Microwave-free vector magnetometry and crystal orientation determination with Nitrogen-Vacancy centers using Bayesian inference

Nitrogen-vacancy (NV) centers in diamond provide a solid-state platform for quantum sensing. While optically detected magnetic resonance techniques offer high sensitivity, their reliance on microwaves introduces heating and stray electromagnetic fields that can perturb nearby samples. Optical approaches based on cross-relaxation between differently oriented NV centers remove this constraint but have so far required stringent alignment of the external field with crystallographic axes, restricting their practicality. Here we introduce a general framework for microwave-free vector magnetometry at near-zero field that leverages Bayesian inference to extract both the magnetic field vector and the NV orientation directly from photoluminescence maps. An analytical model of cross-relaxation resonances enables efficient inference under arbitrary field and orientation configurations, while naturally incorporating the discrete degeneracies of the NV symmetry. We experimentally demonstrate robust orientation determination and vector-field reconstruction, establishing a general route toward compact and alignment-free NV magnetometers for practical sensing applications.

💡 Research Summary

This paper presents a general, microwave‑free framework for vector magnetometry using nitrogen‑vacancy (NV) centers in diamond, combined with a Bayesian inference scheme that simultaneously determines the external magnetic‑field vector and the crystal orientation from photoluminescence (PL) maps. Conventional NV magnetometers rely on optically detected magnetic resonance (ODMR), which requires microwave (MW) fields to drive spin transitions. While ODMR offers high sensitivity, the presence of MWs introduces heating, electromagnetic interference, and wiring complexity, limiting applicability in cryogenic, biological, or compact‑device contexts.

The authors instead exploit cross‑relaxation (CR) between NV ensembles of different crystallographic orientations. When two inequivalent NV axes i and j satisfy |B·n_i| = |B·n_j|, the Zeeman‑shifted m_s = ±1 levels become degenerate, enabling dipolar flip‑flop processes that accelerate spin relaxation. This enhanced relaxation transfers population from the bright m_s = 0 state to the dark m_s = ±1 manifold, producing a sharp dip in PL intensity. The resonance condition (Eq. 3) defines nine distinct planar surfaces in magnetic‑field space: six symmetry planes (B_sx = ± B_sy, etc.) corresponding to pairwise NV resonances, and three anti‑symmetry planes (B_sx = 0, etc.) where two resonances coincide, yielding deeper PL contrast.

Experimentally, a static external field B_ext (unknown) is combined with a tunable bias field B_bias applied along a laboratory‑frame z‑axis. The diamond sample is rotated about this axis by an angle ϕ, so that the total field in the sample frame is B_s = O_slab · R_z(−ϕ)·(B_ext + B_bias u_z). The PL signal is modeled phenomenologically as

 PL(B_bias, ϕ) = 1 − C ∑_i w_i L