  We consider the quasi-2D two-component Bose-Einstein condensates with Rashba
spin-orbit (SO) coupling in a rotating trap. An external Zeeman term favoring
spin polarization along the radial direction is also considered, which has the
same form as the non-canonical part of the mechanical angular momentum. The
rotating condensate exhibits rich structures as varying the strengths of
trapping potential and interaction. With a strong trapping potential, the
condensate exhibits a half-quantum vortex-lattice configuration. Such a
configuration is driven to the normal one by introducing the external radial
Zeeman field. In the case of a weak trap potential, the condensate exhibits a
multi-domain pattern of plane-wave states under the external radial Zeeman
field.
