Transmission through correlated ${\text{Cu}}_n\text{Co}{\text{Cu}}_n$ heterostructures

We propose a method to compute the transmission through correlated heterostructures by combining density functional and many-body dynamical mean field theories. The heart of this combination consists in porting the many-body self-energy from an all electron basis into a pseudopotential localized atomic basis set. Using this combination we study the effects of local electronic interactions and finite temperatures on the transmission across the ${\text{Cu}}_4\text{Co}{\text{Cu}}_4$ metallic heterostructure. It is shown that as the electronic correlations are taken into account via a local but dynamic self-energy, the total transmission at the Fermi level gets reduced (predominantly in the minority-spin channel), whereby the spin polarization of the transmission increases. The latter is due to a more significant $d$-electron contribution, as compared to the noncorrelated case in which the transport is dominated by $s$ and $p$ electrons.

Figure 1

Schematic representation of the supercell used in calculations. The length of the cell and the distances between Cu1, Cu2, Cu3, Cu4, and Co are given in the text. The unit cell dimensions of the leads are kept at the relaxed bulk value 3.65 Å. The ABCABC sequence describes the lead periodicity along the 111 direction.

Figure 2

Total (unit cell) and Co density of states computed within the siesta and EMTO technique.

Figure 3

Densities of states calculated by EMTO in relaxed geometries. Dashed black lines: GGA results; solid red lines: GGA+DMFT results. (a) Total DOS per scattered region; (b) local DOS per central Co atom of the heterostructure; (c) local DOS per atomic sphere of the same size in pure fcc bulk cobalt. The values of total and local Co magnetic moments for the scattered region are indicated in (a).

Figure 4

Orbital-resolved DOS for Cu4 in the ${\text{Cu}}_4\text{Co}{\text{Cu}}_4$ heterostructure computed within the GGA (black dashed line) and GGA+DMFT (red solid line) for $U=3$ eV and $J=0.9$ eV.

Figure 5

Left: Spin-resolved transmission: majority spins $T_{\uparrow }$ (upper panel), minority spins $T_{\downarrow }$ (middle panel), and total (lower panel). Black dashed/red solid lines are the GGA/GGA+DMFT results. Right: Transmission spin polarization around the Fermi energy obtained within the GGA (black dashed) and at finite temperatures $T=80$ K (red dot dashed), $T=200$ K (blue solid). The Coulomb and exchange parameters are $U=3$ eV, $J=0.9$ eV.

Figure 6

Transmission for different values of Coulomb parameters: (a) with a fixed ratio $U/J$, (b) fixed $J$, and (c) fixed $U$, at $T=200$ K.

Figure 7

Comparison between the transmission functions obtained for different model forms of $W^{1\zeta ,2\zeta }$.