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Spin-phonon relaxation times in centrosymmetric materials from first principles

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

Technical Documentation & Analysis: Elliott-Yafet Spin-Phonon Relaxation in Diamond

Section titled “Technical Documentation & Analysis: Elliott-Yafet Spin-Phonon Relaxation in Diamond”

This document analyzes the research paper “Elliott-Yafet Spin-Phonon Relaxation Times from First Principles” to provide technical specifications and align the findings with 6CCVD’s advanced MPCVD diamond material capabilities, specifically targeting spintronics and quantum technology applications.


The following points summarize the core technical achievements and material requirements outlined in the research:

  • First-Principles Methodology: A novel, fully-relativistic first-principles approach was developed to compute the intrinsic phonon-limited $T_1$ Spin Relaxation Time (SRT) via the Elliott-Yafet (EY) mechanism.
  • Diamond as a Quantum Material: The study confirms diamond’s potential for spintronics and quantum technologies due to its weak Spin-Orbit Coupling (SOC) and exceptionally long predicted intrinsic SRTs.
  • Intrinsic SRT Prediction: The intrinsic (phonon-limited) SRT in diamond is predicted to be 540 ”s (0.54 ms) at 77 K and 2.3 ”s at 300 K. These values set the upper limit for device performance.
  • Non-Proportional Scattering: The research definitively shows that spin-flip and momentum-scattering electron-phonon (e-ph) interactions are not directly proportional, highlighting the necessity of high-fidelity, atomistic calculations.
  • Temperature Dependence: Diamond SRT exhibits a sharp transition in temperature dependence: T-2 below 170 K and a much stronger T-5.5 trend above 170 K.
  • Material Requirement: Achieving these intrinsic limits experimentally requires ultra-high purity, low-defect Single Crystal Diamond (SCD) substrates, directly aligning with 6CCVD’s core MPCVD capabilities.

The table below extracts key quantitative data points and simulation results relevant to diamond and silicon spin relaxation:

ParameterValueUnitContext
Predicted SRT (Diamond)540”sIntrinsic limit at 77 K
Predicted SRT (Diamond)2.3”sIntrinsic limit at 300 K
Temperature Dependence (Diamond, Low T)T-2N/ABelow ~170 K
Temperature Dependence (Diamond, High T)T-5.5N/AAbove ~170 K
Predicted SRT (Silicon)4.9nsAt 300 K (Room Temperature)
Lattice Constant (Diamond)3.56ÅInput for DFT calculation
Kinetic Energy Cutoff (Diamond)120RyInput for DFT calculation
Momentum Relaxation Time (Diamond, Low T)T-1.5N/AWeaker dependence than SRT
Momentum Relaxation Time (Diamond, High T)T-2.5N/AWeaker dependence than SRT

The calculation of spin-flip electron-phonon (e-ph) coupling matrix elements and $T_1$ SRTs relies on a sophisticated, multi-step first-principles workflow:

  1. Ground State Calculation: Density Functional Theory (DFT) is used with fully-relativistic norm-conserving pseudopotentials to accurately incorporate Spin-Orbit Coupling (SOC) effects.
  2. Phonon and Perturbation Potential: Density Functional Perturbation Theory (DFPT) is employed to compute phonon dispersions and the Kohn-Sham potential perturbation ($\Delta V_{v\mathbf{q}}$) on coarse Brillouin Zone (BZ) grids.
  3. Effective Spin State Determination: The spin matrix $S(\mathbf{k})$ is computed and diagonalized at each k-point to define the effective up ($\uparrow$) and down ($\downarrow$) spin states in the Kramers degenerate subspace.
  4. Spin-Flip Matrix Element Calculation: The spin-flip e-ph matrix elements ($g^{\text{flip}}_{mn\nu}$) are computed by combining the effective spin states with the perturbation potentials.
  5. Wannier Interpolation: Due to the high computational cost, the spin-flip matrix elements are interpolated using Wannier functions onto extremely fine BZ grids (up to 2003 k-points) to ensure convergence of the BZ sum.
  6. SRT Calculation: The band- and k-dependent spin-flip relaxation times ($T^{\text{flip}}_{n\mathbf{k}}$) are calculated using lowest-order perturbation theory, followed by ensemble averaging via tetrahedron integration to yield the temperature-dependent SRT, $T_s(T)$.

The research highlights the critical need for ultra-pure diamond to experimentally validate the predicted intrinsic spin relaxation limits. 6CCVD is uniquely positioned to supply the necessary high-quality MPCVD diamond materials and customization services required for advanced spintronic and quantum device fabrication.

Research Requirement6CCVD Applicable MaterialCustomization Potential & Advantage
Intrinsic Limit Validation: Requires material purity sufficient to minimize defect-induced scattering, approaching the phonon-limited SRT (540 ”s at 77 K).Optical Grade Single Crystal Diamond (SCD): Ultra-high purity, low-nitrogen (< 1 ppb) MPCVD diamond.Provides the ideal platform for fundamental research, ensuring that measured SRTs are dominated by intrinsic phonon interactions, not extrinsic defects.
Device Integration & Contacts: Spintronic devices require precise metal contacts for spin injection and detection.Custom Metalization Services: In-house deposition of Au, Pt, Pd, Ti, W, and Cu.Enables researchers to receive ready-to-use substrates with tailored metal stacks, crucial for minimizing contact resistance and maximizing spin injection efficiency.
Custom Dimensions & Geometry: Need for specific wafer sizes for experimental setups and device scaling.Custom Dimensions (Plates/Wafers): SCD thickness from 0.1 ”m up to 500 ”m. PCD wafers up to 125mm diameter.Supports both small-scale, high-precision SCD experiments and larger-scale Polycrystalline Diamond (PCD) device prototyping.
Surface Quality: Minimizing surface scattering effects is essential for high-fidelity spin measurements.Advanced Polishing: SCD surfaces polished to Ra < 1 nm. Inch-size PCD polished to Ra < 5 nm.Ultra-low surface roughness ensures minimal surface-related spin decoherence, preserving the intrinsic material properties.
Extension to Doped Materials: Future work involves studying defect-induced spin scattering (e.g., in semiconductors).Boron-Doped Diamond (BDD): Available in both SCD and PCD formats with controlled doping levels.Allows researchers to systematically investigate the impact of controlled doping and defects on spin dynamics, extending the scope beyond the pure EY mechanism.

6CCVD’s in-house PhD team specializes in the growth and characterization of MPCVD diamond for quantum and electronic applications. We offer comprehensive consultation on material selection, doping control, and surface preparation necessary to replicate or extend this research on Elliott-Yafet Spin-Phonon Relaxation and other spin dynamics projects.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

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

  1. 1963 - Solid State Physics