relaxation Times (SRTs) relies on a complex, multi-step first-principles computational workflow:

  1. Ground State and SOC Inclusion:

    • The electronic ground state and band structure were computed using Density Functional Theory (DFT) (QUANTUM ESPRESSO code).
    • Fully-relativistic norm-conserving pseudopotentials were employed to correctly incorporate Spin-Orbit Coupling (SOC).

  2. Phonon and Perturbation Potential:

    • Phonon dispersions and the electron-phonon (e-ph) perturbation potential (ΔVv,q) were calculated using Density Functional Perturbation Theory (DFPT).
    • Calculations were performed on coarse q-point grids (e.g., 8x8x8 for diamond, 10x10x10 for silicon).

  3. Effective Spin State Determination:

    • The effective up (↑) and down (↓) spin states were determined by calculating the spin matrix S(k) and diagonalizing the Sz operator within the Kramers degenerate subspace at each k-point.

  4. Spin-Flip Matrix Element Interpolation:

    • The e-ph matrix elements were initially computed on coarse BZ grids.
    • Wannier functions (WANNIER90 code) were used to interpolate the spin matrices and the spin-flip e-ph matrix elements to fine BZ grids (up to 2003 k-points).

  5. Spin Relaxation Time Calculation:

    • The band- and k-dependent spin-flip relaxation times (Tflipnk) were computed using lowest-order perturbation theory (Fermi’s Golden Rule).
    • An importance sampling method was developed and applied to efficiently converge the Brillouin Zone (BZ) sum required for Tflipnk, which is necessary due to the extreme variation in spin-flip matrix elements across the BZ.

  6. Thermal Averaging:

    • The final temperature-dependent SRT, Ts(T), was obtained by ensemble averaging the k-dependent Tflipnk using tetrahedron integration, weighted by the derivative of the Fermi-Dirac occupation function (dfnk/dE).

Commercial Applications

Section titled “Commercial Applications”

The ability to accurately predict intrinsic spin relaxation limits is crucial for engineering high-performance spintronic and quantum devices.

  • Quantum Computing and Sensing:

    • Diamond Qubits: Provides the intrinsic phonon limit for T1 coherence time in diamond, essential for optimizing Nitrogen-Vacancy (NV) center-based quantum memories and sensors.
    • Cryogenic Electronics: Guides the selection of materials and operating temperatures for quantum hardware where long spin coherence at low temperatures (e.g., 77 K) is paramount.

  • Advanced Spintronics:

    • Spin Transistors: Enables the design of energy-efficient spin field-effect transistors (Spin-FETs) by predicting the maximum achievable spin lifetime in channel materials like silicon.
    • Spin Memory: Optimization of spin injection and transport in magnetic and non-magnetic heterostructures by understanding the dominant relaxation pathways (e.g., intravalley vs. intervalley scattering).

  • Semiconductor R&D:

    • Materials Screening: The general methodology can be used as a predictive tool to screen new centrosymmetric materials for spintronic applications, focusing on those with weak SOC and favorable phonon coupling characteristics.
    • Defect Engineering: The workflow can be extended to model spin relaxation induced by specific defects, guiding manufacturing processes to minimize unwanted spin decoherence.
View Original Abstract

We present a first-principles approach for computing the phonon-limited $T_1$\nspin relaxation time due to the Elliot-Yafet mechanism. Our scheme combines\nfully-relativistic spin-flip electron-phonon interactions with an approach to\ncompute the effective spin of band electrons in materials with inversion\nsymmetry. We apply our method to silicon and diamond, for which we compute the\ntemperature dependence of the spin relaxation times and analyze the\ncontributions to spin relaxation from different phonons and valley processes.\nThe computed spin relaxation times in silicon are in excellent agreement with\nexperiment in the 50$-$300 K temperature range. In diamond, we predict\nintrinsic spin relaxation times of 540 $\mu$s at 77 K and 2.3 $\mu$s at 300 K.\nOur work enables precise predictions of spin-phonon relaxation times in a wide\nrange of materials, providing microscopic insight into spin relaxation and\nguiding the development of spin-based quantum technologies.\n

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 1963 - Solid State Physics

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