Skip to content
6CCVD Research

Spin decontamination for magnetic dipolar coupling calculations - Application to high-spin molecules and solid-state spin qubits

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2020-04-30
JournalPhysical Review Research
AuthorsTimur Biktagirov, Wolf Gero Schmidt, Uwe Gerstmann, Timur Biktagirov, Wolf Gero Schmidt
InstitutionsPaderborn University
Citations21
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This analysis summarizes a novel computational strategy for accurately determining Zero-Field Splitting (ZFS) in high-spin systems, critical for solid-state quantum technology.

  • Core Value Proposition: Introduction of an efficient and robust spin decontamination strategy for Density Functional Theory (DFT) calculations of magnetic dipolar coupling (D tensor).
  • Methodology: The correction relies on calculating the difference between the magnetic dipolar coupling tensors of the high-spin state (ms = S) and the broken-symmetry (BS) state (ms = S - 1).
  • Accuracy Improvement: The method successfully eliminates unphysical ‘on-site’ spin-dipolar interaction terms, which typically cause significant overestimation of ZFS values in standard DFT.
  • Key Achievement (SiC Qubits): The corrected ZFS values for Nitrogen-Vacancy (NV-) and Silicon-Carbon Divacancy (VV°) centers in 4H-SiC show near-perfect agreement with experimental data, resolving a previously reported ~30% discrepancy.
  • Robustness: The approach is demonstrated to be highly robust, minimizing the dependence of the calculated ZFS on the choice of the exchange-correlation functional (e.g., PBE, B3LYP, HSE).
  • Applicability: The strategy is suitable for both finite-size molecular systems and extended periodic systems (solids), making it broadly applicable to S ≄ 1 quantum defects.

Technical Specifications

Section titled “Technical Specifications”

The following table summarizes key computational parameters and corrected results for critical spin qubits studied in the paper.

ParameterValueUnitContext
DFT FormalismPAWN/AProjector Augmented Wave method used for core reconstruction
Plane-Wave Cutoff700eVKinetic energy cutoff for the basis set
Diamond NV- ZFS (Corrected D)2.7207GHzCalculated DSS value for axially symmetric S=1 defect
Diamond NV- ZFS (Experimental)2.867GHzReference experimental value for NV- in diamond
4H-SiC NV-/hh ZFS (Direct D)1.7673GHzUncorrected DSS value (PBE functional)
4H-SiC NV-/hh ZFS (Corrected D)1.2996GHzCorrected DSS value (close to experimental 1.331 GHz)
4H-SiC VSi/h ZFS (Corrected D)1.8GHzCorrected DSS value for high-spin S = 3/2 Silicon Vacancy
Computational Supercell Size (Diamond)512atomsUsed for periodic boundary condition calculations
Computational Supercell Size (4H-SiC)432atomsUsed for periodic boundary condition calculations
Remaining Error (SiC Qubits)< 100MHzDiscrepancy between corrected DSS and measured D values

Key Methodologies

Section titled “Key Methodologies”

The proposed spin decontamination scheme is implemented within the DFT framework using the following steps:

  1. DFT Setup: Calculations utilize spin-polarized self-consistent field (SCF) methods, employing the Projector Augmented Wave (PAW) formalism for accurate reconstruction of the electron density in the atomic core region.
  2. Functional Selection: The PBE exchange-correlation functional is primarily used, though the method is verified to be robust across various functionals (e.g., LDA, GGA, and Hybrid functionals like B3LYP and HSE).
  3. High-Spin State Calculation (ms = S): The magnetic dipolar coupling tensor (d(ms=S)) is calculated for the target high-spin state (e.g., ms = 1 for S = 1 defects).
  4. Broken-Symmetry (BS) State Calculation (ms = S - 1): The system is calculated in a low-spin configuration (ms = S - 1). This state is generated by changing the occupation of one half-filled Kohn-Sham orbital from spin-up to spin-down.
  5. Symmetry Averaging (for Solids): For defects in solids (like NV- in SiC) where the ms = S - 1 state exhibits reduced symmetry, the resulting BS tensors are averaged (e.g., C3v symmetrized average for axial defects) to restore the symmetry of the triplet state.
  6. Spin Decontamination: The corrected spin-spin ZFS tensor (DSS) is derived using the difference between the two calculated tensors, effectively canceling the spin contamination error: DSS = (d(ms=S) - d(ms=S-1)) / (2S - 1)

Commercial Applications

Section titled “Commercial Applications”

This highly accurate computational methodology is critical for the design, characterization, and optimization of materials used in emerging quantum technologies.

  • Solid-State Quantum Computing: Enables precise theoretical characterization of spin qubits (NV-, VV°, VSi) in wide-bandgap semiconductors (Diamond, SiC), accelerating the development of quantum processors and memory.
  • Quantum Sensing and Metrology: Provides reliable ZFS parameters essential for calibrating and modeling defect centers used as high-sensitivity magnetic, electric, and temperature sensors at the nanoscale.
  • Materials Design and Screening: Allows materials engineers to accurately predict the magnetic properties of newly synthesized or engineered high-spin defects, guiding the selection of host materials and defect configurations.
  • Spin Dynamics Modeling: Improves the accuracy of simulations involving magnetic dipolar interactions between distant spin centers, crucial for modeling qubit coupling to spin-baths or surface electron spins.
  • Computational Chemistry: Offers a robust, functional-independent tool for calculating intrinsic spin-spin coupling in complex organic molecules and biradicals, relevant for molecular electronics and spintronics research.
View Original Abstract

An accurate description of the two-electron density, crucial for magnetic coupling in spin systems, provides in general a major challenge for density functional theory calculations. It affects, e.g., the calculated zero-field splitting (ZFS) energies of spin qubits in semiconductors that frequently deviate significantly from experiment. In the present work (i) we propose an efficient and robust strategy to correct for spin contamination in both extended periodic and finite-size systems, (ii) verify its accuracy using model high-spin molecules, and finally (iii) apply the methodology to calculate accurate ZFS of spin qubits (NV$^-$ centers, divacancies) in diamond and silicon carbide. The approach is shown to reduce the dependence on the used exchange-correlation functional to a minimum.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2013 - Electron Paramagnetic Resonance of Transition Ions
  2. 1978 - Theoretical Foundations of Electron Spin Resonance

Reads Similar to This

Solution-processed tin oxide thin film for normally-off hydrogen terminated diamond field effect transistor Wireless Sensor Platform for Dry Spent Fuel Cask Monitoring Adjoint-optimized nanoscale light extractor for nitrogen-vacancy centers in diamond