Patent Document ID: 8082130
Application ID: 12015133
Patent Flag: 1

Claim One:
1. A method for calculating spin polarized quantum transport in a 3-dimensional nanoelectronic device under non-equilibrium conditions at finite bias voltage, comprising the steps of: a) determining parameter of an atomic structure and electronic states at non-equilibrium of the device by self-consistently obtaining an Hamiltonian H of the device using density function theory (DFT) within a standard local spin density approximation for open device structures using a calculator; b) evaluating a non-equilibrium density matrix for different spin channels of the device using Keldysh non equilibrium Green's functions in spin space; c) sampling a transverse momentum of the Brillouin zone for contribution of each transverse Bloch state in directions perpendicular to the current flow for converging the density matrix; and d) calculating spin-dependent transmission coefficients from the Green's functions, wherein calculating the spin-dependent transmission coefficients from Green's functions is calculated as: T σ (E, V b )=Σk x , k y T σ kx.ky (E, V b ), where T Tσ kx,ky ≡Tr[Im(Σ r L)G r Im(Σ r R)G a ] is a transverse momentum resolved transmission coefficient; and obtaining spin-polarized charge current as: I σ (V b )=e/h∫ μR μL T σ (E,V b )[f L (E−μ L )−f R (E−μ R )]dE where μ R,L is an electrochemical potential of the left/right leads and μ L −μ R =eV b ; f L,R (E−μ R,L ) are Fermi functions; wherein said transverse momentum sampling allows obtaining bulk and surface magnetism of magnetic materials serving as electrodes for the device.