Static and Dynamical Susceptibility of LaO$_{1}$$_{−}$$_{x}$F$_{x}$FeAs M. Monni $^{1}$, F. Bernardini$^{1}$, G. Profeta$^{2}$, A. Sanna3 , 4 , 1 , $^{5}$, S. Sharma3 , $^{5}$, J. K. Dewhurst 3 , 4 , $^{5}$, C. Bersier3 , 4 , $^{5}$, A. Continenza$^{2}$, E.K.U. Gross3 , $^{5}$, S. Massidda1 1 SLACS-INFM/CNR, and Dipartimento di Scienze Fisiche, Universit` a degli Studi di Cagliari, I-09042 Monserrato (CA), Italy 2 CNISM - Dipartimento di Fisica, Universit` a degli Studi dell’Aquila, Via Vetoio 10, I-67010 Coppito (L’Aquila) Italy 4 Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, D-14195 Berlin, Germany. and 3 Institut f¨ ur Theoretische Physik, Freie Universit¨ at Berlin, Arnimallee 14, D-14195 Berlin, Germany 5 Max-Planck-Institut f¨ ur Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany. The mechanism of superconductivity and magnetism and their possible interplay have recently been under debate in pnictides. A likely pairing mechanism includes an important role of spin fluctuations and can be expressed in terms of the magnetic susceptibility χ . The latter is therefore a key quantity in the determination of both the magnetic properties of the system in the normal state, and of the contribution of spin fluctuations to the pairing potential. A basic ingredient to obtain χ is the independent-electron susceptibility χ$_{0}$ . Using LaO$_{1}$ − $_{x}$F$_{x}$ FeAs as a prototype material, in this report we present a detailed ab-initio study of χ$_{0}$ ( q , ω ), as a function of doping and of the internal atomic positions. The resulting static χ$_{0}$ ( q , 0) is consistent with both the observed M -point related magnetic stripe phase in the parent compound, and with the existence of incommensurate magnetic structures predicted by ab-initio calculations upon doping. 1 arXiv:1001.5154v1 [cond-mat.supr-con] 28 Jan 2010 Abstract