How muons alter spin ice and what they probe

Muons implanted into spin ice sit at a well-defined site that is now determined using DFT+$\mu$ calculations. It is also known [Foronda et al., PRL {\bf 114}, 017602 (2015)) that the muon-induced distortion in Pr-containing pyrochlores leads to a dominating effect on the muon-induced response. We show that the effect in Dy- and Ho-containing systems is quite different, even though the muon site and muon-induced distortions are similar. By using further DFT+$\mu$ calculations and in experiments on Dy$_2$Ti$_2$O$_7$, Ho$_2$Ti$_2$O$_7$, as well as Sc-doped samples, we show that this picture can be understood quantitatively and allows us to understand the relationship between the muon-induced response and the magnetic properties. We assess the extent to which muon measurements in these systems can be sensitive to monopole behaviour.