Effect of phonons on the electron spin resonance absorption spectrum
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-06-17 |
| Journal | New Journal of Physics |
| Authors | Ariel Norambuena, Alejandro Jiménez, Christoph Becher, Jeronimo R. Maze, Ariel Norambuena |
| Institutions | Saarland University, Universidad Mayor |
| Citations | 8 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Phonon Effects on Diamond Color Center ESR
Section titled âTechnical Documentation & Analysis: Phonon Effects on Diamond Color Center ESRâThis documentation analyzes the theoretical modeling of electron spin resonance (ESR) suppression in diamond color centers (specifically SiV$^{-}$ and NV$^{0}$) due to phonon interactions, highlighting the critical material requirements for replicating and advancing this quantum research.
Executive Summary
Section titled âExecutive Summaryâ- Core Finding: The suppression of the Electron Spin Resonance (ESR) signal in diamond color centers (e.g., SiV$^{-}$) at high temperatures ($T > 100$ K) is conclusively attributed to phonon broadening induced by two-phonon Raman processes, not orbital quenching.
- Mechanism: A strong dynamical Jahn-Teller (JT) effect modifies the orbital states (Ham reduction factor $p$), causing a motional shift in the resonant frequency $\omega_{41}$ from $\sim 50$ GHz (at 0 K) down to the Zeeman frequency ($\gamma_{s}B_{z}$) at high temperatures.
- Thermal Dependence: The effective relaxation rate $\Gamma_{14}$ exhibits a strong thermal dependence, scaling as $T^{7}$ at high temperatures, which drastically reduces the ESR signal amplitude above 100 K.
- Modeling Approach: The study utilizes a microscopic model incorporating the linear JT interaction, spin-orbit coupling, Zeeman effect, and phonon-induced relaxation processes via a Lindblad master equation.
- Application Relevance: This model is crucial for characterizing spin-1/2 systems in diamond used for metrology and quantum information applications, emphasizing the necessity of ultra-low temperature operation for high-contrast ESR signals.
- Material Requirement: Replication of this research requires ultra-high purity, low-strain Single Crystal Diamond (SCD) substrates to host stable, well-defined color centers.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the theoretical model parameters and results, primarily focusing on the SiV$^{-}$ center in diamond.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| JT Energy ($E_{JT}$) | 42.3 | meV | Estimated for SiV$^{-}$ center. |
| Barrier Energy ($\delta_{JT}$) | 3.0 | meV | Estimated for SiV$^{-}$ center. |
| Linear Vibronic JT Coupling ($F$) | 83.34 | meV | Derived from $E_{JT}$ and $\delta_{JT}$. |
| Local Vibrational Mode Energy ($\hbar\omega$) | 85.2 | meV | Associated with the JT coupling. |
| JT Time Scale ($\tau_{JT}$) | $\sim 0.3$ | ps | Fast dynamics time scale. |
| Phonon Relaxation Time Scale ($\tau_{ph-relax}$) | $\sim 0.1$ | ”s | Slow dynamics time scale. |
| Ham Reduction Factor ($p_{num}$) | $\sim 0.308$ | Dimensionless | Numerical calculation at zero temperature. |
| Acoustic Phonon Cut-off Frequency ($\omega_{c}$) | $\sim 2$ | THz | Used in the super-Ohmic spectral density model. |
| Static Magnetic Field ($B_{z}$) | 1000 | G | Used for modeling the transition $ |
| Zero-Temp Resonance Frequency ($\omega_{41}(0)$) | $\sim 50$ | GHz | Transition frequency $ |
| Magnetic Noise ($\Gamma_{mag}$) | 3 | MHz | Phenomenological constant used in relaxation rate $\Gamma$. |
| Two-Phonon Coupling Constant ($\Lambda_{00}$) | $\sim 2.4$ | ”eV | Estimated for SiV$^{0}$ center comparison. |
| ESR Suppression Temperature | > 100 | K | Temperature above which ESR signal intensity approaches zero. |
Key Methodologies
Section titled âKey MethodologiesâThe study employed a rigorous quantum mechanical approach to model the coupled orbital, spin, and phonon dynamics:
- Hamiltonian Formulation: The total Hamiltonian $H$ was constructed, including the Jahn-Teller interaction ($H_{JT}$), Spin-Orbit coupling ($H_{SO}$), Zeeman effect ($H_{Z}$), Strain ($H_{strain}$), and the time-dependent oscillating magnetic field $V(t)$.
- Unitary Transformation (Ham Reduction): A unitary transformation $\hat{U}$ was applied to decouple the orbital and momentum operators, leading to an effective Hamiltonian $H_{eff}$ dressed by the JT effect. This transformation yields the thermally dependent Ham reduction factor $p(T)$.
- Spectral Density Modeling: The phononic spectral density function $J(\omega)$ was modeled using a super-Ohmic acoustic model ($J_{acous}(\omega) = \alpha\omega^{3}e^{-\omega/\omega_{c}}$) to calculate the thermal dependence of $p(T)$ for a continuum of $e$-phonon modes.
- Open Dynamics (Lindblad Master Equation): The phonon-induced relaxation processes were introduced using a Markovian Lindblad master equation for the orbital and spin degrees of freedom, valid for time scales $t \gg \tau_{JT}$.
- Relaxation Rate Calculation: The effective relaxation rate $\Gamma_{ij}$ was decomposed into one-phonon (linear $T$ scaling at high T) and two-phonon (Raman $T^{7}$ scaling) contributions, derived using Fermi golden rule theory.
- ESR Absorption Spectrum: The absorption spectrum $I(\omega)$ was derived using linear response theory, resulting in a sum of Lorentzian functions with peaks at the resonant frequencies $\omega_{ij}$ and broadened by the calculated phonon relaxation rates $\Gamma_{ij}$.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research underscores the critical role of high-quality diamond material in advancing solid-state quantum systems. 6CCVD is uniquely positioned to supply the necessary materials and engineering support to replicate and extend these findings into practical quantum devices.
Applicable Materials
Section titled âApplicable MaterialsâTo replicate the SiV$^{-}$ and NV$^{0}$ color center physics studied in this paper, researchers require diamond with extremely low nitrogen and defect concentrations to ensure the stability and coherence of the spin systems.
| 6CCVD Material Solution | Specification & Relevance |
|---|---|
| Optical Grade Single Crystal Diamond (SCD) | Essential. Ultra-high purity, low-strain SCD is required for controlled creation of SiV$^{-}$ and NV$^{0}$ centers via implantation or in-situ doping. Our SCD offers superior lattice quality necessary for long spin coherence times ($T_{2}$). |
| Low-Strain SCD Substrates | The model incorporates strain effects ($\gamma_{x,y}$). 6CCVD provides SCD with certified low internal strain, minimizing unwanted static distortions that could complicate spectral analysis. |
| Custom SCD Thickness | We offer SCD plates from 0.1 ”m up to 500 ”m. This flexibility allows researchers to optimize implantation depth and optical coupling for specific experimental setups (e.g., thin membranes for photonic integration). |
Customization Potential
Section titled âCustomization PotentialâThe experimental realization of these quantum systems often requires precise geometric and electrical interfaces. 6CCVD offers comprehensive customization capabilities:
- Custom Dimensions: We supply SCD wafers and plates up to 125 mm (PCD) and custom dimensions for SCD, ensuring compatibility with standard cryogenic and microwave setups.
- Precision Polishing: Qubit research demands atomically smooth surfaces. 6CCVD guarantees Ra < 1 nm polishing on SCD, crucial for minimizing surface defects that contribute to phonon scattering and decoherence.
- Advanced Metalization: While this paper is theoretical, future devices based on these color centers will require electrical contacts for spin manipulation or readout. 6CCVD offers in-house deposition of standard metals (Au, Pt, Pd, Ti, W, Cu) in custom patterns via lithography or shadow masking.
Engineering Support
Section titled âEngineering SupportâThe complex interplay between the Jahn-Teller effect, phonons, and spin dynamics requires deep material expertise.
- PhD-Level Consultation: 6CCVDâs in-house team of PhD material scientists specializes in MPCVD growth parameters and defect engineering. We can assist researchers in selecting the optimal diamond grade (e.g., nitrogen concentration, isotopic purity) necessary for specific ESR and Quantum Information projects.
- Thermal Management: Understanding phonon broadening is critical for thermal management in quantum devices. We provide material specifications tailored to applications requiring operation across a wide temperature range (mK to 300 K).
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Abstract The unavoidable presence of vibrations in solid-state devices can drastically modify the expected electron spin resonance (ESR) absorption spectrum in magnetically active systems. In this work, we model the effect of phonons and temperature on the ESR signal in molecular systems with strong E â e Jahn-Teller (JT) effect and an electronic spin-1/2. Our microscopic model considers the linear JT interaction with a continuum of phonon modes, the spin-orbit coupling, the Zeeman effect, and the response of the system under a weak oscillating magnetic field. We derive a Lindblad master equation for the orbital and spin degrees of freedom, where one- and two-phonon processes are considered for the phonon-induced relaxation, and the thermal dependence of Ham reduction factors is calculated. We find that the suppression of ESR signals is due to phonon broadening but not based on the common assumption of orbital quenching. Our results can be applied to explain the experimentally observed absence of the ESR signal in color centers in diamond, such as the neutral nitrogen-vacancy and negatively charged silicon-vacancy color centers in diamond.