Spin-Valley Magnetic Anisotropy in Ferromagnetic Metals of Rhombohedral Multilayer Graphene

Recent experiments have uncovered strongly correlated phases including unconventional ferromagnetism, fractional Chern insulator, and superconductivity in lightly-doped rhombohedral multilayer graphene. Notably, Han. et al. (arXiv:2408.15233) reported superconductivity emerging from a parent state with broken orbital time-reversal symmetry and exhibits strong anomalous Hall effect. In this work, we investigate the magnetic anisotropy energy landscape in such generalized ferromagnetic metals within multilayer graphene.

The order parameter space of these ferromagnetic metals is described by the 15 generators of the SU(4) group which arises from the tensor product of valley (τ) and spin (s) subspace. Using a restricted Hartree-Fock approximation with Lagrange multipliers, we explore the magnetic anisotropy energy landscape in this 15-dimensional space. In addition to mapping the anisotropic energy landscape, we also study the energy required to excite generalized spin and valley ferromagnetic Bloch domain wall. Our analysis reveals the nature of low-energy excitations at finite temperatures and provides an estimate of the ferromagnetic critical temperature. We also discuss the relationship between these low lying excitations and the recently observed chiral superconductor (arXiv:2408.15233).