Electric-field driven isospin order in Bernal bilayer graphene

The trigonally warped bands of Bernal-stacked bilayer graphene contain saddle points that give rise to divergences in the density of states. The magnitude of these divergences is tunable by an external electric field, providing a direct tuning knob of the density of states in a narrow window of energies. Here, we show that ultraclean samples of bilayer graphene display a cascade of electric-field driven broken-symmetry states with spontaneous spin and valley isospin ordering at zero magnetic field. We tune the carrier density and electric displacement field independently to explore the phase space of isospin order. Itinerant ferromagnetic states emerge near the conduction and valence band edges with complete spin and valley polarization. At larger hole densities, two-fold degenerate quantum oscillations manifest in an additional broken symmetry state that is enhanced by the application of an in-plane magnetic field. Both types of symmetry-broken states display enhanced layer polarization, suggesting a coupling to the layer degree of freedom. These states occur in the absence of a moiré superlattice and are intrinsic to natural graphene bilayers. These results demonstrate that bilayer graphene presents a related but distinct approach to produce interacting behavior from flat electronic dispersion, complementary to engineered moiré structures.