The impact of proximity-induced spin-orbit and exchange coupling on the correlated phase diagram of rhombohedral trilayer graphene (RTG) is investigated theoretically. By employing ab initio-fitted effective models of RTG encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ (exchange proximity effect), we incorporate the Coulomb interactions within the random-phase approximation to explore potential correlated phases at different displacement fields and doping. We find a rich spectrum of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin-orbit proximity effects, such as the emergence of a spin-valley-coherent phase due to the presence of valley-Zeeman coupling. Similarly, proximity exchange removes the phase degeneracies by biasing the spin direction, enabling a magnetocorrelation effect—strong sensitivity of the correlated phases to the relative magnetization orientations (parallel or antiparallel) of the encapsulating ferromagnetic layers.

中文翻译：

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邻近自旋轨道和交换耦合诱导菱面体三层石墨烯中的新兴相关相

从理论上研究了邻近诱导的自旋轨道和交换耦合对菱形三层石墨烯（RTG）相关相图的影响。通过采用从头算拟合的过渡金属二硫化物（自旋轨道邻近效应）和铁磁封装的 RTG 有效模型${铬}_2{锗}_2{碲}_6$（交换邻近效应），我们将库仑相互作用纳入随机相位近似中，以探索不同位移场和掺杂下的潜在相关相位。我们发现了由自旋轨道邻近效应引起的丰富的自旋谷解析的斯托纳和谷间相干不稳定性谱，例如由于谷-塞曼耦合的存在而出现的自旋谷相干相。类似地，邻近交换通过偏置自旋方向来消除相位简并，从而实现磁相关效应——相关相位对封装铁磁层的相对磁化方向（平行或反平行）具有很强的敏感性。