  To clarify a crucial role of a spin-orbit coupling in the emergence of novel
spin-orbital states in $5d$-electron compounds such as Sr$_{2}$IrO$_{4}$, we
investigate ground state properties of a $t_{\rm 2g}$-orbital Hubbard model on
a square lattice by Lanczos diagonalization. In the absence of the spin-orbit
coupling, the ground state is spin singlet. When the spin-orbit coupling is
strong enough, the ground state turns into a weak ferromagnetic state. The weak
ferromagnetic state is a singlet state in terms of an effective total angular
momentum. Regarding the orbital state, we find the so-called complex orbital
state, in which real $xy$, $yz$, and $zx$ orbital states are mixed with complex
coefficients.
