RKKY Interaction Mediated By Spin-Orbit Coupled Electrons

The RKKY interaction mediated by Rashba spin-orbit Coupling electrons in one-and two-dimensions was theoretically studied in this thesis. First we reviewed the related research field named Spintronics. Spintronics is a new branch of condensed matter physics. It mainly involves Giant Magnetoresistance (GMR) and semiconductors Spintronics. GMR was discovered by Fert's group in 1988. After that, the spin-related phenomena becomes a hot topic. Parkin also Discovered the phenomena that the magnetoresistance could change with the thickness of the non-magnetic(NM) interlayers of Cr and Cu. This is because that the exchange coupling interaction of the magnetic interlayers can change from NM to ferromagnet. To study it, people proposed a few theoretical models such as RKKY, free electrons and Anderson models. About tunneling magnetoresistance (TMR), Slonczewski proposed that the tunnel conductance was related to the magnetization direction of the two magnetic electrodes. Then Julliere observed the tunneling magnetoresistance of magnetic tunnel valve. Presently, the investigation of TMR has gone into practical application, so we can use it to develop MRAM and disk write head. About semiconductors Spintronics, we have mainly reviewed that spin injection, spin transport and spin-orbit interaction.The RKKY interaction is an indirect exchange interaction between two localized spins via the spin polarization of conduction electrons. The theory of RKKY was first proposed by Ruderman , Kittel , Kasuya and Yosida . In recent years, it was applied to different systems with different methods. Such as, N.F. Schwabe et al. employed the Keldysh nonequilibrium perturbation formalism to study the RKKY interaction between two magnetic s-d spin impurities across a tunneling junction when the system was driven out of equilibrium through biasing the junction. They derived a general nonequilibrium solution for the RKKY interaction for various dimensionalities and arrangements of spins within this structured system. In 1998, V.K. Dugave et al. introduced a method of one-loop diagram in one and two dimensions for calculating the RKKY interaction. The method can handle correctly the nonanalytical behavior of the integrand in the range function in the one-dimensional electron gas. In 2004, C.H. Ziener et al. studied the RKKY theory for Semiconductors, and they derived the RKKY interaction by means of both perturbation theory and Kubo theory. Then it was showed that the equivalence was obtained and they derived the effective RKKY Hamiltonian for low-dimensional semiconductors. In 2004, H. Imamura et al. used the method of Green's function for studying the RKKY interaction in one- and two- dimensions in presence of the Rashba spin-orbit coupling. They showed that a twisted RKKY interaction between localized spins due to the Rashba spin-orbit coupling. However they got this result in two dimensional in the limit situation qFr>>1.In this thesis, a method for treatment of the Rashba spin-orbit coupling in RKKY theory was presented, and we derived the RKKY interaction mediated by one- and two-dimensional spin-orbit coupled electrons. Our treatment is based on taking the eigenfunctions of the single-particle Rashba Hamiltonian as the basis of the second quantization. The obtained RKKY interaction between two localized spins consists of three different terms: Heisenberg interaction in 2D, Dzyaloshinsky-Moriya interaction, and Ising interaction in 1D. This provides a basis to study magnetic property in the related systems.