The spin and density response functions in the random phase approximation
(RPA) are derived by linearizing the kinetic equation including a magnetic
field, the spin-orbit coupling, and mean fields with respect to an external
electric field. Different polarization functions appear describing various
precession motions showing Rabi satellites due to an effective Zeeman field.
The latter turns out to consist of the mean-field magnetization, the magnetic
field, and the spin-orbit vector. The collective modes for charged and neutral
systems are derived and a threefold splitting of the spin waves dependent on
the polarization and spin-orbit coupling is shown. The dielectric function
including spin-orbit coupling, polarization and magnetic fields is presented
analytically for long wave lengths and in the static limit. The dynamical
screening length as well as the long-wavelength dielectric function shows an
instability in charge modes, which are interpreted as spin segregation and
domain formation. The spin response describes a crossover from damped
oscillatory behavior to exponentially damped behavior dependent on the
polarization and collision frequency. The magnetic field causes ellipsoidal
trajectories of the spin response to an external electric field and the
spin-orbit coupling causes a rotation of the spin axes. The spin-dephasing
times are extracted and discussed in dependence on the polarization, magnetic
field, spin-orbit coupling and single-particle relaxation times.Comment: PRB 201
