Monopole-limited nucleation of magnetism in Eu$_{2}$Ir$_{2}$O$_{7}$

We present an in-depth analysis of muon-spin spectroscopy measurements of Eu$_{2}$Ir$_{2}$O$_{7}$ under the effect of the Eu$_{1-x}$Bi$_{x}$ isovalent and diamagnetic substitution as well as of external pressure. Our results evidence an anomalously slow increase of the magnetic volume fraction upon decreasing temperature only for stoichiometric Eu$_{2}$Ir$_{2}$O$_{7}$, pointing towards highly unconventional properties of the magnetic phase developing therein. We argue that magnetism in Eu$_{2}$Ir$_{2}$O$_{7}$ develops based on the nucleation of magnetic droplets at $T_{N}$, whose successive growth is limited by the need of a continuous generation of magnetic hedgehog monopoles.