The fine structure of cyclotron and spin resonances at their crossing: Interplay between spin-orbit and Coulomb interactions

We compare the anticrossing of the spin and cyclotron resonances in spin-polarized and non-polarized phases of a two-dimensional electron gas subjected to a strong tilted magnetic field. The spin-orbit coupling splits these resonances into three lines with the gaps between them exactly equal to delta _2n+1=V_so rho _F and delta _2n=v_so rho _F/ square root 2 at odd- and even-integer factors, respectively. The 1/ square root 2 factor difference between the gaps delta _2n and delta _2n+1 arises from the existence of two collective spin-wave-density modes in the polarized phase of interacting electrons in the system with two filled Landau levels. This allows us to predict a new type of spectral Shubnikov-de Haas oscillations, which indicates the re-entrance of the system into the spin-polarized state.