Real-space pseudopotential calculations of spin-dependent electron transport in magnetic molecular junctions

A real-space pseudopotential approach is developed to calculate the spin-dependent transport in nanoscale junctions. Our method is based on self-consistent solution of the Kohn-Sham equation of density functional theory with asymptotic boundary conditions. This method is applied to a simple magnetic molecule, the Sc dimer, bridging nonmagnetic, planar jellium electrodes for a series of molecule-lead spacing. We find that the spin-dependent conductance within this formalism is rather robust over a wide range of electronic coupling parameters. The minority channel of parallel-aligned ${\mathrm{Sc}}_2$ produces a fairly stable conductance of roughly half of a quantum unit $(e^2∕h)$. Other systems show sensitive dependence on the coupling strength. Atomic origins of the dependence are discussed.

Figure 1

Additional density of states due to the presence of a Na atom in the middle of two planar electrodes. The electrodes are represented by semi-infinite jellium contacts with $r_s=2$. The Na-lead distance is given by $D$. The Fermi level is set to zero.

Figure 2

Spin polarization as a function of Na-lead separation for a single Na atom between two planar jellium contacts with $r_s=2$.

Figure 3

Conductance as a function of Na-lead spacing for a single Na atom between the two planar leads. Results from non-spin polarized calculation by Lang (Ref. 18) are the dashed line.

Figure 4

Schematic of a ${\mathrm{Sc}}_2$ in contact with two planar electrodes. $d$ is the bond length between the two atoms. The distance between the lead and the center of the ${\mathrm{Sc}}_2$ molecule is given by $D$.

Figure 5

Conductance as a function of $D$, the molecule-lead spacing, for the ${\mathrm{Sc}}_2$ molecular junction. Results for both parallel and antiparallel spin orientations are shown. Jellium electrodes with $r_s=2.38$ are used. The distance between the two Sc atoms is fixed at $5\mathrm{a.u.}$ The solid lines with diamonds and stars indicate the results for parallel and antiparallel spin alignments, respectively. In the parallel-aligned systems, the dashed line with up triangles represents the majority (spin-up) channel, and the dashed line with down triangles the minority (spin-down) channel.

Figure 6

Transmission per spin channel for the ${\mathrm{Sc}}_2$ molecular junction for (a) majority and (b) minority channels for the case of aligned spins; in (c), transmission for the antiparallel-aligned system is shown. The molecule-lead spacing is given by $D$ in the legend. The Fermi level is set at zero on all plots. Other details are as given in the caption of Fig. 5.

Figure 7

(Color online) Partial density of states projected to molecular orbitals of isolated ${\mathrm{Sc}}_2$. The top panels of (a)–(c) show the energy levels of the isolated ${\mathrm{Sc}}_2$ with an artificially broadened width. Other details are as provided in the Fig. 5 caption.

Figure 8

(Color online) Eigenchannel transmission as a function of energy at $\Gamma (k_{\parallel }=0)$ point for the ${\mathrm{Sc}}_2$ junction.