  We investigate the ground-state properties of a one-dimensional $t_{\rm
2g}$-orbital Hubbard model including an atomic spin-orbit coupling by using
numerical methods, such as Lanczos diagonalization and density-matrix
renormalization group. As the spin-orbit coupling increases, we find a
ground-state transition from a paramegnetic state to a ferromagnetic state. In
the ferromagnetic state, since the spin-orbit coupling mixes spin and orbital
states with complex number coefficients, an antiferro-orbital state with
complex orbitals appears. According to the appearance of the complex orbital
state, we observe an enhancement of $\Gamma_{4u}$ octupole correlations.
