An anisotropic band model for helimagnetism and spin-density waves, with application to Cr and MnP

An expression for a general q-dependent static spin susceptibility is derived by means of perturbation theory, including a two-electron exchange operator and spin-orbit coupling. Numerical calculations for hypothetical sets of two bands close to the Fermi level show that significantly stronger magnetic response can occur for q not=0 than for q=0, but only for interband transitions and if the bands intersect the Fermi surface in such a way that the region of close contact between the q-shifted bands and the Fermi surface is larger than the corresponding area for the unshifted bands. According to performed band calculations, this can be the case for Cr (spin-density wave, SDW) and MnP (helix). A symmetry consideration of a helical spin distribution shows that the symmetric and antisymmetric parts of the anisotropic exchange correspond to different bunching and modulation of the spins. For example, a longitudinal SDW (as in Cr) corresponds to a vanishing antisymmetric exchange (AE), while a circular uniform helix minimises the AE and has a vanishing non-diagonal symmetric exchange.