Enhanced Magnetoresistance under Bias Voltage in $\mathrm{Fe}$/$\mathrm{Mg}\mathrm{O}$/${\mathrm{Mg}\mathrm{Al}}_2{\mathrm{O}}_4$/$\mathrm{Mg}\mathrm{O}$/$\mathrm{Fe}$ Trilayer Tunneling Barrier Junction

Experiments on magnetic tunnel junctions (MTJs) show that the use of a (001)-oriented spinel ${\mathrm{Mg}\mathrm{Al}}_2{\mathrm{O}}_4$ barrier improves the robustness of the tunneling magnetoresistance (TMR) ratio against bias voltage [Sukegawa et al., Appl. Phys. Lett. 96, 212505 (2010)]; however, the maximum TMR ratio is very small compared with that of the $\mathrm{Mg}\mathrm{O}$-based MTJ. To overcome this problem, we propose a MTJ with a trilayered tunnel-barrier junction, $\mathrm{Fe}$/$\mathrm{Mg}\mathrm{O}$/${\mathrm{Mg}\mathrm{Al}}_2{\mathrm{O}}_4$/$\mathrm{Mg}\mathrm{O}$/$\mathrm{Fe}$, from first-principles calculations. The presence of the $\mathrm{Mg}\mathrm{O}$ interlayer between $\mathrm{Fe}$ and ${\mathrm{Mg}\mathrm{Al}}_2{\mathrm{O}}_4$ has the effect of enhancing the TMR ratio to more than $1000\mathrm{\%}$ at zero bias. The large TMR is maintained under a bias voltage. The results indicate the potential of a hybrid-type tunnel barrier that combines the advantages of MTJs containing a single $\mathrm{Mg}\mathrm{O}$ barrier (high TMR) and a single ${\mathrm{Mg}\mathrm{Al}}_2{\mathrm{O}}_4$ barrier (robustness to bias voltages). The $\mathrm{Mg}\mathrm{O}$ interlayer is found to play a key role in suppressing the transmittance of the minority-spin channel, and thus, the tunneling conductance of antiparallel magnetization is significantly reduced.

Figure 1

Geometry of the $\mathrm{Fe}$/$\mathrm{Mg}\mathrm{O}$/${\mathrm{Mg}\mathrm{Al}}_2{\mathrm{O}}_4$/$\mathrm{Mg}\mathrm{O}$/$\mathrm{Fe}$ MTJ with the 3-ML $\mathrm{Mg}\mathrm{O}$ interlayer inserted at the $\mathrm{Fe}$/${\mathrm{Mg}\mathrm{Al}}_2{\mathrm{O}}_4$ interface (scattering region) as an example. Balls represent $\mathrm{Fe}$ (gray), $\mathrm{Mg}$ (magenta), $\mathrm{Al}$ (blue), and $\mathrm{O}$ (white).

Figure 2

Transmittance spectra for ${\mathbf{k}}_{\parallel }$ space in the $\mathrm{Mg}\mathrm{O}$-inserted MTJ for (a) majority- and (b) minority-spin states of P magnetization and (c) AP magnetization.

Figure 3

Transmittance profiles as a function of energy, $T(E)$, at $\mathrm{\Gamma }$ for (a) $\mathrm{Mg}\mathrm{O}$-inserted and (b) pristine MTJs. Red (solid) and orange (dashed) lines represent the majority- and minority-spin states for P, and blue (solid) and sky-blue (dashed) lines represent the majority- and minority-spin states for AP. Filled area ($-0.9$ to $0.1\mathrm{eV}$) corresponds to the energy region in which steplike $T(E)$ profiles exist for P (minority spin) and AP (majority and minority spins). (For the AP state, the spin channels and majority- and minority-spin states are defined for electrons incident from the left $\mathrm{Fe}$ electrode; i.e., the former refers to the tunnel from the majority spin of the left electrode to the minority spin of the right electrode, whereas the latter refers to the tunnel from the minority spin of the left electrode to the majority spin of the right electrode.) Illustrations of tunnel processes at the Fermi level for (c) $\mathrm{Mg}\mathrm{O}$-inserted and (d) pristine MTJs. Solid arrows indicate dominant tunneling, while dashed arrows indicate blocked tunneling in a specific barrier region or less dominant tunneling.

Figure 4

Illustrations of BZs and band-folding effect for (a) ${\mathrm{Mg}\mathrm{Al}}_2{\mathrm{O}}_4$, (b) $\mathrm{Mg}\mathrm{O}$, and (c) $\mathrm{Fe}$ in bulk states (see text). Band structures along the conductive direction ($\mathrm{\Gamma }\to Z$) for (d) ${\mathrm{Mg}\mathrm{Al}}_2{\mathrm{O}}_4$ given by $1\times 1$ cell and (e) $\mathrm{Mg}\mathrm{O}$ given by $2\times 2$ supercell, where right panel shows real part of $k_z$ and left panel shows imaginary part of it, i.e., decay rate $\kappa$. Electronic structures for $\mathrm{Fe}$, $2\times 2$ supercell, projected on the ${\mathrm{\Delta }}_1$ state for (f) majority- and (g) minority-spin states. Left panel shows the band structure along $\mathrm{\Gamma }$–$Z$ path [$Z$ corresponds to $(0,0,1/2)$] and right panel shows the corresponding DOS projections onto $s$, $p_z$, and $d_{z^2}$ orbitals. Fermi energy is set to zero. In (e)–(g), label FB indicates bands being folded from ${\mathrm{\Gamma }}^{\prime }\to Z^{\prime }$ path, and those of ${\mathrm{\Delta }}_{1,\mathrm{Fe}}$ and ${\mathrm{\Delta }}_{1,\mathrm{F}{\mathrm{e}}_{\mathrm{FB}}}$ are explained in the text.

Figure 5

TMR ratios as a function of applied bias voltage for $\mathrm{Mg}\mathrm{O}$-inserted (blue) and pristine (orange) MTJs. Arrows indicate $V_c$ and $V_{\mathrm{half}}$ for each MTJ model.

Figure 6

(a) $I$–$V$ and (b) $dI/dV$ curves for the $\mathrm{Mg}\mathrm{O}$-inserted MTJ. (c),(d) Same as (a),(b) for the pristine MTJ. Solid (open) circles represent P (AP) magnetization. Vertical dashed line indicates $V_c$ for each model.

Figure 7

Transmittance profile as a function of energy calculated at $\mathrm{\Gamma }$ under finite bias voltage for the $\mathrm{Mg}\mathrm{O}$-inserted MTJ: (a) $V=0.2$, (b) 0.6, (c) 1.0, (d) 1.2, (e) 1.4, (f) 1.6, (g) 1.8, and (h) 2.0 V. Energy region to be integrated in Eq. (1) is shown as the filled area, referred to as the bias window. Arrows indicate the peak $T(E)$ of the minority-spin state in the AP state (see text). $V_c$ corresponds to (d) $V_{\mathrm{bias}}=1.2\mathrm{V}$. Notation is the same as in Figs. 3 and 3.

Figure 8

Top views of four models of $\mathrm{Mg}\mathrm{O}$ on the ${\mathrm{Mg}\mathrm{Al}}_2{\mathrm{O}}_4$ surface: (a) hollow, (b) on-top, (c) bridge-1, and (d) bridge-2 configurations. Large (white), medium (magenta), and small (blue) circles represent $\mathrm{O}$, $\mathrm{Mg}$, and $\mathrm{Al}$, respectively, for ${\mathrm{Mg}\mathrm{Al}}_2{\mathrm{O}}_4$; square (gray) and cross (light magenta) marks represent $\mathrm{O}$ and $\mathrm{Mg}$, respectively, for $\mathrm{Mg}\mathrm{O}$. Solid diamond (orange) in (c) shows the $\mathrm{O}$ anions of $\mathrm{Mg}\mathrm{O}$ at the cation-bridge site of $\mathrm{Al}$–c-$V$, and the solid and dashed diamonds in (d) show $\mathrm{O}$ at the cation-bridge sites of $\mathrm{Al}$–$\mathrm{Al}$ and c-$V$–c-$V$ (see the text for details).

Figure 9

Relaxed interfacial structures of $\mathrm{Fe}$/$\mathrm{Mg}\mathrm{O}$/${\mathrm{Mg}\mathrm{Al}}_2{\mathrm{O}}_4$, where $\mathrm{O}$ of $\mathrm{Mg}\mathrm{O}$ is located at the (a) hollow, (b) on-top, (c) bridge-1, and (d) bridge-2 sites. Atoms are represented by balls in different colors, as shown in Fig. 1.