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In this paper, we investigate the dynamical spin susceptibility in the bi-directional charge density wave (BCDW) state by adopting a random-phase approximation. In the BCDW state, we find that no spin resonance exists and only a broad commensurate peak appears for the frequency dependence of the dynamical spin susceptibility at Q = ( π, π), though a low-energy spin gap feature can also be found as in the superconducting state. While the 'hourglass' type of the dispersion for the BCDW state bears some similarities with that in the superconducting state, the momentum distribution of Im χ( Q, ω) is just the opposite with the incommensurate peaks lying along the diagonal direction for the energy below ω and along the axial direction above ω. In the coexistence of SC and BCDW, the frequency dependence of the dynamical spin susceptibility at Q = ( π, π) generally shows the two-peak structure, reflecting two energy scales of the spin excitations. These unique features may serve as signatures to verify whether or not the BCDW state is responsible for the formation of the Fermi arcs. [ABSTRACT FROM AUTHOR]

The nesting of electron Fermi pocket with one of the two hole pockets around the Brillouin zone center has been attributed to the spin density wave (SDW) instability in the parent compound of superconducting iron pnictides. We propose here that the second hole Fermi pocket may be nested with the electron pocket in the doped case, which results in a new SDW instability. Our work is motivated by and may explain the recent scanning tunneling spectroscopy (STM) measurements on NaFe1−xCoxAs, which show an asymmetric gap-like feature near the Fermi level in the overdoped regime (Zhou X. et al., Phys. Rev. Lett., 109 (2012) 037002). We use a multi-band model to examine this feature within random phase approximation to include the coupling between the itinerant electron and the local spins. [ABSTRACT FROM AUTHOR]