  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.
