Bias field-free resolution of symmetry-induced ambiguity in ensemble NV magnetometry via orthogonal rotations

Ensemble nitrogen-vacancy (NV) centers enable vector magnetic-field sensing, but the tetrahedral symmetry of the four NV orientations renders the field direction intrinsically ambiguous in ensemble optically detected magnetic resonance (ODMR) measurements. For a fixed field magnitude, up to 48 symmetry-related orientations can produce identical spectra. Here, we introduce a double-rotation protocol that resolves this symmetry-induced ambiguity without applying bias magnetic fields or other symmetry-breaking perturbations. By comparing reconstructed field directions obtained from ODMR spectra before and after two controlled rigid rotations about orthogonal axes, the protocol geometrically restricts the solution space to a unique angular region up to the intrinsic inversion symmetry B↔−B. The method is purely geometric and independent of the specific magnetic-field reconstruction algorithm. It is particularly suited for moderate magnetic fields (from a few millitesla to a few tens of millitesla) and for experimental situations where additional bias fields would perturb the magnetic system under investigation.