Predicting a Gapless Spin-1 Neutral Collective Mode branch for Graphite

Using the standard tight binding model of 2d graphite with short range electron repulsion, we find a gapless spin-1, neutral collective mode branch {\em below the particle-hole continuum} with energy vanishing linearly with momenta at the $\Gamma$ and $K$ points in the BZ. This spin-1 mode has a wide energy dispersion, 0 to $\sim 2 eV$ and is not Landau damped. The `Dirac cone spectrum' of electrons at the chemical potential of graphite generates our collective mode; so we call this `spin-1 zero sound' of the `Dirac sea'. Epithermal neutron scattering experiments, where graphite single crystals are often used as analyzers (an opportunity for `self-analysis'!), and spin polarized electron energy loss spectroscopy (SPEELS) can be used to confirm and study our collective mode.