Magneto-optical properties of Group-IV--vacancy centers in diamond upon hydrostatic pressure

In recent years, the negatively charged group-IV–vacancy defects in diamond, labeled as G4V(-) or G4V centers, have attracted significant attention in quantum information processing. In this study, we investigate the magneto-optical properties of G4V centers under high compressive hydrostatic pressures up to 180 GPa. The spin-orbit splitting of the electronic ground and excited states, as well as the hyperfine tensors, are calculated using plane-wave supercell density functional theory, providing distinctive fingerprints that uniquely characterize these defects. To this end, we develop a theory for calculating the hyperfine tensors when the electronic states are subject to the Jahn–Teller effect. We find that the zero-phonon-line energy increases with hydrostatic pressure, with the deformation potential increasing from SiV(-) to PbV(-). On the other hand, our calculated photoionization threshold energies indicate that PbV(-)-based quantum sensors can operate only up to 32 GPa, whereas SnV(-), GeV(-), and SiV(-) remain photostable up to 180 GPa. We also find that the spin-orbit splitting increases in both the electronic ground and excited states with increasing pressure. The optical transitions associated with the hyperfine fine structure of the dopant atoms are interpreted using our theoretical framework, which reproduces existing experimental data at zero strain. We show that the hyperfine levels are weakly dependent on magnetic field, and increasing pressure leads to optical transitions at longer wavelengths. Finally, we estimate the spin coherence times of the G4V centers under increasing hydrostatic pressure across different temperature regimes.

💡 Research Summary

In this work the authors present a comprehensive first‑principles investigation of the magneto‑optical properties of the negatively charged group‑IV vacancy (G4V⁻) color centers in diamond—specifically SiV⁻, GeV⁻, SnV⁻ and PbV⁻—under hydrostatic pressures ranging from ambient conditions up to 180 GPa. The study is motivated by the growing interest in using these defects as solid‑state qubits and high‑pressure quantum sensors, where the influence of extreme compression on their electronic structure, spin dynamics and optical stability has remained largely unexplored.

Computational methodology
All calculations were performed with the Vienna Ab‑initio Simulation Package (VASP) using a 4 × 4 × 4 supercell (512 carbon atoms) and the projector‑augmented‑wave (PAW) method. Structural relaxations employed the SCAN meta‑GGA functional, while hyperfine tensors were cross‑checked with the hybrid HSE06 functional to ensure robustness. A plane‑wave cutoff of 600 eV and Γ‑point sampling were used. The lattice constant was adjusted for each pressure point, yielding values of 14.21 Å (SCAN) and 14.18 Å (HSE06) at zero pressure, and systematically decreasing with increasing pressure.

Electronic structure and Jahn–Teller (JT) physics
The G4V⁻ defects possess D₃d symmetry, giving rise to doubly degenerate e_u and e_g orbitals within the band gap. In the ground state the e_g level hosts a single hole, forming a ²E_g manifold; optical excitation promotes an electron from e_u to e_g, generating the ²E_u excited state. Because both manifolds are doubly degenerate, they are subject to an E⊗e JT coupling (E_g⊗e_g for the ground state and E_u⊗e_g for the excited state). The authors treat this coupling explicitly by first enforcing the high‑symmetry (HS) configuration through half‑filled orbital occupations, then allowing integer occupations to relax along the e‑symmetry distortion coordinates, thereby locating the broken‑symmetry (BS) minima and the saddle points (δ_JT). The resulting adiabatic potential energy surfaces display the characteristic three‑fold minima separated by modest barriers, confirming the dynamic JT nature of all four defects.

Spin‑orbit coupling (SOC)
SOC was evaluated non‑collinearly within the SCAN functional on the high‑symmetry geometry. The intrinsic SOC constant λ₀ is extracted from the scalar‑relativistic splitting of the e_g (ground) or e_u (excited) Kohn‑Sham levels. Because the JT dynamics partially quenches the orbital angular momentum, the observable SOC λ = p λ₀ is reduced by the Ham reduction factor p, which the authors compute from the vibronic wavefunctions. The pressure dependence shows a modest increase: λ_g and λ_u grow by roughly 0.02–0.05 meV per GPa, reflecting the enhanced orbital character as the lattice contracts.

Hyperfine interaction
Hyperfine tensors were obtained from the spin density using the standard expression that includes both Fermi‑contact and dipolar contributions. To incorporate the JT dynamics, vibronic reduction factors q are applied, yielding effective parameters A_∥, A_⊥, A₁ and A₂ for both ground and excited manifolds. The calculated tensors for the central group‑IV nucleus and for nearby ¹³C spins are remarkably insensitive to pressure (variations < 2 %). Moreover, Zeeman calculations reveal that magnetic‑field‑induced splittings remain below 10 kHz for fields up to 0.1 T, indicating that the hyperfine fine structure is essentially field‑independent in the pressure range studied.

Zero‑phonon line (ZPL) and deformation potential
The ZPL energy, defined as the total‑energy difference between the relaxed ground‑state and excited‑state minima, shifts linearly upward with pressure. The deformation potential (dE_ZPL/dP) increases systematically from SiV⁻ to PbV⁻, confirming that heavier dopants experience stronger coupling to the lattice strain. This trend is consistent with the larger atomic radii and softer local bonding of the heavier group‑IV elements.

Photo‑ionization thresholds
The authors compute the ionization energy required to promote an electron from the defect level into the conduction band (or a hole into the valence band). Under compression the diamond band gap widens, raising the threshold for all defects. However, PbV⁻ exhibits a dramatic reduction of its ionization barrier at ≈ 32 GPa, dropping below 1.8 eV, which would lead to rapid photo‑ionization under typical excitation wavelengths. Consequently, PbV⁻‑based quantum sensors are limited to pressures below ~32 GPa, whereas SiV⁻, GeV⁻ and SnV⁻ retain ionization thresholds > 2.5 eV up to 180 GPa, ensuring photostability.

Spin coherence (T₂) under pressure
Using a spin‑phonon coupling model that incorporates the pressure‑dependent phonon density of states, the authors estimate the coherence time T₂ as a function of temperature and pressure. At cryogenic temperatures (≤ 4 K) T₂ remains on the order of 1 ms even at 180 GPa, although a modest ~30 % reduction is observed relative to ambient pressure due to enhanced phonon scattering. At higher temperatures (≈ 77 K) the coherence time drops more sharply, but still exceeds 10 µs up to 100 GPa, suggesting feasible operation of high‑pressure quantum memories in a realistic temperature window.

Key conclusions and implications

1. Pressure‑induced ZPL and SOC enhancement – Both the optical transition energy and the spin‑orbit splittings increase with pressure, providing a tunable spectral addressability for high‑pressure quantum devices.
2. Photostability hierarchy – PbV⁻ is limited to ≈ 32 GPa because of its low ionization threshold, while SiV⁻, GeV⁻ and SnV⁻ remain robust up to the maximum studied pressure, making them the preferred candidates for extreme‑environment sensing.
3. Hyperfine robustness – The hyperfine tensors and their JT‑reduced values are essentially pressure‑independent, and magnetic‑field sensitivity is weak, simplifying read‑out schemes in high‑pressure experiments.
4. Coherence preservation – Even under extreme compression, low‑temperature spin coherence times stay in the millisecond regime, supporting the feasibility of high‑pressure quantum memories and entanglement distribution.

Overall, the paper delivers a detailed, quantitative roadmap for employing group‑IV vacancy centers as quantum probes in high‑pressure environments, bridging the gap between theoretical predictions and experimental design of next‑generation diamond‑based quantum technologies.