Half and quarter metals in rhombohedral trilayer graphene

TL;DR

This paper demonstrates that rhombohedral trilayer graphene exhibits gate-tuned ferromagnetic phases, including half- and quarter-metal states, driven by van Hove singularities and interactions, with implications for understanding itinerant magnetism in moiré materials.

Contribution

It reveals the phase diagram of ferromagnetism in rhombohedral trilayer graphene, including novel half- and quarter-metal phases, and shows their robustness against moiré superlattice effects.

Findings

Identification of spin- and valley-polarized phases via capacitance measurements

Observation of phase transitions with negative electronic compressibility

Detection of topologically nontrivial gapped states at superlattice fillings

Abstract

Ferromagnetism is most common in transition metal compounds but may also arise in low-density two-dimensional electron systems, with signatures observed in silicon, III-V semiconductor systems, and graphene moir\'e heterostructures. Here we show that gate-tuned van Hove singularities in rhombohedral trilayer graphene drive the spontaneous ferromagnetic polarization of the electron system into one or more spin- and valley flavors. Using capacitance measurements on graphite-gated van der Waals heterostructures, we find a cascade of density- and electronic displacement field tuned phase transitions marked by negative electronic compressibility. The transitions define the boundaries between phases where quantum oscillations have either four-fold, two-fold, or one-fold degeneracy, associated with a spin and valley degenerate normal metal, spin-polarized `half-metal', and spin and valley polarized `quarter metal', respectively. For electron doping, the salient features are well captured by a phenomenological Stoner model with a valley-anisotropic Hund's coupling, likely arising from interactions at the lattice scale. For hole filling, we observe a richer phase diagram featuring a delicate interplay of broken symmetries and transitions in the Fermi surface topology. Finally, by rotational alignment of a hexagonal boron nitride substrate to induce a moir\'e superlattice, we find that the superlattice perturbs the preexisting isospin order only weakly, leaving the basic phase diagram intact while catalyzing the formation of topologically nontrivial gapped states whenever itinerant half- or quarter metal states occur at half- or quarter superlattice band filling. Our results show that rhombohedral trilayer graphene is an ideal platform for well-controlled tests of many-body theory and reveal magnetism in moir\'e materials to be fundamentally itinerant in nature.