Non-equilibrium Green’s Function Methods for Spin Transport and Dynamics

Spin-orbit induced equilibrium spin currents in materials

“…The external potential includes the Hartree and the exchangecorrelation potential, while the Zeeman field includes the exchange correlation magnetic field. We employ the SIESTA package 44 and the SMEAGOL [45][46][47] quantum transport code. They use a linear combination of atomic orbitals basis set {|φ n } n=1,N , where each integer n stands for the atom index, the principal quantum number, the angular momentum quantum number and the magnetic quantum number; N is the total number of basis orbitals.…”

“…In particular, following ref. 47,49 we define the components of S n in terms of the symmetrized Mulliken population…”

“…( 15) by e/ . The bond current method was first introduced within the tight-binding approach for models 48,50,51 and, recently, used in KS-DFT with localized basis orbitals to evaluate spin-transfer torque 47,52 and spin Hall effect 53,54 in nano-devices from first-principles. Bond currents have however no physical meaning per se in KS-DFT calculations.…”

“…To set a reference for the magnitude, we calculate the transport spin-current through an ideal Fe/MgO/Fe magnetic tunnel junction with 4 MgO layers and with the magnetizations of the two Fe electrodes set in the parallel configuration. Notably, an applied bias voltage as large as 4.5 V is required to drive a spin current density of ∼ 10 −8 A/ Å2 through such device 47 , which behaves as an almost perfect spin -filter 67 . Hence, the case of Te indicates that bulk ESCs are by no means small compared to transport spin-currents used in spintronics.…”

Coupling resonance mechanism of interfacial stratification of sandwich plate structures excited by SH waves

“…31–39 Using variational iteration methods, homotopy perturbation methods, integral transformation methods, Green’s function methods, separation of variables methods, and so on, wave equations are solved. 40–53 The analytical model of wave motion in laminates is established with the boundary conditions by stiffness-matrix methods, transfer-matrix methods, and global-matrix methods. 54–59…”