Indirect Spin Exchange Coupling Between Magnetic Impurities In 2D Materials

We study theoretically the long-range Ruderman-Kittel-Kasuya-Yosida(RKKY)interactions in two-dimensional hexagonal lattices with Rashba spin-orbit coupling and intrinsic spin-orbit coupling induced by the proximity coupling effect of magnetic materials utilizing the Green's function technique.Since Rashba spin-orbit coupling could induce crystalline structural inversion asymmetry,we find that the RKKY interaction consists of not only the well-known Heisenberg,Ising,and DzyaloshinskiiMoira(DM)terms reported previously in topological insulators and topological semimetals but also an additional DM-like in-plane spin-spin interaction.With the Fermi energy residing in the bandgap induced by the intrinsic spin-orbit coupling,the RKKY interaction degenerates to the Bloembergen-Rowland(BR)interaction.The BR interaction is not the long range oscillatory decayed interaction like the RKKY interaction,but a short range exponentially-decay interaction.The content and structure of this paper are as follows:In chapter 1,the origin of magnetism in two-dimensional materials and the development and fundamental mechanism of anomalous Hall effect are introduced.In the last section,we explain the significance of this thesis.In chapter 2,we introduce the tight-binding method about how to construct the low energy effective Hamiltonian,and we apply it to construct the Hamiltonian of a twodimensional hexagonal graphene lattice.We also give the derivation of the Rashba spinorbit Hamiltonian.In chapter 3,we derive the Hamiltonian of contacted s-d interaction between electron and local magnetic moment in detail,and the RKKY interaction in two-dimensional and three-dimensional electron gas by the second order perturbation theory of quantum mechanics.The general expressions of RKKY interaction is expressed by using green's function technique in the second quantization representation.In chapter 4,the RKKY interaction on hexagonal graphene lattice with Rashba spinorbit interaction and intrinsic spin-orbit interaction induced by proximity effect was calculated by field theoretical approach.The integral expressions of different types of interaction are numerically calculated and carefully analyzed.At last,we discuss the BR interaction with virtual carriers.The effect of RKKY interaction degenerate to the BR interaction on anomalous hall effect on graphene proximity coupled to an antiferromagnetic insulator are discussed.And the explanation of the origin of the DM interaction between ferromagnet and graphene interface.In chapter 5,we briefly summarize the content of our thesis,and discuss the potential applications of RKKY interaction in quantum information and quantum computing.