Bias voltage effects on tunneling magnetoresistance in Fe/${\mathrm{MgAl}}_2{\mathrm{O}}_4/\mathrm{Fe}\left(001\right)$ junctions: Comparative study with Fe/MgO/Fe(001) junctions

We investigate bias voltage effects on the spin-dependent transport properties of Fe/$\mathrm{MgAl}{}_2\mathrm{O}{}_4$/Fe(001) magnetic tunneling junctions (MTJs) by comparing them with those of Fe/MgO/Fe(001) MTJs. By means of the nonequilibrium Green's function method and the density functional theory, we calculate bias voltage dependencies of magnetoresistance (MR) ratios in both the MTJs. We find that in both the MTJs, the MR ratio decreases as the bias voltage increases and finally vanishes at a critical bias voltage $V_{\mathrm{c}}$. We also find that the critical bias voltage $V_{\mathrm{c}}$ of the $\mathrm{MgAl}{}_2\mathrm{O}{}_4$-based MTJ is clearly larger than that of the MgO-based MTJ. Since the in-plane lattice constant of the Fe/$\mathrm{MgAl}{}_2\mathrm{O}{}_4$/Fe(001) supercell is twice that of the Fe/MgO/Fe(001) one, the Fe electrodes in the $\mathrm{MgAl}{}_2\mathrm{O}{}_4$-based MTJs have an identical band structure to that obtained by folding the Fe band structure of the MgO-based MTJs in the Brillouin zone of the in-plane wave vector. We show that such a difference in the Fe band structure is the origin of the difference in the critical bias voltage $V_{\mathrm{c}}$ between the $\mathrm{MgAl}{}_2\mathrm{O}{}_4$- and MgO-based MTJs.

Figure 1

Supercells of (a) Fe(5)/MgO(5)/Fe(5) and (b) Fe(5)/${\mathrm{MgAl}}_2{\mathrm{O}}_4$(9)/Fe(5), optimized by the procedures of Sec. 2.

Figure 2

Majority-spin transmittance at ${\mathbf{k}}_{\parallel }=(0,0)$ in Fe/MgO/Fe(001) MTJs with parallel magnetization of electrodes. (a) The energy dependence of the total transmittance in the [001] direction. (b) The band-resolved transmittance in the [001] direction. At each point of the Fe majority-spin bands in the [001] direction, the logarithmic magnitude of the resolved transmittance is shown as a color in the color palette. In each band, constituent orbitals are listed from largest to smallest contribution. (c) and (d) The same as (a) and (b) for minority-spin channel, respectively. (e) The same as (a) for antiparallel magnetization of electrodes.

Figure 3

The same as Fig. 2 for Fe/${\mathrm{MgAl}}_2{\mathrm{O}}_4$/Fe(001) MTJs.

Figure 4

The bias voltage dependencies of currents in (a) Fe/MgO/Fe(001) and (b) Fe/${\mathrm{MgAl}}_2{\mathrm{O}}_4$/Fe(001) MTJs. The bias voltage dependencies of (c) MR ratios and (d) current polarizations in both the MTJs (see text for details).

Figure 5

Energy dependencies of transmittance integrated over ${\mathbf{k}}_{\parallel }$ in Fe/MgO/Fe(001) MTJs for (a) $V=0.0\mathrm{V}$, (b) $V=0.5\mathrm{V}$, (c) $V=1.0\mathrm{V}$, and (d) $V=1.6\mathrm{V}$. In each panel, the red solid (dashed) curve corresponds to the majority- (minority)-spin transmittance in the case of parallel (P) magnetization of electrodes. The blue solid (dashed) curve represents the majority- (minority)-spin transmittance in the case of antiparallel (AP) magnetization of electrodes. The shaded area represents the integral region for the calculation of the current following Eq. (7).

Figure 6

The same as Fig. 5 for Fe/${\mathrm{MgAl}}_2{\mathrm{O}}_4$/Fe(001) MTJs with (a) $V=0.0\mathrm{V}$, (b) $V=0.5\mathrm{V}$, (c) $V=1.0\mathrm{V}$, and (d) $V=1.9\mathrm{V}$.