Magneto-optical imaging of stepwise magnetic domain disintegration at characteristic temperatures in Eu B 6

Prior to the onset of the ferromagnetic transition in semimetallic $\mathrm{Eu}{\mathrm{B}}_{6}$, 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 $\mathrm{Eu}{\mathrm{B}}_{6}$ 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 a modified Arrott's plot analysis of isothermal bulk magnetization data, we determine the critical exponents $\ensuremath{\beta}=0.22\ifmmode\pm\else\textpm\fi{}0.01,\ensuremath{\gamma}=0.88\ifmmode\pm\else\textpm\fi{}0.05$ and $\ensuremath{\delta}=5.0\ifmmode\pm\else\textpm\fi{}0.1$ and a $\mathrm{critical}\phantom{\rule{0.16em}{0ex}}\mathrm{transition}\phantom{\rule{0.16em}{0ex}}\mathrm{temperature}=12.0\ifmmode\pm\else\textpm\fi{}0.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, 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. Deep inside the ferromagnetic state at $T$ below ${T}_{c2}$, we observe the presence of large magnetized domains along with the observation of Barkhausen-like jumps in local magnetization. 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.