Figure 1

Atomic structure of $\mathrm{Fe}/\mathrm{MgO}/\mathrm{Fe}$ junction with a 13-layer MgO barrier. Blue spheres, Fe; red spheres, O; green spheres, Mg; white spheres, oxygen vacancy. The junction is periodically extended in the transverse directions. The numbers label MgO layers from the left to the right.Reuse & Permissions

Figure 2

(a),(b) Conductance versus OV concentration $x$ at equilibrium for spin-up and -down (insets) channels in PC (a) and AP  (b). Layer 1 of MgO is fixed with 3% OV; layer 13 with $x\%$. Green up-triangles, total conductance; red squares, coherent part; black circles, vertex correction part. (c) TMR versus $x$ for several MTJs. Red squares, for symmetric junctions with $x\%$ OV at both layers 1 and 13. Black circles, for asymmetric junctions with 3% OV on layer 1 and $x\%$ on layer 13. Green stars, same disorder distribution as the black circles but for a junction having 7-layer MgO barrier. Inset: Log-10 scaled resistance versus number of disordered MgO layers ($3,3–43–4–5,3–4–5–6,\dots .$) for spin-up channel in PC: green squares are for 3% OV; black up-triangles for 5%. (d) TMR versus $x$ for a 13-layer junction where interfacial OVs are filled by nitrogen atoms; namely, $x\%$ nitrogen atoms replace oxygen atoms on the 1st and 13th MgO layer. Inset: TMR versus $x$ for a junction with 3% OV on both layer 1 and layer 13, at the same time $x\%$ OV on layer 7.Reuse & Permissions

Figure 3

$k_{\parallel }$ resolved transmission coefficient $T=T(E_f,k_x,k_y)$ in two-dimensional BZ for coherent and vertex parts of the spin-up and -down channels in PC and APC, for a junction with 3% OV on both layers 1 and 13. Here $E_f$ is the Fermi energy of the Fe electrodes. (a)–(d) PC, (e),(f) APC. (a),(c),(e),(g) Spin-up channel, (b),(d),(f),(h) spin-down channel. (a),(b),(e),(f) Coherent part [1st term of Eq. (2)], (c),(d),(g),(h) vertex correction part [2nd term of Eq. (2)].Reuse & Permissions

Figure 4

TMR versus bias voltage for a 7-layer $\mathrm{Fe}/\mathrm{MgO}/\mathrm{Fe}$ MTJ. (a) Perfect junction without OV. (b) Junction with 3% OV on the interfacial layers 1 and 7 MgO.Reuse & Permissions