  We theoretically study the tunnel magnetoresistance (TMR) effect in
(111)-oriented magnetic tunnel junctions (MTJs) with SrTiO$_{3}$ barriers,
Co/SrTiO$_{3}$/Co(111) and Ni/SrTiO$_{3}$/Ni(111). Our analysis combining the
first-principles calculation and the Landauer formula shows that the Co-based
MTJ has a high TMR ratio over 500%, while the Ni-based MTJ has a smaller value
(290%). Since the in-plane lattice periodicity of SrTiO$_{3}$ is about twice
that of the primitive cell of fcc Co (Ni), the original bands of Co (Ni) are
folded in the $k_x$-$k_y$ plane corresponding to the $ab$ plane of the MTJ
supercell. We find that this band folding gives a half-metallic band structure
in the $\Lambda_1$ state of Co (Ni) and the coherent tunneling of such a
half-metallic $\Lambda_1$ state yields a high TMR ratio. We also reveal that
the difference in the TMR ratio between the Co- and Ni-based MTJs can be
understood by different $s$-orbital weights in the $\Lambda_1$ band at the
Fermi level.
