Correlation induced out-of-phase plasmon in an electron liquid

Abstract: We derive from first principles the existence of a low-frequency plasmon in a strongly coupled three-dimensional homogeneous electron gas (HEG). From its dispersion and its satisfaction of the 3rd frequency sum rule we identify it with the conjectured magnetic excitation in the HEG. This excitation, is maintained by the out-of-phase oscillations of the spin-up and spin-down densities of the electron liquid, but governed solely by the Coulomb interaction between the particles. The frequency square of this mode is proportional to the overlap ($r=0$) (absolute) value of the spin-up/spin-down correlation function, and thus slightly affected by, but not contingent upon the degree of polarization of the electron liquid. We estimate the spectral weight of the mode: it is expected to be governed by electron-electron collision induced spin drag. The spectral weight is manifest in the partial spin-resolved dynamical structure functions and it is proportional to the product of the densities of the two spin components. An independent derivation based on a generalized Feynman Ansatz corroborates our result. The relationship to the recently identified "spin plasmon" excitation is discussed. It is pointed out that a scattering experiment with polarized neutrons or polarized X-rays may be possible avenues to observe equilibrium fluctuations associated with these modes and also to provide information on the spin drag coefficient in the HEG.