Electronic transport through EuO spin-filter tunnel junctions

Epitaxial spin-filter tunnel junctions based on the ferromagnetic semiconductor europium monoxide (EuO) are investigated by means of density functional theory. In particular, we focus on the spin transport properties of Cu(100)/EuO(100)/Cu(100) junctions. The dependence of the transmission coefficient and the current-voltage curves on the interface spacing and EuO thickness is explained in terms of the EuO density of states and the complex band structure. Furthermore, we also discuss the relation between the spin transport properties and the Cu-EuO interface geometry. The level alignment of the junction is sensitively affected by the interface spacing, since this determines the charge transfer between EuO and the Cu electrodes. Our calculations indicate that EuO epitaxially grown on Cu can act as a perfect spin filter, with a spin polarization of the current close to 100$\%$, and with both the Eu-5$d$ conduction-band and the Eu-4$f$ valence-band states contributing to the coherent transport. For epitaxial EuO on Cu, a symmetry filtering is observed, with the ${\Delta }_1$ states dominating the transmission. This leads to a transport gap larger than the fundamental EuO band gap. Importantly, the high spin polarization of the current is preserved up to large bias voltages.

Figure 1

Lattice structure of EuO constructed with (a) the primitive fcc unit cell and (b) the tetragonal unit cell. The shaded gray atoms indicate the full cubic cell. Atom code: large spheres (blue) $=$ Eu, small spheres (red) $=$ O.

Figure 2

Supercell used for the spin-filter tunnel junction. This consists of six Cu MLs (left lead), nine Eu MLs (scattering region), and five Cu MLs (right lead). Atom code: large spheres (blue) $=$ Eu, medium spheres (brown) $=$ Cu, small spheres (red) $=$ O.

Figure 3

LDA$+U$ band structure of EuO for the primitive fcc unit cell [see Fig. 1a]. Left panel: majority-spin bands; right panel: minority-spin bands. The band structure shows an indirect band gap from $\Gamma$ to $X$ of about 1.0 eV. Note that the line $\Gamma$-$X^{\prime }$ contains the same information as the line $\Gamma$-$X$.

Figure 4

EuO density of states projected over the following atomic orbitals: O-2$p$, Eu-6$s$, Eu-5$d$, and Eu-4$f$.

Figure 5

LDA$+U$ band structure of EuO for the primitive tetragonal unit cell [see Fig. 1b], with majority-spin bands in the left panel and minority-spin bands in the right panel. Due to the doubled size unit cell, compared to the primitive fcc one, a band down-folding makes the $\Gamma$ point and the fcc $X^{\prime }$ point equivalent. This leads to a direct gap at $\Gamma$.

Figure 6

Complex band structure of EuO in its tetragonal cell [see Fig. 1b], where the symmetries are indicated for the bands relevant to our transport setup. Red lines $=$ minority spins, black lines $=$ majority spins.

Figure 7

PDOS for Cu, O, and Eu for a junction comprising nine MLs EuO. The PDOS is calculated at (a) the center of the junction and (b) the interface for $d=2.4$ Å, and at (c) the center of the junction and (d) the interface for $d=2.8$ Å. Here, $d$ is the distance between the Cu and the EuO planes at the EuO/Cu interface.

Figure 8

Transmission coefficient of a Cu/EuO/Cu junction formed by nine EuO MLs for $d=2.4$ Å and $d=2.8$ Å, plotted on a (a) linear and a (b) logarithmic scale. Note that for $d=2.8$ Å, $T\left(E\right)$ shifts to higher energy when compared to the case of $d=2.4$ Å.

Figure 9

Transmission coefficient for a Cu/EuO/Cu junction with a nine MLs EuO barrier and with different interface geometries: (a) $d=2.4$ Å and (b) $d=2.8$ Å. The solid lines represent the majority-spin transmission, whereas the dashed ones are for minority spins. Note that overall the transmission depends little on the lateral position of the O atoms with respect to the Cu surface.

Figure 10

Thickness dependence of $T\left(E\right)$ at zero bias for (a) $d=2.4$ Å and (b) $d=2.8$ Å. The solid and dashed lines refer to the majority and minority spins, respectively. At $d=2.4$ Å, the tunneling gap of the majority spins is found from $-0.45$ to 1.0 eV, while for the minority ones it extends from $-2.5$ to 1.6 eV. At $d=2.8$ Å, the tunneling gaps of the majority and minority spins for all thicknesses range between $-0.1$ to 1.75 eV and $-2.3$ to 2.5 eV, respectively.

Figure 11

Damping coefficient $\kappa$ calculated from $T\left(E\right)$ for the (a),(b) majority and (c),(d) minority spins at $d=2.4$ Å and $d=2.8$ Å. $\kappa$ is calculated from Eq. (3) by using the transmission coefficient calculated for nine and 11 EuO MLs. The solid lines refer to the total transmissions and the dashed lines refer to the transmissions at $k_x=k_y=0$ only. The green lines show $\mathrm{Im}\left[k_z\right]$ from Fig. 6, which is also calculated for $k_x=k_y=0$.

Figure 12

Dependence of $T\left(E_F\right)$ on $t$ for (a) $d=2.4$ Å and (b) $d=2.8$ Å. (c) The spin-filtering efficiency at $E_F$ for both values of $d$.

Figure 13

Spin-polarized current and spin polarization as functions of the bias voltage for different EuO thicknesses. (a1) Majority-spin current at $d=2.4$ Å, (a2) majority-spin current at $d=2.8$ Å, (b1) minority-spin current at $d=2.4$ Å, (b2) minority-spin current at $d=2.8$ Å, (c1) spin polarization at $d=2.4$ Å, and (c2) spin polarization at $d=2.8$ Å.

Figure 14

Total current and differential conductance for a Cu/EuO/Cu junction with a nine EuO MLs barrier at $d=2.4$ and $2.8$ Å with different interface geometries. (a1) Current at $d=2.4$ Å, (a2) current at $d=2.8$ Å, (b1) conductance at $2.4$ Å, and (b2) conductance at $2.8$ Å.