Ramsey Envelope Modulation in NV Diamond Magnetometry*

Nitrogen-vacancy (NV) ensembles in diamond offer promising applications in magnetic sensing and imaging, including studies of biological, geological and solid-state systems. The recent development of high-purity ¹⁵N-doped CVD diamond (Ι = 1/2) offers advantages over the naturally occurring ¹⁴N isotope (I = 1) for magnetometry. However, the lack of a quadruple moment in ¹⁵N-doped diamond leads to pronounced envelope modulation effects in sensing modalities that require a misaligned bias magnetic field. While such effects in spin echo experiments have been well studied, discussion of analogous effects in Ramsey measurements and the implications for magnetometry remain under-explored. We derive the modulated Ramsey response and compare to experimental results, revealing significant beating and sensitivity loss if left unaddressed. Double-quantum coherences that utilize the full spin-1 ground state system can suppress these modulations, while additionally proving robust to local strain and temperature shifts.