Density-Functional Approximation for the Spin Dependent Quantum Transport in Magnetic Nanostructures

Abstract

In quasi‐classical theoretical framework, the transport of electrons and holes in semiconductor devices is treated with the Boltzmann transport equation (BTE) or quantum‐mechanical energy band theory—viz., the effective mass approximation and the random phase approximation. On the other hand, in the mesoscopic, nanoelectronic devices, for three‐ and lower‐ dimensional structures with nanometer scaling, the wave properties, spin, charge and the interactions between spin and charge of electrons are fully utilized such as in artificial mini‐Brillouin zones, quantum size effects, Coulomb blockade of single‐electron tunneling and spin‐polarized giant magnetoresistance (GMR) tunneling. The complexity associated with the classical quantum‐mechanical formalism in the study of transport in magnetic nanostructures can be avoided by applying the so‐called, Hohenberg‐Kohn’s density functional theory. Because of the limitations of quasi‐classical theory, it is more appropriate to treat the magneto‐transport problem in nanostructures by using quantum many‐body theory. The starting point of the quantum trans‐port theory is to take an external field as a perturbation for the many‐particle system in equilibrium. This leads to a linear response and gives corresponding transport coefficients. One useful application of the Green’s function techniques in quantum magneto‐transport is to convert a homogeneous differential equation into an integral equation, viz., as in the time‐dependent Schrödinger equation. We have applied it to scattering of nanostructural defects (impurities) in the electron gas (metal) as many‐body effect’s model and derived an expression for its residual resistivity. Calculations of magnetic impurities in noble‐metal hosts are in good agreement with the previously published results.