Unconventional Metallic Magnetism: Non-analyticity and Sign-changing Behavior of Orbital Magnetization in ABC Trilayer Graphene

We study an unique form of metallic ferromagnetism in which orbital moments surpasses the role of spin moments in shaping the overall magnetization. This system emerges naturally upon doping a topologically non-trivial Chern band in the recently identified quarter metal phase of rhombohedral trilayer graphene. Our comprehensive scan of the density-interlayer potential parameter space reveals an unexpected landscape of orbital magnetization marked by two sign changes and a line of singularities. The sign change originates from an intense Berry curvature concentrated close to the band-edge, and the singularity arises from a topological Lifshitz transition that transform a simply connected Fermi sea into an annular Fermi sea. Importantly, these variations occur while the groundstate order-parameter (i.e. valley and spin polarization) remains unchanged. This unconventional relationship between the order parameter and magnetization markedly contrasts traditional spin ferromagnets, where spin magnetization is simply proportional to the groundstate spin polarization via the gyromagnetic ratio. We compute energy and magnetization curves as functions of collective valley rotation to shed light on magnetization dynamics and to expand the Stoner-Wohlfarth magnetization reversal model. We provide predictions on the magnetic coercive field that can be readily tested in experiments. Our results challenge established perceptions of magnetism, emphasising the important role of orbital moments in two-dimensional materials such as graphene and transition metal dichalcogenides, and in turn, expand our understanding and potential manipulation of magnetic behaviors in these systems.