  Spin transfer torque in a two dimensional electron gas system without space
inversion symmetry was theoretically investigated by solving the
Pauli-Schr\"{o}dinger equation for the itinerant electrons inside magnetic
domain walls. Due to the presence of the Rashba spin-orbit coupling induced by
the broken inversion symmetry, the spin transfer torque is chiral and the
nonadiabaticity, which is defined to measure the relative importance of the
nonadiabatic, field-like torque to the adiabatic, damping-like torque, exhibits
an inverse power law decay as the domain wall width is increased. This
algebraic decay is much slower than the exponential decay observed for systems
without the Rashba spin-orbit coupling, and may find applications in innovative
design of spintronic devices utilising magnetic topological textures such as
magnetic domain walls and skyrmions.
