The measurement of vector magnetic fields with high sensitivity and spatial resolution is important for both fundamental science and engineering applications. In particular, magnetic-field sensing with nitrogen-vacancy (NV) centers in diamond is a promising approach that can outperform existing methods. Recent studies have demonstrated vector DC magnetic-field sensing with perfectly aligned NV centers, which showed a higher readout contrast than NV centers having four equally distributed orientations. However, to estimate the azimuthal angle of the target magnetic field with respect to the NV axis in these previous approaches, it is necessary to apply a strong reference DC magnetic field, which can perturb the system to be measured. This is a crucial problem, especially when attempting to measure vector magnetic fields from materials that are sensitive to applied DC magnetic fields. Here, we propose a method to measure vector DC magnetic fields using perfectly aligned NV centers without reference DC magnetic fields. More specifically, we used the direction of linearly polarized microwave fields to induce Rabi oscillation as a reference and estimated the azimuthal angle of the target fields from the Rabi frequency. We further demonstrate the potential of our method to improve sensitivity by using entangled states to overcome the standard quantum limit. Our method of using a reference microwave field is a novel technique for sensitive vector DC magnetic-field sensing.

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