  Prior to the onset of the ferromagnetic transition in semimetallic EuB_6,
unusual magnetic and electric behavior have been reported. Using a highly
sensitive magneto-optical imaging (MOI) technique, we visualize the behavior of
magnetic domains in a EuB_6 single crystal.The transformation from a
paramagnetic to a ferromagnetic state is shown to be non-Curie Weiss like and
proceeds via multiple breaks in the curvature of the temperature-dependent
local magnetization. From our experiments, we identify three characteristic
boundaries, T^*(H),T^*_c1(H) and T_c2(H),in a field - temperature magnetic
phase diagram.Using scaling and Modified Arrott plot analysis of isothermal
bulk magnetization data, we determine the critical exponents $\beta$ = 0.22
$\pm$ 0.01, $\gamma$ = 0.88 $\pm$ 0.05 and $\delta$= 5.0 $\pm$ 0.1 and a
critical transition temperature = 12.0 $\pm$ 0.2 K which is found to be equal
to T_c2. The critical exponents are close to those associated with the
universality class of tricritical mean field model. The absence of a model with
which the exponents correspond with directly, suggests the presence of large
critical fluctuations in this system. The critical fluctuations in this system
are sensitive to the applied magnetic field, which leads to field dependence of
boundaries in the magnetic phase diagram. With increasing T the magnetic
domains disintegrate into finger-like patterns before fragmenting into disjoint
magnetized puddles at T^*_c1 and ultimately disappearing at T*. At T^*_c1 we
observe a significant increase in the spatial inhomogeneity of the local
magnetic field distribution associated with the magnetic domain structure
disintegrating into smaller magnetized structures. We explain our results via
the formation of magnetic polaronic clusters and their coalescing into larger
domains.
