Doping evolution of itinerant magnetic excitations in Fe-based   oxypnictides
  Employing the four-band tight-binding model we study theoretically the doping dependence of the spin response in the normal state of novel Fe-based pnictide superconductors. We show that the commensurate spin density wave (SDW) transition that arises due to interband scattering between the hole $\alpha$-pockets and the electron $\beta$-pockets disappears already at the doping concentration $x \approx 0.04$ reflecting the evolution of the Fermi surfaces. Correspondingly, with further increase of the doping the antiferromagnetic fluctuations are suppressed for $x > 0.1$ and the Im$\chi({\bf Q_{AFM}},\omega)$ becomes nearly temperature independent. At the same time, we observe that the uniform susceptibility deviates from the Pauli-like behavior and is increasing with increasing temperature reflecting the activation processes for the $\alpha$-Fermi surfaces up to temperatures of about T=800K. With increase of the doping the absolute value of the uniform susceptibility lowers and its temperature dependence changes. In particular, it is a constant at low temperatures and then decreases with increasing temperature. We discuss our results in a context of recent experimental data. 
M.M. Korshunov and I. Eremin