Extended Data Fig. 8: Spatial studies of flux trapping in S2.

We compare the effects of zero field cooling (ZFC) and field cooling (FC) at several spatial points in sample S2 [fluorescence scan in the inset of (d)]: two locations [blue and red points in inset of (d)] on top of the CeH₉ region and one ___location [yellow point in inset of (d)] away from this region. (a-c) We field cool the sample at H_z = 79 G to a temperature T = 36 K and measure the ODMR spectra (dark blue) after quenching the external field to H_z = 0 G. Light blue data show the ODMR spectra measured at the respective spatial locations upon zero field cooling to temperatures (a,b) T = 36 K, and (c) T = 86 K. We see markedly higher splittings on top of the CeH₉ region (a,b) upon field cooling indicating the presence of a flux trapped field. Away from the CeH₉ region (c), we do not observe a significant difference between ZFC and FC data. In particular, Δ for the ZFC spectrum (measured at T = 86 K) is larger by 7 MHz; this difference is likely due to temperature dependence of the stress splitting, 2Π_⊥, at this spatial point. (d-f) Following the field quench after FC, we determine the local B_z field at the three spatial locations on ramping H_z to positive values (green data points). We make the same measurements on ramping H_z to negative values (orange data points). We also measure B_z as a function of H_z after zero field cooling (blue data points). (d,e) On top of the CeH₉ region, our measurements indicate the presence of a flux trapped field upon FC. This contrasts with a local suppression of H_z measured at the same locations upon ZFC. In particular, the slope s = ΔB_z/ΔH_z on field cooling is in quantitative agreement with the slope on zero field cooling. (f) Away from CeH₉ region, we see no significant difference in response on ramping H_z after FC and ZFC. To extract B_z at each point, we use the 2Π_⊥ splitting measured upon zero field cooling at the respective spatial ___location [light blue spectra in (a-c)].