  Ground-state phase diagram of two-component Bose gases with Rashba spin-orbit
coupling is determined via a variational approach. A phase in which the fully
polarized condensate occupies zero momentum is identified. This zero-momentum
phase competes with the spin density wave phase when interspecies interaction
is stronger than intraspecies interaction, and the former one is always the
ground state for weak spin-orbit coupling. When the energies of these two
phases are close, there is a phase separation between them. At finite
temperature, such a zero-momentum condensation can be induced by a
ferromagnetic phase transition in normal state. The spontaneous spin
polarization removes the degeneracy of quasiparticles' energy minima, and
consequently the modified density of state accommodates a Bose condensation to
appear below a critical temperature.
