Spin-orbit coupling-induced magnetic phases in the rhombohedral trilayer graphene.

We study the effect of proximity-induced intrinsic and Rashba spin-orbit coupling on the magnetic phase diagram of rhombohedral trilayer graphene (RTG). The magnetic phase diagram of RTG is calculated in the parametric space of an external electric field and the electron doping level for several sets of spin-orbit coupling parameters corresponding to the proximity effect of real substrates. In our calculations, RTG without spin-orbit coupling has two magnetic phases, such as interlayer antiferromagnetic ordering or intervalley antiferromagnetic ordering. It has been found that the introduction of a spin-orbit coupling into RTG significantly affects its magnetic phase diagram. Spin-orbit coupling causes splitting between magnetic phases into phases with out-of-plane or in-plane spin ordering. Finally, we calculated the dependence of the RTG magnetic ordering at a fixed level of electron doping and an external electric field on the amplitude of intrinsic spin-orbit coupling. We discuss a possibility of a significant modification of the RTG magnetic ordering by the design of the van der Waals heterostructure and proximity-induced spin-orbit coupling.