spins were decoupled (full-decoupling case). The (red) solid lines are measured spectra, while the grey dots are the calculated ones like in Fig. \[fig\_fid\_th\]. The most left one is the reference without “magnetic field”. The upper spectra are in the cases that “magnetic field”s were applied on CC , while the lower ones on CSs. []{data-label="fig:p_meas"}](pC_pS){width="8.6cm"}

Secondly, we show that the “magnetic field sensing” was affected by “noise” generated by the engineered environment and that the “noise” can be suppressed by a dynamical decoupling technique (XY-8 [@RevModPhys.88.041001]). Experimental details are as follows. We consider two cases: the full-decoupling (Fig. \[fig\_st\](c)) and selective-decoupling case (Fig. \[fig\_st\](b)). In the full-decoupling case, there are only weak direct effects of magnetic impurities on CC and CSs [@Binho2019] and thus we can approximate that “magnetic field sensing” was performed under noiseless environment in the short time scale of less than 50 ms in the experiment. This approximation was confirmed with the fact that the signal did not decay almost at all in this time scale, see Fig. \[fig:sen\_rel\](a). In the selective decoupling case, CSs should be affected by the engineered time-inhomogeneous noisy environment formed by HSs and magnetic impurities. This noisy environment was also confirmed 