Resonant electronic states and $I\text{−}V$ curves of Fe/MgO/Fe(100) tunnel junctions

The bias dependence of the tunnel magnetoresistance (TMR) of Fe/MgO/Fe tunnel junctions is investigated theoretically with a fully self-consistent scheme that combines the nonequilibrium Green’s-function method with density-functional theory. At voltages smaller than 20 mV the $I\text{−}V$ characteristics and the TMR are dominated by resonant transport through narrow interface states in the minority-spin band. In the parallel configuration this contribution is quenched by a voltage comparable to the energy width of the interface state, whereas it persists at all voltages in the antiparallel configuration. At higher bias the transport is mainly determined by the relative positions of the ${\Delta }_1$ band edges in the two Fe electrodes, which causes a decrease in the TMR.

Figure 1

(Color online) (a) Planar average $\Delta V_H$ of the difference between the Hartree potential at 0.5 V and the one at zero bias. (b) Planar average $\Delta \rho$ of the difference between the charge density at 0.5 V and the one at zero bias. The diamonds and dots indicate the location of the Fe and MgO layers.

Figure 2

(Color online) Transmission coefficient $T\left(E;V\right)$ as a function of energy $E$ and for different biases $V$. The vertical lines are placed at $E=E_F\pm eV/2$ and enclose the bias window. The dashed (solid) line is for the $\uparrow$ $(\downarrow )$ spin band in the P configuration, while the dashed-dotted line is for the AP configuration. The lowest panel is $T\left(E;0\right)$ for the AP configuration and different broadening $\delta$.

Figure 3

(Color online) (a) Bulk Fe band structure along the $\Gamma \to H$ direction (the bands with ${\Delta }_1$ symmetry are emphasized), (b) $T\left(E;0\right)$ in the P configuration, (c) average number of channels per ${\mathbf{k}}_{\perp }$ point for bulk Fe, $n_c$, (d) bulk Fe DOS, and (e) interface Fe-layer DOS. Note that the ${\Delta }_1$ band edges coincide with a sharp increase in the transmission coefficient $T\left(E;0\right)$ and with a large $n_c$.

Figure 4

(Color online) Schematic representation of the bias dependence of surface states localized at the interfaces between the magnetic electrodes and the tunnel barrier. (a) and (b) are for the left (L) and right (R) interface states having the same energy and therefore resonating at $V=0$; (c) and (d) are for the L and R interface states not resonating at zero bias.

Figure 5

(Color online) Spin-polarized current $I$ as function of voltage $V$ for (a) P and (b) AP alignments. Dashed lines are for the $\uparrow$ current and solid lines are for the $\downarrow$ current.

Figure 6

(Color online) Current $I$, $S\left(V\right)$, and TMR as functions of voltage $V$ for different values of the imaginary part of the energy $\delta$: (a) $I\text{−}V$ for P, (b) $I\text{−}V$ for AP, (c) $S\left(V\right)$ for P, (d) $S\left(V\right)$ for AP, and (e) TMR. In the inset of panel (e) we show the TMR in the low-bias region for $\delta =0$.