Negatively charged boron vacancy center in diamond

Impurity-vacancy complexes in diamond are an attractive family of spin defects since $\mathrm{N}{V}^{–}, \mathrm{Si}{V}^{–}, \mathrm{Ge}{V}^{–}$, and $\mathrm{Sn}{V}^{–}$ have emerged as promising platforms for quantum applications. Although boron is most easily incorporated into diamond, a boron-vacancy complex in the negative charge state $\left(\mathrm{B}{V}^{–}\right)$ has eluded experimental observation. This center was theoretically predicted as another promising spin qubit. In this work, we experimentally observed an electron paramagnetic resonance (EPR) spectrum identified as $\mathrm{B}{V}^{–}$ in synthetic diamonds via a Fermi-level tuning. Fingerprints of $\mathrm{B}{V}^{–}$ such as the spin multiplicity of $S=1, C_{3\mathrm{v}}$ symmetry, and the zero-field splitting ($D=2913$ MHz), in addition to ${}^{10}\mathrm{B}$ and ${}^{11}\mathrm{B}$ hyperfine (HF) interactions, have been confirmed. Moreover, optically pumped spin polarization has been observed with 3.0–3.6 eV excitation. However, unlike the $\mathrm{N}{V}^{–}$ center, the photoluminescence as well as optically detected magnetic resonance from $\mathrm{B}{V}^{–}$ have not been confirmed even at low temperatures. We speculate that the Jahn-Teller instability in the triplet excited states of the $\mathrm{N}{V}^{–}$ and $\mathrm{B}{V}^{–}$ centers results in different optical properties.

Figure 1

Electronic configurations of three analog color centers in diamond. (a) $\mathrm{N}{V}^{–}$ center with six valence electrons. (b) $\mathrm{O}{V}^0$ center with six valence electrons. (c) $\mathrm{B}{V}^{–}$ center with four valence electrons. Within a defect-molecular-orbital model (see Appendix pp1), one-electron states $a_1$ (black color) and ${a_1}^{\prime }$ (color of each impurity) dominantly originate from atomic orbitals of carbon and impurity atoms, respectively [1]. Doubly degenerate $e$ states also comprise two carbon-related orbitals (denoted by $e_x$ and $e_y$) adjacent to a vacancy [1]. In the $\mathrm{O}{V}^0$ center, ${a_1}^{\prime }$ and $a_1$ are rewritten by $1a_1$ and $2a_1$, respectively, and another ${a_1}^{\prime }$ state (denoted by $3a_1$) is generated from an antibonding state of C-O bonds with three back-bonded carbon atoms [35]. Their energy positions are approximately shown in a band diagram [1, 32, 35, 36, 37], where $E_{\mathrm{C}}$ and $E_{\mathrm{V}}$ are the conduction-band top and the valence-band bottom, respectively.

Figure 2

EPR spectra of N and B codoped diamond. (a) Rapid-passage (RP) EPR spectrum shows EPR signals of $\mathrm{N}{V}^{–}$ ($S=1$), in addition to strong primary signals of $P1$ (${{\mathrm{N}}_{\mathrm{s}}}^0, S=1/2$). This spectrum was recorded for a magnetic-field angle $\theta ={90}^{\circ }$. (b), (c) Magnified EPR spectra show low- and high-field side EPR signals of $\mathrm{N}{V}^{–}$ as well as those of $\mathrm{B}{V}^{–}$ with a fourfold splitting. These spectra were recorded at two principal-axis directions. At 54.75° with $B$ // [111], a site-1 center [cf., Fig. 3] of $\mathrm{B}{V}^{–}$ or $\mathrm{N}{V}^{–}$ shows its symmetry axis parallel to $B$. On the other hand, at 35.25°, $B$ is perpendicular to a symmetry axis of site-2-type $\mathrm{B}{V}^{–}$ and $\mathrm{N}{V}^{–}$ centers [cf., Fig. 3]. Out-of-phase EPR spectra (slow passage) were recorded by using a field-modulation amplitude of 0.004 mT, microwave power of 0.1 mW, and an accumulation of 8–13 h.

Figure 3

(a) Experimental coordinate and corresponding atomic configurations of the $\mathrm{B}{V}^{–}$ and $\mathrm{N}{V}^{–}$ centers. A single impurity atom is located at one of the site-1 to site-4 positions, and a monovacancy is inserted into the origin of the coordinate. In EPR experiments, the external magnetic field ($B$) was rotated in the $\left(0\overline{1}1\right)$ plane from $\theta =0^{\circ }$ at $B$ // [100] to $\theta ={90}^{\circ }$ at $B$ // [011]. (b) Angular dependences of EPR signal positions of $\mathrm{B}{V}^{–}$ and $\mathrm{N}{V}^{–}$. “+” symbols and solid lines express experimental data and theoretical curves, respectively. Both of the spin-1 systems of $\mathrm{B}{V}^{–}$ and $\mathrm{N}{V}^{–}$ show the same $C_{3\mathrm{v}}$ symmetry and very similar D tensors. Numbers in the figure denote the site number. The site-3 and -4 centers are always indistinguishable within the $B$ rotation in the $\left(0\overline{1}1\right)$ plane.

Figure 4

Hyperfine (HF) interactions of ${}^{10}\mathrm{B}$ and ${}^{11}\mathrm{B}$ in the $\mathrm{B}{V}^{–}$ center, which generate fourfold and sevenfold HF splittings, respectively. A fitted curve was calculated by a combination of fourfold and sevenfold HF split structures with the given natural abundances. The RP-EPR spectra was recorded by using a field-modulation amplitude of 0.002 mT, microwave power of 0.2 mW, and an accumulation period of 16 000 s.

Figure 5

(a) Optical spin-polarization loop of $\mathrm{N}{V}^{–}$. Electronic configurations corresponding to ${}^3{A}_2, {}^{3}E, {}^1{A}_1$, and ${}^{1}E$ are shown in terms of electron representation (black) and hole representation (red) [60, 61]. For instance, ${\left(a_1\right)}^2{e}^2$ and ${\left(a_1\right)}^1{e}^3$ for ${}^3{A}_2$ and ${}^{3}E$ in the electron representation are rewritten as ($ee$) and ($ae$) in the hole representation, respectively. Intermediate states of ${}^1{A}_1$ and ${}^{1}E$ are assigned to ($ee$) in the hole representation. Likewise $\mathrm{N}{V}^{–}$ system, ${}^3{A}_2$ ground state and ${}^{3}E$ excited state of $\mathrm{B}{V}^{–}$ are assigned to ($ee$) and ($ae$) in the electron representation, respectively. We assumed that $\mathrm{B}{V}^{–}$ has a similar four-level scheme, judging from its spin-polarization behavior similar to that of $\mathrm{N}{V}^{–}$. Their ground and photoexcited states commonly have triplet spin states with $m_S=-1$, 0, +1. Green line expresses an optical pumping from the ground ${}^3{A}_2$ state to the excited ${}^{3}E$ state. For $\mathrm{N}{V}^{–}$, the optical-pumping threshold is 1.945 eV [1, 45], and that of 3.0 eV for $\mathrm{B}{V}^{–}$ was determined in this study. The photoexcited state is decayed into the ground state via two pathways: a PL emission (red line) or a nonradiative decay via an intermediate state (black lines). The latter process converts $m_S=\pm 1$ states into an $m_S=0$ state, causing spin polarization such that the $m_S=0$ state has a nonequilibrium large population. The PL line of $\mathrm{N}{V}^{–}$ appears at 1.945 eV, while that of $\mathrm{B}{V}^{–}$ is still unclear. (b) Spin polarization of the $m_S=0$ level via optical pumping, which generates a high-field-side emission line in the EPR spectrum. (c) Temperature dependence of spin polarization seen in high-field-side EPR spectra before and after optical pumping by a filtered light of 365 ± 15 nm (3.40 ± 0.15 eV). Light power was ∼1 mW just at the end of a fiber guide. The actual power at the sample was rather decreased due to a transmission loss from fiber end to microwave cavity. Due to spin polarization, low-field-side lines can be enhanced, while high-field-side lines can be reduced or reversed, as shown here.

Figure 6

Photo-EPR measurements on $\mathrm{B}{V}^{–}$ and $\mathrm{N}{V}^{–}$ centers at 60 K for $B$ // [111]. Light power was $5–10\mu \mathrm{W}$ at the end of a fiber guide. Highlighted parts in (a) and (b) indicate optical pumping ranges for spin polarizations of $\mathrm{N}{V}^{–}$ and $\mathrm{B}{V}^{–}$, respectively. Most outer weak resonances in (b) arise from ${}^{13}\mathrm{C}$ HF satellites of $\mathrm{N}{V}^{–}$. (c) EPR intensity profiles of $\mathrm{N}{V}^{–}$ and $\mathrm{B}{V}^{–}$ centers (averaged intensities of their threefold-split and fourfold-split lines, respectively). Solid and dashed lines are calculated using high-field-side and low-field-side lines, respectively. Optical thresholds are also indicated.

Figure 7

Growth sectors in N and B codoped diamond. (a) Preparation of a (100) diamond plate for EPR imaging and PL/CL study. Plate-II (1.34 mm thick) was cut out from the upper middle of a HPHT crystal by laser-cutting. (b) A “DiamondView” image of the plate. Image of the seed-side face (right) is mirrored to make the view direction the same as that of the growth-side face (left). Brighter and darker areas indicate {100} and {111} growth sectors, respectively.

Figure 8

Two-dimensional EPR imaging of (a) $P1$ distribution and (b) $\mathrm{N}{V}^{–}$ distribution. Both $P1$ and $\mathrm{N}{V}^{–}$ are revealed to be dominantly distributed in the {100} growth sector. $\mathrm{N}{V}^{–}$ distribution was recorded under 532-nm optical excitation. (c), (d) Room-temperature PL spectra using 514.5-nm excitation and CL spectra at 83 K obtained for {100} and {111} growth sectors, respectively. In CL spectra, luminescence from a neutral-boron bound exciton (${\mathrm{BE}}_{\mathrm{TO}}$) was only observed for the {111} growth sector. These CL spectra were normalized by each free-exciton luminescence (${\mathrm{FE}}_{\mathrm{TO}}$) intensity. PL spectra indicate that a nitrogen vacancy exists in the {111} growth sector, mostly in the form of the $\mathrm{N}{V}^0$ center (ZPL: 575 nm).

Figure 9

(a) Confocal microscope image of N and B codoped diamond. “MW wire” is used for microwave radiation when ODMR is recorded. The excitation wavelength was 375 nm, which can generate triplet-to-triplet excitation and spin polarization for $\mathrm{B}{V}^{–}$. In the {100} growth sectors, a strong luminescence was observed due to ensemble $\mathrm{N}{V}^{–}$ centers, while in the {111} sectors, no strong luminescence was detected in spite of the presence of $\mathrm{B}{V}^{–}$. (b) Typical PL spectra from {100} and {111} growth sectors (acquisition times are the same). In the region around 414 nm, luminescence from the {100} area remains stronger compared to the {111} area. Peak intensity of the 389-nm line is ∼1/50 times smaller than that of the 575-nm line of $\mathrm{N}{V}^0$ under 375-nm excitation. The 389-nm center is a nitrogen-related radiation-induced defect. Sharp peaks around 412 nm are likely to be local mode replicas of 389-nm ZPL [74].

Figure 10

Typical wide-range PL spectra measured with 375-nm excitation at 4 K from {100} and {111} growth sectors (acquisition times are the same).