Theoretical study of hyperfine interactions and optically detected magnetic resonance spectra by simulation of the C₂₉₁[NV]^-H₁₇₂diamond cluster hosting nitrogen-vacancy center

Abstract

Single nitrogen-vacancy (NV) centers in diamond coupled to neighboring nuclear spins are promising candidates for room-temperature applications in quantum information processing, quantum sensing and metrology. Here we report on a systematic density functional theory simulation of hyperfine coupling of the electronic spin of the NV center to individual 13 C nuclear spins arbitrarily disposed in the H-terminated C 291 [NV] -H 172 cluster hosting the NV center. For the 'families' of equivalent positions of the 13 C atom in diamond lattices around the NV center we calculated hyperfine characteristics. For the first time the data are given for a system where the 13 C atom is located on the NV center symmetry axis. Electron paramagnetic resonance transitions in the coupled electron-nuclear spin system 14 NV-13 C are analyzed as a function of the external magnetic field. Previously reported experimental data from Dréau et al (2012 Phys. Rev. B 85 134107) are described using simulated hyperfine coupling parameters.

Non-flipping13C spins near an NV center in diamond: hyperfine and spatial characteristics by density functional theory simulation of the C510[NV]H252cluster

“…Having calculated, along with the hfi characteristics, the coordinates of all C sites in the relaxed cluster, we determined the locations of the above-mentioned 'colored' stable positions in the cluster, which are shown in figure 2 where the corresponding positions are presented by the same colors as their 'lifetimes' shown in figure 1(b). The four most stable positions-7, 8, 269 and 505, shown in figure 1(b) in red-are just the expected, and previously considered [18][19][20], 'axial' positions. The other near-stable 'colored' positions in figure 1(b) having numbers in the 200s (plus positions 4, 5, and 6, shown in black) are located in the diamond lattice bilayer (see, e.g., [32]) being perpendicular to the NV axis and passing through the vacancy (see figure 2 for better illustration).…”

“…The geometric structure of the C 510 [NV] -H 252 cluster was optimized, and spin density distribution over the cluster was calculated using the DFT/B3LYP/UKS/MINI/3-21 G level of the theory which has been previously [18] used for calculating the hfi characteristics of smaller diamond clusters, for which it showed good agreement with the available experimental data. Calculations have been performed for the singly negatively charged cluster in the triplet ground state (S=1).…”

“…Under these conditions the time-averaged n-spin flip rates are proportional to G = D   ( ) T B B nd 2 2 (see also [24]). At zero magnetic field the 13 C n-spin flips with a rate proportional to the parameter G = 18,24]. Note that by applying a strong external magnetic field B||OZ (γ n B ?…”

“…The nearest-to-the-vacancy 'axial' 13 C position for such an 'NV-axial− 13 C' system exhibiting strongest hfi with the NV center is disposed at the distance of about 6.5 Å from the N atom on the vacancy side at the NV axis [18]. In [18], for this specific 'NV-axial− 13 C' spin system, the characteristic zero-field hfi-induced splitting = 187 kHz of the substates m S = ±1, was predicted by density functional theory (DFT) simulation of the H-terminated cluster C 291 [NV] -H 172 hosting the NV center. More recently [19,20], analogous DFT simulation of hfi characteristics has been done for the larger C 510 [NV] -H 252 clusters, and the spatial and hfi characteristics for eight more distant 'NV-axial− 13 C' systems were found [19].…”

“…Among various hfi-coupled NV− 13 C spin systems with different positions of the 13 C n-spin in the diamond lattice, there are several positions located at the NV axis [9,[18][19][20] wherein, by analogy with the 14 N/ 15 N e−n spin systems, the 13 C n-spin does not undergo hfi-induced flip-flops due to the coincidence of the e-and n-spins' quantization axes. The nearest-to-the-vacancy 'axial' 13 C position for such an 'NV-axial− 13 C' system exhibiting strongest hfi with the NV center is disposed at the distance of about 6.5 Å from the N atom on the vacancy side at the NV axis [18]. In [18], for this specific 'NV-axial− 13 C' spin system, the characteristic zero-field hfi-induced splitting = 187 kHz of the substates m S = ±1, was predicted by density functional theory (DFT) simulation of the H-terminated cluster C 291 [NV] -H 172 hosting the NV center.…”