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Purpose This study aims to fabricate and manipulate ensemble spin of negative nitrogen-vacancy (NV−) centres optimally for future solid atomic magnetometers/gyroscope. Parameters for sample preparation most related to magnetometers/gyroscope are, in particular, the concentration and homogeneity of the NV− centres, the parameters’ microwave antenna of resonance frequency and the strength of the microwave on NV− centres. Besides, the abundance of other impurities such as neutral NV centres (NV0) and substitutional nitrogen in the lattice also plays a critical role in magnetic sensing. Design/methodology/approach The authors succeeded in fabricating the assembly of NV centres in diamond and they determined its concentration of (2-3) × 1016 cm−3 with irradiation followed by annealing under a high temperature condition. They explored a novel magnetic resonance approach to detect the weak magnetic fields that takes advantage of the solid-state electron ensemble spin of NV− centres in diamond. In particular, the authors set up a magnetic sensor on the basis of the assembly of NV centres. They succeeded in fabricating the assembly of NV centres in diamond and determined its concentration. They also clarified the magnetic field intensity measured at different positions along the antenna with different lengths, and they found the optimal position where the signal of the magnetic field reaches the maximum. Findings The authors mainly reported preparation, initialization, manipulation and measurement of the ensemble spin of the NV centres in diamond using optical excitation and microwave radiation methods with variation of the external magnetic field. They determined the optimal parameters of irradiation and annealing to generate the ensemble NV centres, and a concentration of NV− centres as high as 1016 cm−3 in diamond was obtained. In addition, they found that sensitivity of the magnetometer using this method can reach as low as 5.22 µT/Hz currently. Practical implications This research can shed light on the development of an atomic magnetometer and a gyroscope on the basis of the ensemble spin of NV centres in diamond. Social implications High concentration spin of NV− in diamond is one of the advantages compared with that of the atomic vapor cells, because it can obtain a higher concentration. When increasing the spin concentration, the spin signal is easy to detect, and macro-atomic spin magnetometer become possible. This research is the first step for solid atomic magnetometers with high spin density and high sensitivity potentially with further optimization. It has a wide range of applications from fundamental physics tests, sensor applications and navigation to detection of NMR signals. Originality/value As has been pointed out, in this research, the authors mainly worked on fabricating NV− centres with high concentration (1015-1016 cm−3) in diamond by using optimal irradiation and annealing processes, and they quantitatively defined the NV− concentration, which is important for the design of higher concentration processes in the magnetometer and gyroscope. Until now, few groups can directly define the NV− concentration. Besides, the authors optimized the microwave antenna parameters experimentally and explored the dependence between the splitting of the magnetic resonance and the magnetic fields, which dictated the minimum detectable magnetic field.

In this paper, the potential sensitivity in Kelvin probe force microscopy (KPFM) was investigated in frequency modulation (FM) and heterodyne amplitude modulation (AM) modes. We showed theoretically that the minimum detectable contact potential difference (CPD) in FM-KPFM is higher than in heterodyne AM-KPFM. We experimentally confirmed that the signal-to-noise ratio in FM-KPFM is lower than that in heterodyne AM-KPFM, which is due to the higher minimum detectable CPD dependence in FM-KPFM. We also compared the corrugations in the local contact potential difference on the surface of Ge (001), which shows atomic resolution in heterodyne AM-KPFM. In contrast, atomic resolution cannot be obtained in FM-KPFM under the same experimental conditions. The higher potential resolution in heterodyne AM-KPFM was attributed to the lower crosstalk and higher potential sensitivity between topographic and potential measurements.