ArXiv · 2026
The boron vacancy V_B⁻ in hexagonal boron nitride is a leading two-dimensional spin sensor, but the microscopic connection between nearby charge positions and its spin Hamiltonian remains poorly understood. Calculations for carbon and oxygen donors 3.85–8.08 mathringA away show that direction matters, not only distance. In the frozen lattice, reversing a carbon donor's azimuth at 4.35 mathringA (C1 to C1m) more than halves |E| and turns its axis across the mirror line. The ratio is 0.467 with the Perdew–Burke–Ernzerhof (PBE) functional, against 1 for distance alone. A field-plus-gradient model fitted to six donor configurations, including C1 but excluding C1m, predicted a ratio of 0.443 before C1m was calculated. Heyd–Scuseria–Ernzerhof hybrid statics give 0.432 and PBE relaxation 0.600. Exploratory analysis suggests why direction matters: a charge's potential differs at the three vacancy nitrogens and moves the spin of the two e' holes among them, more when the charge faces one nitrogen than the gap between two. E follows this spin imbalance through one constant, c≈8 GHz per μ_B, across donors and applied fields, whereas in PBE D is nearly insensitive to it. A three-site model with one fitted screening constant reproduces the frozen-lattice E to 83 MHz rms. Results are for one charge state in a free-standing monolayer; absolute |E| varies by tens of percent across approximations.
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