First-principles investigation of spin-polarized conductance in atomic carbon wires

We analyze spin-dependent energetics and conductance for one-dimensional (1D) atomic carbon wires consisting of terminal magnetic (Co) and interior nonmagnetic (C) atoms sandwiched between gold electrodes, obtained by employing first-principles gradient-corrected density functional theory and Landauer’s formalism for conductance. Wires containing an even number of carbon atoms are found to be acetylenic with $\sigma \text{−}\pi$ bonding patterns, while cumulene structures are seen in wires containing an odd number of carbon atoms as a result of strong $\pi$ conjugation. In the case of even C-atom wires, the antiparallel Co spin state remains the ground state up to 12 carbon atoms. For odd C-wire systems, the antiparallel spin configuration between the two terminal Co atoms remains the ground state irrespective of the number of C atoms in the wire. The 14-carbon atom wire is seen to have a parallel Co spin configuration in the ground state. The stability of the antiferromagnetic state in the wires is ascribed to the superexchange effect. For the cumulenic wires, this effect is constant for all wire lengths. For the acetylenic wires, the superexchange effect diminishes as the wire length increases, with the exception of the wire containing two carbon atoms. The superexchange characteristic length in acetylenic C wires is found to be $\sim 20\mathrm{\AA }$. Conductance calculations at the zero-bias limit show spin-valve behavior, the parallel Co spin-configuration state giving higher conductance than the corresponding antiparallel state, and a nonmonotonic variation of conductance with the length of the wires for both spin configurations.

Figure 1

(Color online) Schematic of the bonding pattern in a carbon wire containing (a) 11 and (b) 12 carbon atoms. Terminal black spheres are cobalt atoms and gray spheres are carbons. All the optimized bond distances are indicated for both parallel (ferromagnetic) and antiparallel (antiferromagnetic) spin configurations of the atomic carbon wire.

Figure 2

The energy difference $[\Delta E=E(\uparrow \uparrow )-E(\uparrow \downarrow )]$ between parallel and antiparallel spin configurations in carbon atom wires, as a function of the number of carbon atoms in the wire, $n$. Even $n$ chains are connected with a dashed line and odd $n$ chains are connected with a solid line. Values for $n=1–5$ carbon atoms are taken from Ref. 14.

Figure 3

Atomic spin density of the terminal Co atoms for both parallel and antiparallel Co spin configurations, shown as a function of the number of carbon atoms in the wire, $n$.

Figure 4

Conductance (in units of $e^2∕h$) evaluated at the Fermi energy for both parallel (ferromagnetic) and antiparallel (antiferromagnetic) spin configurations in the carbon wires, as a function of the number of carbon atoms in the wires, $n$.

Figure 5

Dependence of magnetoconductance (MC), Eq. (4), on the number of carbon atoms in the atomic wire, $n$.