  Interactions among charge carriers in graphene can lead to the spontaneous
breaking of multiple degeneracies. When increasing the number of graphene
layers following rhombohedral stacking, the dominant role of Coulomb
interactions becomes pronounced due to the significant reduction in kinetic
energy. In this study, we employ phonon-polariton assisted near-field infrared
imaging to determine the stacking orders of tetralayer graphene devices.
Through quantum transport measurements, we observe a range of spontaneous
broken-symmetry states and their transitions, which can be finely tuned by
carrier density n and electric displacement field D. Specifically, we observe a
layer antiferromagnetic insulator at n = D = 0 with a gap of approximately 15
meV. Increasing D allows for a continuous phase transition from a layer
antiferromagnetic insulator to a layer polarized insulator. By simultaneously
tuning n and D, we observe isospin polarized metals, including
spin-valley-polarized and spin-polarized metals. These transitions are
associated with changes in Fermi surface topology and are consistent with the
Stoner criteria. Our findings highlight the efficient fabrication of specially
stacked multilayer graphene devices and demonstrate that crystalline multilayer
graphene is an ideal platform for investigating a wide range of broken
symmetries driven by Coulomb interactions.
