Effects of disorder and Coulomb interaction on the spatial dispersion of spin susceptibility in two-dimensional structures
Victor M. Edelstein
Phys. Rev. B 87, 155312 (2013) - Published 23 April, 2013
The wave-vector- and frequency-dependent spin susceptibility of an interacting disordered two-dimensional electron gas at frequencies near the spin resonance has been considered. It is assumed that the external magnetic field is moderately strong and the Coulomb interaction is weak ( stands for the magnetic length). The spin susceptibility has been calculated within the ladder diagram approximation. A way of dealing with the degeneracy of Landau levels has been proposed and a transport-type equation free from the degeneracy indexes has been derived. It has been shown that the resonant part of the spin susceptibility has the form , where in the hydrodynamic limit ( stands for the Larmour frequency ) and to first order in the imaginary part, which stems from the diffusion of the spin magnetization due to the stochastic scattering on impurities, has a conventional form, , while the real part, which characterizes the coherent motion of the spin excitations through the crystal, is , where is the effective mass of the spin excitation in the clean system. Thus, at , the disorder strongly impedes the coherent motion of the excitations though it does not forbid it completely. The resonant frequency is unaffected by the Coulomb interaction, , just as in the clean case. The results may be applied to experiments on the spin-flip Raman scattering, where the finite wave-vector susceptibility can be directly measured, as well to the electromagnetic absorption studying by means of a grating superimposed on the structure.