DFT SIMULATION OF HYPERFINE INTERACTIONS IN THE NV HOSTING CARBON CLUSTER C₅₁₀[NV]⁻ H₂₅₂: PREDICTIONS FOR THE “ON-NV-AXIS” ¹³C SITES

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).…”

“…Among possible positions of the 13 C n-spin in the diamond lattice near the NV center there are few evidently stable positions viz. those located at the NV axis [9,[21][22][23]. Nearest-tothe-vacancy "axial" 13 C position of such "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 [21] on the vacancy side at the NV axis.…”

“…For this specific "NV-axial 13 C"spin system the characteristic zero-field hfi-induced splitting Δ 0 =187 kHz of the substates m S =±1 was predicted in [21] by DFT simulation of hfi in the H-terminated cluster C 291 [NV] -H 172 hosting the NV center. The analysis of hfi data obtained in [21,22] revealed the presence of additional non-axial positions for the n-spin 13 C also exhibiting negligible off-diagonal elements nd T in respectively calculated hfi matrices KL A suggesting that at these positions the 13 C n-spin will not subjected to hfi-induced flip-flops. More recently [22,23] analogous DFT simulation of hfi characteristics has been done for the larger C 510 [NV] -H 252 clusters and the hfi matrices KL A for all possible 510 locations of the 13 C n-spin in the clusters have been calculated (see the Supplement for complete set of the calculated data).…”

“…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. 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]. In any case, the number of available 'axial' 13 C positions is insignificant and the question arises of whether there are other stability (or nearstability) positions for 13 C spins near the NV center in diamond.…”