Boron Vacancy (VB-) in hBN

• Boron Vacancy (VB-) is a negatively charged point defect in hexagonal boron nitride featuring a missing boron atom and a spin-triplet ground state ideal for quantum sensing.
• Advanced ODMR spectroscopy and ESR techniques reveal key spin Hamiltonian parameters such as zero-field splitting, hyperfine, and quadrupole interactions under varied conditions.
• Engineered creation pathways, charge-state control, and integration with nanophotonic structures enable tunable optical response and enhanced nanoscale sensing performance.

The negatively charged boron vacancy, $V_\text{B}^-$, is a point defect in hexagonal boron nitride (hBN) formed by a missing boron atom in the $-1$ charge state. It is an optically addressable spin defect with a spin-triplet ground state, room-temperature optically detected magnetic resonance (ODMR), and a broad photoluminescence band centered near $800$ nm, and it has emerged as a platform for quantum sensing at nanometer-scale or atomic-scale proximity in van der Waals materials (Mathur et al., 2021, Xu et al., 2022, Gale et al., 2023).

1. Defect structure, symmetry, and spin Hamiltonians

In a single hBN layer, each boron atom is bonded to three $sp^2$-hybridized nitrogen atoms. The $V_\text{B}^-$ defect is the absence of one boron atom, leaving three nitrogen dangling bonds equally spaced around the vacancy. In the symmetry-based description used for the ground state, the local point group is $D_{3h}$, with the principal $z$-axis of the fine-structure tensor aligned with the crystallographic $c$-axis (Gracheva et al., 2023).

The ground-state electronic spin is $S=1$. A standard effective Hamiltonian used across ODMR and ESR studies is

$$H = hD\bigl(S_z^2 - S(S+1)/3\bigr) + hE\bigl(S_x^2 - S_y^2\bigr) + \mu_B g\,\mathbf{B}\cdot\mathbf{S},$$

with $-1$0 the axial zero-field splitting, $-1$1 the transverse splitting, and $-1$2 the electronic $-1$3-factor (Mathur et al., 2021). In related formulations the same physics is written as

$-1$4

or, when hyperfine structure is included explicitly, as a full spin Hamiltonian containing Zeeman, fine-structure, hyperfine, nuclear Zeeman, and nuclear quadrupole terms (Gracheva et al., 2023, Clua-Provost et al., 2023).

Reported ground-state parameters are consistent at the level of a few percent but vary somewhat with method, sample, and temperature. Room-temperature ODMR work reported $-1$5 GHz, $-1$6 MHz, and $-1$7 (Mathur et al., 2021). A cryogenic/room-temperature excited-state ODMR study reported $-1$8 MHz at $-1$9 K and $800$0 MHz at $800$1 K, with $800$2 MHz at room temperature and $800$3 (Mu et al., 2021). Conventional ESR and high-frequency ENDOR reported $800$4 GHz and $800$5 (Gracheva et al., 2023). In ensemble studies the transverse splitting is typically much smaller than $800$6, often $800$7 MHz, and is sensitive to rhombic distortion, strain, and local charge disorder (Solanki et al., 22 Jul 2025, Carbone et al., 30 Jan 2025).

The charge state is a defining part of the defect’s functionality. The boron monovacancy can adopt several charge states, but only the $800$8 state is optically active and spin-triplet, making $800$9 the relevant spin-photon interface for ODMR-based control and readout (Gale et al., 2023).

2. Hyperfine structure, quadrupole couplings, and spin-density localization

For the ground state coupled to the three nearest nitrogen nuclei, a symmetry-aware Hamiltonian is

$sp^2$0

Here the three $sp^2$1 tensors are related by $sp^2$2 rotations about the $sp^2$3-axis, and the local principal axes of the hyperfine and quadrupole tensors follow the dangling-bond directions of the three nitrogen atoms (Gracheva et al., 2023).

Experimentally, the nearest-neighbor hyperfine interaction is axially symmetric to good approximation. ESR and $sp^2$4 GHz ENDOR gave $sp^2$5 MHz and $sp^2$6 MHz for each nearest $sp^2$7N, while the nuclear quadrupole interaction is characterized by $sp^2$8 MHz and $sp^2$9 (Gracheva et al., 2023). A linear-combination-of-atomic-orbitals analysis based on these values yielded the result that approximately $V_\text{B}^-$0 of the total $V_\text{B}^-$1 electron-spin density resides on the three nearest nitrogen atoms, directly demonstrating strong in-plane localization within a single BN layer (Gracheva et al., 2023).

Isotopic control modifies both line multiplicity and linewidth. In natural $V_\text{B}^-$2N material, the splitting per nitrogen is $V_\text{B}^-$3 MHz, giving the familiar seven-line ESR pattern. In $V_\text{B}^-$4N-purified $V_\text{B}^-$5, the longitudinal coupling becomes $V_\text{B}^-$6 MHz and only four ESR lines appear. The unresolved broadening from second-neighbor boron nuclei also depends on isotope: the ESR full width at half maximum changes from $V_\text{B}^-$7 MHz to $V_\text{B}^-$8 MHz, so $V_\text{B}^-$9B purification narrows the linewidth by about $D_{3h}$0 MHz (Clua-Provost et al., 2023).

The nuclear-spin degrees of freedom are not restricted to nearest neighbors. ENDOR measurements identified $D_{3h}$1N spins in the third nearest-neighbor shell, denoted N(3), at a distance of approximately $D_{3h}$2 nm from the vacancy. For these sites the measured principal hyperfine values are $D_{3h}$3 MHz, $D_{3h}$4 MHz, and $D_{3h}$5 MHz; the corresponding isotropic and dipolar parts are $D_{3h}$6 MHz and $D_{3h}$7 MHz (Mamin et al., 9 Apr 2025). This establishes $D_{3h}$8 as a probe of more remote nuclear moments in the host lattice.

Optical pumping can also polarize the host nuclei. In $D_{3h}$9, optically induced $z$0N polarization was demonstrated near the ground-state level anticrossing. A four-level rate model gave

$z$1

and the experimental power-dependent fit at $z$2 mT yielded $z$3 and $z$4 mW (Clua-Provost et al., 2023).

3. Excited-state spectroscopy and the symmetry question

A defining development in the $z$5 literature has been the direct observation of spin resonance in the orbital excited state. Continuous-wave ODMR revealed an additional set of resonances distinct from the ground-state transitions, and pulsed ODMR then verified their excited-state origin by eliminating any microwave-driven spin rotation after the system had fully relaxed into the ground state (Mathur et al., 2021, Yu et al., 2021, Mu et al., 2021).

At room temperature, one study determined the excited-state parameters to be $z$6 GHz, $z$7 MHz, and $z$8 (Mathur et al., 2021). A related room-temperature study reported $z$9 GHz, $c$0 MHz, and $c$1, and also resolved two types of excited-state hyperfine splitting, approximately $c$2 MHz from the three equivalent $c$3N nuclei and $c$4 MHz from a more distant $c$5B nucleus (Yu et al., 2021). At cryogenic temperature, a separate ODMR study reported $c$6 MHz at $c$7 K, $c$8 MHz at $c$9 K, and an excited-state ODMR contrast of $S=1$0 at cryogenic temperature (Mu et al., 2021).

Level anticrossings provide a second route to excited-state characterization. In photoluminescence-versus-field measurements without microwaves, dips appear near the excited-state level anticrossing at about $S=1$1 G or $S=1$2 G, and near the ground-state anticrossing at about $S=1$3 G, $S=1$4 G, or $S=1$5 G, depending on the dataset and fitting procedure (Mathur et al., 2021, Mu et al., 2021, Yu et al., 2021). These anticrossings are associated with field-induced mixing of $S=1$6 and $S=1$7 under the spin Hamiltonian.

The symmetry of the excited state has been a central issue. One theoretical possibility is $S=1$8 symmetry with a $S=1$9 orbital doublet; another is lowered $$H = hD\bigl(S_z^2 - S(S+1)/3\bigr) + hE\bigl(S_x^2 - S_y^2\bigr) + \mu_B g\,\mathbf{B}\cdot\mathbf{S},$$0 symmetry with a $$H = hD\bigl(S_z^2 - S(S+1)/3\bigr) + hE\bigl(S_x^2 - S_y^2\bigr) + \mu_B g\,\mathbf{B}\cdot\mathbf{S},$$1 orbital singlet. The experimental observation of a single excited-state spin-triplet resonance from $$H = hD\bigl(S_z^2 - S(S+1)/3\bigr) + hE\bigl(S_x^2 - S_y^2\bigr) + \mu_B g\,\mathbf{B}\cdot\mathbf{S},$$2 to $$H = hD\bigl(S_z^2 - S(S+1)/3\bigr) + hE\bigl(S_x^2 - S_y^2\bigr) + \mu_B g\,\mathbf{B}\cdot\mathbf{S},$$3 K, with no loss of contrast at low temperature, was interpreted as consistent with an orbital-singlet excited state. In that analysis, the robust low-temperature ODMR and the strong temperature dependence of the transverse splitting $$H = hD\bigl(S_z^2 - S(S+1)/3\bigr) + hE\bigl(S_x^2 - S_y^2\bigr) + \mu_B g\,\mathbf{B}\cdot\mathbf{S},$$4 pointed to lowered $$H = hD\bigl(S_z^2 - S(S+1)/3\bigr) + hE\bigl(S_x^2 - S_y^2\bigr) + \mu_B g\,\mathbf{B}\cdot\mathbf{S},$$5 symmetry and a $$H = hD\bigl(S_z^2 - S(S+1)/3\bigr) + hE\bigl(S_x^2 - S_y^2\bigr) + \mu_B g\,\mathbf{B}\cdot\mathbf{S},$$6 orbital-singlet excited state (Mathur et al., 2021). By contrast, other excited-state treatments use a triplet $$H = hD\bigl(S_z^2 - S(S+1)/3\bigr) + hE\bigl(S_x^2 - S_y^2\bigr) + \mu_B g\,\mathbf{B}\cdot\mathbf{S},$$7 description as an effective spectroscopic model (Mu et al., 2021). The literature therefore contains both notations.

Temperature dependence strengthens the distinction between axial and transverse excited-state terms. From $$H = hD\bigl(S_z^2 - S(S+1)/3\bigr) + hE\bigl(S_x^2 - S_y^2\bigr) + \mu_B g\,\mathbf{B}\cdot\mathbf{S},$$8 to $$H = hD\bigl(S_z^2 - S(S+1)/3\bigr) + hE\bigl(S_x^2 - S_y^2\bigr) + \mu_B g\,\mathbf{B}\cdot\mathbf{S},$$9 K, $-1$00 remains essentially constant at $-1$01 GHz within experimental error, whereas $-1$02 changes strongly, from $-1$03 MHz at $-1$04 K to approximately $-1$05 MHz at $-1$06 K (Mathur et al., 2021). This behavior underlies proposals for intrinsic thermometry and strain sensing using the excited-state manifold.

4. Creation pathways, charge-state control, and defect engineering

Several routes have been used to create $-1$07 in hBN, and the outcome depends strongly on ion species, dose, flake thickness, cleaning, and substrate environment. In exfoliated hBN, focused-ion-beam implantation with $-1$08 keV $-1$09 or $-1$10 ions reproducibly generated the $-1$11 nm $-1$12 photoluminescence band and ODMR near $-1$13 GHz, whereas commercial $-1$14 keV implantation did not yield the $-1$15 nm spectral signature under the tested conditions, and electron irradiation up to $-1$16 keV did not efficiently create $-1$17 in the tested flakes (Zabelotsky et al., 2023).

Thickness and cleaning are important in exfoliated samples. For similar nitrogen fluence $-1$18–$-1$19, a $-1$20 nm region gave signal-to-noise ratio $-1$21 whereas a $-1$22 nm region gave $-1$23. Forming-gas annealing at $-1$24C for $-1$25 h, or hot-plate annealing in air at $-1$26C for $-1$27 min, restored $-1$28 photoluminescence in as-exfoliated flakes, and the authors recommended keeping fluence below approximately $-1$29 to avoid amorphization or sputtering (Zabelotsky et al., 2023).

In suspended, large-area CVD-grown hBN, the dominant created defect type depends on projectile mass. Light ions and neutrons favor boron vacancies, while $-1$30 keV electrons predominantly generate a $-1$31 nm emitter assigned to $-1$32. For $-1$33 keV bombardment of suspended $-1$34 nm hBN, the defect-yield proxy $-1$35 peaked at about $-1$36 for He$-1$37 at $-1$38 ions nm$-1$39, about $-1$40 for Ne$-1$41 at $-1$42 ions nm$-1$43, and about $-1$44 for Ar$-1$45 at $-1$46 ion nm$-1$47 (Vlassiouk et al., 24 Mar 2025). Supported hBN behaves differently because ions penetrating through thin hBN can generate secondary particles in the substrate, which then promote other defect species; in that work, boron-vacancy purity depended strongly on hBN thickness relative to the end-of-range of the projectile (Vlassiouk et al., 24 Mar 2025).

Focused He-ion creation has also been quantified at the level of charge-state yield. Using $-1$48 keV $-1$49He$-1$50 irradiation of circular $-1$51 nm patches in $-1$52 nm hBN on graphite, followed by ODMR-based extraction of local electric-field-induced splitting, a lower bound of $-1$53 was obtained for the fraction of all vacancies that end up in the optically active, negatively charged state $-1$54 (Carbone et al., 30 Jan 2025). This separates total vacancy creation from creation of the specific charge state relevant for spin optics.

The charge state can also be actively manipulated. In layered heterostructures under simultaneous laser and electron-beam excitation, deterministic and reversible switching between $-1$55 and $-1$56 was demonstrated through

$-1$57

The ionization rate $-1$58 scales linearly with local electron-beam flux, the recovery rate $-1$59 scales approximately linearly with $-1$60 nm laser power, and the steady-state negative-state fraction follows

$-1$61

Under $-1$62 V bottom-gate bias, quenching under $-1$63 was $-1$64, compared with $-1$65 at $-1$66 V, showing that excess electrons stabilize the $-1$67 charge state (Gale et al., 2023).

5. Coherence, decoherence, and relaxation dynamics

Broadband microwave control has enabled direct measurements of $-1$68 and $-1$69 in isotopically enriched hBN. In a $-1$70 nm thick $-1$71 flake stamped onto a $-1$72m-wide gold stripline and irradiated with $-1$73 keV He$-1$74, the $-1$75 transition near $-1$76 GHz at $-1$77 mT displayed four overlapping hyperfine lines from the three nearest $-1$78N nuclei. Sub-GHz Rabi driving gave $-1$79 MHz at moderate power, corresponding to a $-1$80-pulse of about $-1$81 ns, and coherent oscillations at $-1$82 GHz were observed at three times that power (Nakamura et al., 30 Apr 2026).

Using those pulses, Ramsey interference and Hahn echo gave

$-1$83

The measured values were $-1$84 ns with Gaussian-like decay, and $-1$85 ns with stretch factor $-1$86 (Nakamura et al., 30 Apr 2026). The same work attributed the short $-1$87 primarily to strong inhomogeneous hyperfine fields from nearby $-1$88B and $-1$89N spins, and emphasized that sub-GHz driving reduces pulse errors that can otherwise distort echo-based coherence estimates.

Longitudinal relaxation has been mapped over a much wider field and temperature range. Measurements of $-1$90 from $-1$91 to $-1$92 K and fields up to $-1$93 T revealed three regimes. At low temperature and low field, $-1$94 K and $-1$95 T, the decay is stretched exponential with $-1$96, consistent with spin-spin interactions and disorder; at $-1$97 K and $-1$98 T, $-1$99. At fields above about $800$00 T and $800$01 K, the relaxation rate follows an approximately direct-process scaling

$800$02

with $800$03. At $800$04 K, the relaxation becomes nearly field-independent and follows

$800$05

A combined model used

$800$06

with a spin-bath correlation time $800$07 ps (Solanki et al., 22 Jul 2025).

Defect density also affects $800$08. In CVD-grown hBN irradiated with He$800$09, all-optical measurements at room temperature gave $800$10s at low $800$11 density and less than $800$12s at high density. The transverse splitting $800$13 increased from about $800$14 MHz at low dose to about $800$15 MHz at the highest dose, indicating that dense irradiation also strengthens static disorder or local symmetry breaking (Vlassiouk et al., 24 Mar 2025).

First-principles many-body simulations further predict a field-driven crossover in Hahn-echo decoherence. Below a transition boundary $800$16, decoherence is dominated by independent nuclear-spin dynamics and occurs within submicrosecond timescales; above $800$17, pairwise flip-flop processes dominate and the coherence time reaches tens of microseconds. The predicted transition boundaries are $800$18 G for $800$19-$800$20B$800$21N and $800$22 G for $800$23-$800$24B$800$25N, in excellent agreement with the numerical results in that study (Lee et al., 6 May 2025). This suggests that magnetic field and isotopic composition jointly determine whether the dense nuclear environment acts primarily through single-spin modulation or pairwise dynamics.

6. Photophysics, emission engineering, heterostructures, and sensing modalities

The intrinsic optical signature of $800$26 is a broad photoluminescence band centered near $800$27 nm, with strong electron-phonon coupling and no easily resolved room-temperature zero-phonon line in uncoupled ensemble measurements (Gale et al., 2023, Qian et al., 2022). Coupling to a high-$800$28 Si$800$29N$800$30 nanobeam cavity revealed the room-temperature zero-phonon line at $800$31 nm and showed a maximum cavity-enhanced ZPL intensity increase of $800$32 at the field antinode, consistent with Purcell-enhanced redistribution of the emission (Qian et al., 2022).

The defect’s weak brightness has motivated several enhancement strategies. In a low-loss plasmonic nano-patch antenna, the raw intensity enhancement averaged over the laser spot was about $800$33, while the enhancement localized to the nano-patch region was calculated to be about $800$34. The ODMR contrast was preserved, increasing from about $800$35 on bare SiO$800$36/Si to about $800$37 in the antenna, with linewidth $800$38 MHz unchanged, and a continuous-wave ODMR sensitivity of about $800$39 nT/$800$40 was estimated at $800$41W laser power (Xu et al., 2022).

A van der Waals sensitizer strategy has also been demonstrated. In hBN–PbI$800$42 heterostructures, $800$43 photoluminescence was enhanced by $800$44–$800$45, depending on temperature and excitation, while ODMR contrast remained roughly preserved. Under $800$46 nm excitation the PL count rate increased by about $800$47, under $800$48 nm excitation by about $800$49, and the reported magnetic sensitivity improved by about $800$50 and $800$51, respectively, with a best-case $800$52 at $800$53W (Mayner et al., 2 Feb 2026). That work attributed the enhancement to type-I band alignment, efficient fluorescence resonance energy transfer, and a DFT-predicted photon-ratcheting mechanism with minimal hybridization of the spin defect states.

Mechanical deformation can produce a different kind of enhancement. Suspended regions of hBN exhibited photoluminescence up to $800$54 brighter than substrate-supported regions, while ODMR contrast, linewidth, and spin lifetime were well preserved. In the bright suspended regions, the measured $800$55 was $800$56s, compared with $800$57s in darker supported regions. The increase in brightness correlated with larger local deformation, increased zero-field splitting $800$58, appearance of the deformation-activated $800$59 Raman peak near $800$60 cm$800$61, and shifts in Kelvin-probe surface potential (Geng et al., 31 Aug 2025).

At the same time, proximity to other 2D materials does not necessarily quench the optical readout. A quantitative FRET study found that for hBN sensing layers thicker than approximately $800$62 nm, photoluminescence quenching by monolayer graphene is negligible, with $800$63, meaning $800$64. Below about $800$65 nm, the FRET rate increases rapidly, and at $800$66 nm a quenching factor $800$67 was observed. By simultaneously fitting thickness-dependent photoluminescence and lifetime data, that study extracted an intrinsic radiative rate

$800$68

corresponding to an intrinsic radiative lifetime $800$69s, and concluded that $800$70 is unusually tolerant of integration into ultrathin van der Waals heterostructures because of its intrinsically low quantum yield (Jules et al., 3 Dec 2025). The same work directly verified that $800$71 nm hBN on MoS$800$72 showed no lifetime shortening, whereas MoTe$800$73 did quench the defect photoluminescence, consistent with band-gap-controlled acceptor behavior (Jules et al., 3 Dec 2025).

These optical and spin properties motivate multiple sensing modes. High ODMR contrast in both ground and excited states, strong temperature dependence of $800$74, and sensitivity of $800$75 to in-plane strain support magnetic, thermal, and strain sensing (Mathur et al., 2021). At high magnetic fields up to $800$76 T, the ground-state splitting reaches approximately $800$77 GHz, which has been proposed as a route to sub-terahertz sensing through field-dependent $800$78 relaxometry (Solanki et al., 22 Jul 2025). ENDOR measurements of remote nitrogen moments further indicate that $800$79 can serve as a probe of host-lattice nuclear spins in van der Waals materials (Mamin et al., 9 Apr 2025). The two-dimensional host geometry, together with preserved spin functionality near surfaces and in heterostructures, is the recurring basis for its use as a surface-native quantum sensor (Xu et al., 2022, Jules et al., 3 Dec 2025).