Erratum: Current-induced order parameter dynamics: Microscopic theory applied toCo∕Cu∕Cospin valves [Phys. Rev. B76, 024404 (2007)]

Implementation of a nonequilibrium Green’s function method to calculate spin-transfer torque

“…We find excellent agreement with Ref. 5 and a GMR ratio (g(0 Fig. 3 shows the in-plane torque τ and the out-of-plane torque τ ⊥ as a function of the angle θ for two different k point samples.…”

“…In linear response, the spin torque τ per current I on layer i can be expressed by (see Haney et al 5 )…”

“…For this purpose, we use the same structure used in Ref. 5 consisting of a semi-infinite Co, 9 monolayers Cu, 15 monolayers Co, and semi-infinite Cu. The lattice constant is 0.361 nm.…”

Multiscale approach to spin transport in magnetic multilayers

“…(6). This approach has been applied with good success with ab-initio calculations of FN interfaces [30][31][32]67 .…”

“…Many different approaches have been developed, ranging from purely quantum 16,17 to semi-classical Boltzmann equation [18][19][20] , (generalized) circuit theory [21][22][23][24][25][26][27] or Random Matrix Theory (RMT) 28,29 or full ab-initio (density functional theory) calculations [30][31][32][33] . A good understanding has now been reached of the respective domains of applicability and links between the various approaches 26,29 .…”