Ballistic conductance of magnetic Co and Ni nanowires with ultrasoft pseudopotentials

The scattering-based approach for calculating the ballistic conductance of open quantum systems is generalized to deal with magnetic transition metals as described by ultrasoft pseudopotentials. As an application we present quantum-mechanical conductance calculations for monatomic Co and Ni nanowires with a magnetization reversal. We find that in both Co and Ni nanowires, at the Fermi energy, the conductance of $d$ electrons is blocked by a magnetization reversal, while the $s$ states (one per spin) are perfectly transmitted. $d$ electrons have a nonvanishing transmission in a small energy window below the Fermi level. Here, transmission is larger in Ni than in Co.

Figure 1

Transmission coefficient for a monatomic Al wire with a H atom adsorbed on the side. The corresponding result of Ref. 9 and the transmission coefficient of the perfect infinite wire are shown by a dotted and a dashed line, respectively.

Figure 2

The transmission coefficient for the seven-atom carbon chain between two finite cross-section Al electrodes with the electrode-chain separation $D=1.0\mathrm{\AA }$. The dashed line shows the corresponding result obtained with a localized basis set (Ref. 6).

Figure 3

The transmission coefficient for the four-atom carbon chain between two finite cross-section Al electrodes as in Fig. 2 but with an electrode-chain separation $D=1.9\mathrm{\AA }$. The dashed line shows the corresponding result obtained with a localized basis set (Ref. 7).

Figure 4

Complex band structure of a monatomic Co nanowire for the majority (spin up) and minority (spin down) states. Real bands, complex bands with $\mathrm{Re}k=0$, and $\pi ∕a$ are plotted in the middle, left, and right panels, respectively. Each band is labeled by its main atomic character. The total energy and the magnetic moment per atom as a function of interatomic spacing are shown on the left and right insets, respectively.

Figure 5

The planar average of the magnetization along the Co nanowire.

Figure 6

Transmission coefficients for the spin down electron incident from the left on a magnetization reversal in a monatomic Co nanowire: (a) total transmission (solid curve) and contributions from each band; (b) eigenchannel transmissions $T_i$. The corresponding data for a monatomic Ni nanowire are shown on the insets. The bands and conductance channels are labeled by their main atomic character. The Fermi energy is chosen to be zero (dashed vertical lines).