  Motivated by recent experimental development, we investigate spin-orbit
coupled repulsive Fermi atoms in a one-dimensional optical lattice. Using the
density-matrix renormalization group method, we calculate momentum distribution
function, gap, and spin-correlation function to reveal rich ground-state
properties. We find that spin-orbit coupling (SOC) can generate unconventional
momentum distribution, which depends crucially on the filling. We call the
corresponding phase with zero gap the SOC-induced metallic phase. We also show
that SOC can drive the system from the antiferromagnetic to ferromagnetic Mott
insulators with spin rotating. As a result, a second-order quantum phase
transition between the spin-rotating ferromagnetic Mott insulator and the
SOC-induced metallic phase is predicted at the strong SOC. Here the spin
rotating means that the spin orientations of the nearest-neighbor sites are not
parallel or antiparallel, i.e., they have an intersection angle $\theta \in
(0,\pi )$. Finally, we show that the momentum $k_{\mathrm{peak}}$, at which
peak of the spin-structure factor appears, can also be affected dramatically by
SOC. The analytical expression of this momentum with respect to the SOC
strength is also derived. It suggests that the predicted spin-rotating
ferromagnetic ($k_{\mathrm{peak}% }<\pi /2$) and antiferromagnetic ($\pi
/2<k_{\mathrm{peak}}<\pi $) correlations can be detected experimentally by
measuring the SOC-dependent spin-structure factor via the time-of-flight
imaging.
