  EuB6 has for a long time captured the attention of the physics community, as
it shows a ferromagnetic phase transition leading to a insulator the metal
transition together with colossal magnetoresistance (CMR). EuB6 has a very low
carrier density, which is known to drastically change the interaction between
the localized Eu moments and the conduction electrons. One of early triumphs of
the quantum theory in condensed matter was the presence of Fermi surface, which
is intimately linked to the symmetry of the underlying crystal lattice. This
symmetry can be probed by angle resolved magnetoresistance (AMRO) measurements.
Here, we present angle resolved magnetoresistance (AMRO) measurements that show
a that in EuB6 this symmetry is broken, possibly indicating the presence of a
quantum nematic phase. We identify the region in the temperature-magnetic field
phase diagram where the magnetoresistance shows two-fold oscillations instead
of the expected fourfold pattern. Quantum nematic phases are analogous to
classical liquid crystals. Like liquid crystals, which break the rotational
symmetry of space, their quantum analogs break the point-group symmetry of the
crystal due to strong electron-electron interactions, as in quantum Hall
states, Sr3Ru2O7, and high temperature superconductors. This is the same region
where magnetic polarons were previously observed, suggesting that they drive
the nematicity in EuB6. This is also the region of the phase diagram where EuB6
shows a colossal magnetoresistance (CMR). This novel interplay between magnetic
and electronic properties could thus be harnessed for spintronic applications.
