Dynamical spin susceptibility of a spin-valley half-metal

A few years ago we predicted theoretically that in systems with nesting of the Fermi surface the spin-valley half-metal has lower energy than the spin density wave state. In this paper we suggest a possible way to distinguish these phases experimentally. We calculate the dynamical spin susceptibility tensor for both states in the framework of the Kubo formalism. Discussed phases have different numbers of bands: four bands in the spin-valley half-metal and only two bands in the spin density wave. Therefore, their susceptibilities, as functions of frequency, have different numbers of peaks. Besides, the spin-valley half-metal does not have rotational symmetry, thus, in general the off-diagonal components of the susceptibility tensor are nonzero. The spin density wave obeys robust rotational symmetry and off-diagonal components of the susceptibility tensor are zero. These characteristic features can be observed in experiments with inelastic neutron scattering.