Figure 4

Magnetic field dependence. a) Internal quality factor \(Q_{i}\) as a function of in-plane field amplitude \(B_{\parallel }\). A dip is observed at a field \(B_{s}\) which is attributed to resonant paramagnetic impurities. b) \(B_{s}\) extracted from data similar to the one shown in a) for different resonators as a function of resonance frequency \(\omega _{r}\). The solid lines are fits to \(B_{s}=\hbar \omega _{r}/g_{s}\mu _{B}\) from which we extract the Landé g-factor \(g_{s}\) given in Table 2. c) Internal quality factor \(Q_{i}\) as a function of out-of-plane field. The field B is applied with an angle of 49^∘ with respect to the substrate and the perpendicular component \(B_{\perp}\) is indicated. Once again a dip is observed around \(B=hf_{r}/2\mu _{B}\), being less pronounced for the resonator fabricated on intrinsic silicon. c) Relative frequency shift \(\delta f_{r}=f_{r}(B_{\perp})-f_{r}(0)\) as a function of out-of-plane field component \(B_{\perp}\). The solid lines are fits to Eq. (4). In all sub-figures, the color encodes the dielectric configuration according to Fig. 1b)