| Metadata | Details |
|---|
| Publication Date | 2020-06-17 |
| Journal | New Journal of Physics |
| Authors | Ariel Norambuena, Alejandro JimƩnez, Christoph Becher, Jeronimo R. Maze, Ariel Norambuena |
| Institutions | Universidad Mayor, Pontificia Universidad CatĆ³lica de Chile |
| Citations | 8 |
| Analysis | Full AI Review Included |
- Core Finding: The suppression of the Electron Spin Resonance (ESR) signal in magnetically active systems (like diamond color centers) at room temperature is conclusively attributed to phonon broadening, not the commonly assumed orbital quenching (Ham reduction).
- Mechanism: Phonon broadening is dominated by two-phonon Raman processes at high temperatures (T > 100 K), leading to a drastic increase in the effective relaxation rate (Īij ā T7).
- Jahn-Teller (JT) Effect Role: The strong dynamic JT effect primarily modifies the orbital states, encapsulated by the Ham reduction factor ($p$). This factor causes a motional effectāa temperature-dependent shift in the resonant frequency (Ļ41)ābut does not suppress the signal amplitude.
- Microscopic Model: A Lindblad master equation was derived for generic E ā e ā SU(2) systems (S = 1/2 spin coupled to E-symmetry orbitals and e-phonons), incorporating spin-orbit coupling and Zeeman effects.
- Thermal Dependence: An analytical expression for the thermal dependence of the Ham reduction factor ($p$) was derived, consistent with a super-Ohmic spectral density function for acoustic phonons.
- Signal Recovery: The model predicts, and confirms experimental observations, that the ESR signal is recovered with high intensity at cryogenic temperatures (tens-hundreds mK) where two-phonon processes are inactive.
| Parameter | Value | Unit | Context |
|---|
| Model System Symmetry | D3 | N/A | Trigonal system with degenerate E orbital states and S = 1/2 spin. |
| SiV- Jahn-Teller Energy (EJT) | 42.3 | meV | Numerically estimated for the negatively charged silicon-vacancy center. |
| SiV- Barrier Energy (Ī“JT) | 3.0 | meV | Numerically estimated for the SiV- center. |
| Linear Vibronic Coupling (F) | 83.34 | meV | Associated with a local vibrational mode (ħĻ = 85.2 meV). |
| JT Interaction Time Scale (ĻJT) | ~0.3 | ps | Fast dynamics; determines the time scale for orbital reduction. |
| Phonon Relaxation Time Scale (Ļph-relax) | > 0.1 | Āµs | Time scale for open dynamics (t >> ĻJT). |
| Zero-Temperature Ham Factor (pnum) | ~0.308 | N/A | Calculated for the SiV- center in diamond. |
| Acoustic Phonon Cut-off Frequency (Ļc) | ~2 | THz | Used in the super-Ohmic spectral density function (J(Ļ)). |
| Diamond Lattice Constant (a) | 3.57 | Angstrom | Used for calculating the unit cell volume (Ī© = a3). |
| Speed of Sound (vs) | 1.2 x 104 | m/s | Used for acoustic phonon modeling. |
| High-T Relaxation Rate Scaling (Raman) | ā T7 | N/A | Dominant thermal dependence of the relaxation rate (Ī14) for SiV- and NV0. |
| ESR Suppression Temperature | > 100 | K | Temperature above which the ESR signal intensity is numerically confirmed to be reduced to zero. |
| Estimated Two-Phonon Coupling (Ī00) | ~2.4 | ĀµeV | Estimated by fitting the T7 law to experimental data for the neutral silicon-vacancy center. |
- Effective Hamiltonian Derivation: A unitary transformation (based on Hamās theory) was applied to the full Hamiltonian (H) to decouple the orbital and phonon degrees of freedom in the short-time dynamics (t ~ ĻJT). This yielded an effective Hamiltonian (Heff) incorporating the Ham reduction factors ($p$ and $q$).
- Thermal Ham Reduction Factor Calculation: The thermal dependence of $p$ was calculated by integrating the phononic spectral density function $J(\omega)$. A super-Ohmic model ($J(\omega) \propto \alpha\omega^{3}e^{-\omega/\omega_{c}}$) was used to represent the continuum of acoustic e-phonon modes in the diamond lattice.
- Open System Dynamics: For long-time dynamics (t >> ĻJT), a Lindblad master equation was derived for the orbital and spin degrees of freedom, assuming acoustic phonons are a thermal bath in equilibrium.
- Phonon Relaxation Rate Modeling: Relaxation rates (Īij) were calculated using Fermiās golden rule, including contributions from one-phonon (direct) processes (scaling linearly with T at high T) and two-phonon (Raman) processes.
- High-Temperature Approximation: At room temperature, the Raman process was identified as the dominant relaxation mechanism, modeled phenomenologically as $\Gamma_{ij} \propto A_{ij}T^{n}$ (with $n=7$ for SiV0 and $n=5$ for NV-).
- ESR Absorption Spectrum Calculation: Linear response theory was employed to calculate the ESR absorption spectrum $I(\omega)$. The resulting spectrum is a sum of Lorentzian functions, where peaks are centered at the dressed resonant frequencies ($\omega_{ij}$) and broadened by the effective relaxation rates ($\Gamma_{ij}$).
- Quantum Computing and Information: The model is essential for characterizing and optimizing new spin-1/2 systems (like Group IV-vacancy centers) used as solid-state qubits, particularly where strong electron-phonon coupling limits coherence.
- Quantum Sensing and Metrology: The findings define the operational temperature limits for diamond-based quantum sensors (e.g., those based on NV0 or SiV-) that rely on ESR detection, necessitating cryogenic environments (T < 100 K) for high-contrast signals.
- Solid-State Defect Engineering: Provides a theoretical tool to predict the thermal stability of ESR signals in materials like diamond and silicon carbide (SiC) containing trigonal defects with dynamic Jahn-Teller effects (e.g., Vanadium in SiC).
- Cryogenic Technology Development: Guides the design requirements for cryogenic systems necessary to utilize these spin centers, ensuring that temperatures are low enough to suppress the T7-scaling two-phonon Raman processes.
- Materials Characterization: The methodology offers a microscopic approach to analyze the electron-phonon interaction strength ($g_{JT}$) and Ham reduction factors in novel paramagnetic solid-state systems.
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 ā 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.