Effects of Spin-Orbit Coupling on Magnetic States in Magic-Angle Graphene

Abstract

Magic-angle graphene (MAG), formed by twisting two graphene layers at ~1.1°, hosts flat moiré bands that dramatically enhance electron-electron interactions, enabling strongly correlated phenomena such as superconductivity, Mott-like insulating states, and magnetism. The introduction of spin-orbit coupling (SOC), particularly via proximity to transition metal dichalcogenides like WSe₂, profoundly modifies these correlated states. SOC breaks native time-reversal (C₂T) symmetry, induces valley polarization, and enables spin-valley locking, which selectively stabilizes electrons in specific moiré lattice valleys (K or K′). This interplay between SOC and electron correlations drives orbital ferromagnetism, stabilizes magnetic order at both integer and non-integer moiré fillings, and produces a robust anomalous Hall effect (AHE), with hysteretic Rₓᵧ signaling broken time-reversal symmetry and finite Berry curvature. The SOC-induced Rashba and Ising-type interactions lift spin degeneracy, create topologically non-trivial quasi-flat bands, and enable control over magnetic anisotropy via in-plane and out-of-plane fields, including abrupt magnetization sign reversals near half-filling (ν = ±2). These modifications compete with and often suppress superconductivity, while also interacting with Landau levels under perpendicular magnetic fields, leading to complex band reconstructions. The system thus becomes a versatile platform for exploring topology, magnetism, superconductivity, and valleytronics, offering pathways to electrically tunable quantum phases and potential spintronic applications.