Possible quantum nematic phase in a colossal magnetoresistance material

$\mathrm{Eu}{\mathrm{B}}₆$ 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). $\mathrm{Eu}{\mathrm{B}}₆$ has a very low carrier density, which is known to drastically change the interaction between the localised 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 dependent magnetoresistance oscillations (AMRO) measurements. Here, we present AMRO measurements that show that in $\mathrm{Eu}{\mathrm{B}}₆$ 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 twofold 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, ${\mathrm{Sr}}₃{\mathrm{Ru}}₂{\mathrm{O}}₇$, and high-temperature superconductors. This is the same region where magnetic polarons were previously observed, suggesting that they drive the nematicity in $\mathrm{Eu}{\mathrm{B}}₆$. This is also the region of the phase diagram where $\mathrm{Eu}{\mathrm{B}}₆$ shows a colossal magnetoresistance (CMR). This novel interplay between magnetic and electronic properties could thus be harnessed for spintronic applications.