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

TL;DR

This paper develops a comprehensive kinetic theory for spin-polarized systems under electric and magnetic fields with spin-orbit coupling, deriving response functions, collective modes, and analyzing instabilities and spin dynamics.

Contribution

It provides analytical expressions for RPA response functions and collective modes in spin-polarized systems including spin-orbit effects, extending previous models.

Findings

Identification of threefold splitting of spin waves due to spin-orbit coupling.

Analytical dielectric function showing instabilities leading to spin segregation.

Crossover behavior in spin response from damped oscillations to exponential decay.

Abstract

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.