Rhombohedral graphene multilayers provide a clean and highly reproducible platform to explore the emergence of superconductivity and magnetism in a strongly interacting electron system. Here we reveal a subtle competition between valley-imbalanced orbital ferromagnets and intervalley-coherent states in which electron wavefunctions in the two momentum-space valleys develop a macroscopically coherent relative phase. We focus on a rhombohedral trilayer in the quarter-metal regime—where there is a single Fermi surface that spontaneously breaks spin and valley-isospin symmetry—and employ local magnetometry and global charge sensing techniques. Comparing the in-plane spin susceptibility of the intervalley-coherent and valley-imbalanced phases reveals the influence of graphene’s intrinsic spin–orbit coupling, which drives the emergence of a distinct correlated phase that is their hybrid. Spin–orbit coupling also suppresses the in-plane magnetic susceptibility of the valley-imbalanced phase, allowing us to extract the spin–orbit-coupling strength of approximately 50 μeV for our hexagonal-boron-nitride-encapsulated graphene system. We discuss the implications of a finite spin–orbit coupling on the spin-triplet superconductors observed in both rhombohedral and twisted graphene multilayers.

菱面体石墨烯多层提供了一个干净且高度可重复的平台，用于探索强相互作用电子系统中超导性和磁性的出现。在这里，我们揭示了谷不平衡轨道铁磁体和层间相干态之间的微妙竞争，其中两个动量空间谷中的电子波函数形成宏观相干相对相位。我们专注于四分之一金属体系中的菱面体三层（其中有一个费米表面自发打破自旋和谷同位旋对称性），并采用局部磁力测量和全局电荷传感技术。比较间隔相干相和谷不平衡相的面内自旋敏感性揭示了石墨烯固有的自旋轨道耦合的影响，这推动了作为它们的混合体的独特相关相的出现。自旋轨道耦合还抑制了谷不平衡相的面内磁化率，使我们能够为六方氮化硼封装的石墨烯系统提取大约 50μeV 的自旋轨道耦合强度。我们讨论了有限自旋轨道耦合对在菱面体和扭曲石墨烯多层中观察到的自旋三重态超导体的影响。