Spin correlations in the low-density electron system

We have calculated the spin susceptibility χσ(q,ω) within a microscopic model over the full range of densities of the electron liquid in the paramagnetic state. Electron-electron interactions are described by static random-phase-approximation screening modified by a local-field correction which takes into account the exchange-correlation hole in the low-density regime. We focus attention on the dynamic properties of the system, calculating the spin-spin susceptibility χσ(q,ω). Our results can be represented in terms of a complex Stoner-like enhancement function I(q,ω) with an explicit dependence on the wave number q and frequency ω. We find except for very large q and ω that I(q,ω) has only a weak functional dependence on q and ω and is nearly real, justifying the original Stoner approximation for a wide range of q and ω. We find when I(q,ω) does develop a q dependence, that this corresponds to a buildup of short-range spin correlations in the system that goes beyond the scope of the original Stoner model. Our results provide a first-principles determination of the density dependence of the Stoner enhancement factor. Finally, we find that paramagnons persist well away from the ferromagnetic transition