Real-space imaging and flux noise spectroscopy of magnetic dynamics in Ho$_2$Ti$_2$O$_7$

Holmium titanate (Ho$_2$Ti$_2$O$_7$) is a rare earth pyrochlore and a canonical example of a classical spin ice material. Despite the success of magnetic monopole models, a full understanding of the energetics and relaxation rates in this material has remained elusive, while recent studies have shown that defects play a central role in the magnetic dynamics. We used a scanning superconducting quantum interference device (SQUID) microscope to study the spatial and temporal magnetic fluctuations in three regions with different defect densities from a Ho$_2$Ti$_2$O$_7$ single crystal as a function of temperature. We found that the magnetic flux noise power spectra are not determined by simple thermally-activated behavior and observed evidence of magnetic screening that is qualitatively consistent with Debye-like screening due to a dilute gas of low-mobility magnetic monopoles. This work establishes magnetic flux spectroscopy as a powerful tool for studying materials with complex magnetic dynamics, including frustrated correlated spin systems.