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

We investigate bias voltage effects on the spin-dependent transport properties of Fe/MgAl${}_2$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 dependences 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 $V_{\rm c}$. We also find that the critical bias voltage $V_{\rm c}$ of the MgAl${}_2$O${}_4$-based MTJ is clearly larger than that of the MgO-based MTJ. Since the in-plane lattice constant of the Fe/MgAl${}_2$O${}_4$/Fe(001) supercell is twice that of the Fe/MgO/Fe(001) one, the Fe electrodes in the MgAl${}_2$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 $V_{\rm c}$ between the MgAl${}_2$O${}_4$- and MgO-based MTJs.