Spin Coupling By Conduction Electrons Explored By Double Time Green's Functions

Abstract

The impurities containing unfilled d or f shells may have localized magnetic moments in nonmagnetic metals, semiconductors, and superconductors under certain conditions. These localized moments interact with each other through the spin polarization field of conduction electrons. The indirect coupling between magnetic impurities is referred to as the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction which is important in describing the magnetic and thermodynamic properties of magnetic nanostructures. The interaction may be expressed as a long range oscillatory function. I explored the properties of the indirect exchange interaction between localized moments in different dimensions using the s-d model and the Green's functions method. An effective Hamiltonian for the indirect interaction is obtained in terms of a Green's function using a canonical transformation applied to the s-d exchange model. The equation of motion for the Green's function has been solved by using a Hartree-Fock approximation to truncate higher order Green's functions. The asymptotic form of the indirect spin-spin interaction for large distances R for both polarized and unpolarized conduction electrons has been explored using the theory of generalized functions. The Green's function technique is justified as the three dimensional Hamiltonian is modified by a screened Coulomb potential that is Yukawa-like in nature.