Electric coupling in scanning SQUID measurements

Scanning SQUID is a local magnetometer which can image flux through its pickup loop due to DC magnetic fields ($\Phi$). Scanning SQUID can also measure a sample's magnetic response to an applied current ($d\Phi/dI$) or voltage ($d\Phi/dV$) using standard lock-in techniques. In this manuscript, we demonstrate that electric coupling between the scanning SQUID and a back gate-tuned, magnetic sample can lead to a gate-voltage dependent artifact when imaging $d\Phi/dI$ or $d\Phi/dV$. The electric coupling artifact results in $d\Phi/dV$ and $d\Phi/dI$ images which mimic the spatial variation of the static magnetic fields from the sample (e.g. ferromagnetic domains). In back-gated $EuS/Bi_2Se_3$ bilayers, we show that the electric coupling effect is important, and is responsible for the reported signal from chiral currents in Y.H. Wang, et al. (DOI: 10.1126/science.aaa0508). Previous scanning SQUID current imaging experiments are unaffected by this artifact, as they are either on non-magnetic samples or the spatial distribution of magnetism does not match the features observed in $d\Phi/dI$. In conclusion, $d\Phi/dI$ or $d\Phi/dV$ imaging of magnetic, back-gated samples should only be applied and interpreted with great caution.