Transverse spin susceptibility in Ni, Fe and Co

We calculate the full transverse spin susceptibility $\chi^{\pm}(\bf q, \omega)$ in the time-dependent local density approximation(TDLDA) for elemental Ni, Fe and Co. We extract the Heisenberg exchange parameters from both the energy-dependent $\chi^{\pm}$ and the static one. The results are compared with those given by a method assuming the rigid rotation of the magnetic moments at each site(ref.kotani2008). We observe some differences between these two methods, especially around the Brillouin zone boundaries. We also calculate $\chi^{\pm}$ starting from the non-interacting Hamiltonian generated from the quasiparticle self-consistent GW(QSGW) approximation (ref.Kotani2007). We analyze how the QSGW potential alter the LDA results. \\ Ref.\\ T.Kotani and M van Schilfgaarde, J. PHYS. C 20, 295214 (2008) T.Kotani, M. van Schilfgaarde, S. V. Faleev Phys. Rev. B 76, 165106 (2007)