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The spin and density response functions in the random phase approximation(RPA) are derived by linearizing the kinetic equation including a magneticfield, the spin-orbit coupling, and mean fields with respect to an externalelectric field. Different polarization functions appear describing variousprecession motions showing Rabi satellites due to an effective Zeeman field.The latter turns out to consist of the mean-field magnetization, the magneticfield, and the spin-orbit vector. The collective modes for charged and neutralsystems are derived and a threefold splitting of the spin waves dependent onthe polarization and spin-orbit coupling is shown. The dielectric functionincluding spin-orbit coupling, polarization and magnetic fields is presentedanalytically for long wave lengths and in the static limit. The dynamicalscreening length as well as the long-wavelength dielectric function shows aninstability in charge modes, which are interpreted as spin segregation anddomain formation. The spin response describes a crossover from dampedoscillatory behavior to exponentially damped behavior dependent on thepolarization and collision frequency. The magnetic field causes ellipsoidaltrajectories of the spin response to an external electric field and thespin-orbit coupling causes a rotation of the spin axes. The spin-dephasingtimes are extracted and discussed in dependence on the polarization, magneticfield, spin-orbit coupling and single-particle relaxation times.

Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling: II. RPA response functions and collective modes