Microscopic Theory of Magnetic SU(4) Spin-Valley Domain Walls in Rhombohedral Multilayer Graphene

Rhombohedrally stacked multilayer graphene encapsulated in dual-gated devices hosts flat band edges and tunable Berry curvature, providing an ideal platform for realizing spin-valley ferromagnetism. Several competing magnetic phases have been identified, including the valley-imbalanced orbital ferromagnet, the spin-polarized ferromagnet, and the inter-valley coherent state, whose stability are strongly influenced by spin-orbit coupling and other small energy scales. We develop a microscopic theory of magnetic domain walls in these SU(4) spin-valley ordered phases. Our theory explains how the distinct spatial structures of spin-valley textures depend on magnetic anisotropy energies such as Hund's coupling and spin-orbit coupling. The reconstructed band structure across domain walls provides microscopic insight into electron-domain wall interactions and how they influence transport properties across the domain wall. Our theory provide a foundation to generalize the long-wavelength Landau-Lifshitz dynamics in spintronics to correlated magnetic states with coupled spin and valley degrees of freedom.