Magnetometry by cross-relaxation-resonance detection in ensembles of nitrogen-vacancy centers

We study cross-relaxation-based magnetometry in ensembles of nitrogen-vacancy (NV) centers using the protocol suggested by Akhmedzhanov et al. [R. Akhmedzhanov, L. Gushchin, N. Nizov, V. Nizov, D. Sobgayda, I. Zelensky, and P. Hemmer, Microwave-free magnetometry based on cross-relaxation resonances in diamond nitrogen-vacancy centers, Phys. Rev. A 96, 013806 (2017)]. We suggest a processing scheme that allows us to perform measurements without precise sample orientation. It is shown theoretically and experimentally that using an additional magnetic field can significantly simplify vector magnetic-field measurements.