  In a first approximation, known as the adiabatic process, the direction of
the spin polarization of currents is parallel to the local magnetization vector
in a domain wall. Thus the spatial variation of the direction of the spin
current inside the domain wall results in an adiabatical spin transfer torque
on the magnetization. We show that domain wall motion driven by this spin
torque has many unique features that do not exist in the conventional wall
motion driven by a magnetic field. By analytically and numerically solving the
Landau-Lifshitz-Gilbert equation along with the adiabatic spin torque in
magnetic nanowires, we find the domain wall has its maximum velocity at the
initial application of the current but the velocity decreases to zero as the
domain wall begins to deform during its motion. We have computed domain wall
displacement and domain wall deformation of nanowires, and concluded that the
spin torque based on the adiabatic propagation of the spin current in the
domain wall is unable to maintain wall movement. We also introduce a novel
concept of domain wall inductance to characterize the capacity of the
spin-torque induced magnetic energy stored in a domain wall. In the presence of
domain wall pinning centers, we construct a phase diagram for the domain wall
depinning by the combined action of the magnetic field and the spin current.
