  We report results of the first muon-spin rotation measurements performed on
the low carrier density ferromagnet EuB$_6$. The ferromagnetic state is reached
via two magnetic transitions at $T_{\rm m}=16.5$ K and $T_{\rm c}=12.6$ K. Two
distinct components are resolved in the muon data, one oscillatory and one
non-oscillatory, which arise from different types of magnetic environment, and
we have followed the temperature dependence of these components in detail.
These results provide evidence for magnetic phase separation and can be
interpreted in terms of the gradual coalescing of magnetic polarons.
