Nonanalytic Spin Susceptibility of a Fermi Liquid: The Case of Fe-Based Pnictides

We propose an explanation of the peculiar linear temperature dependence of the uniform spin susceptibility $\chi (T)$ in ferropnictides. We argue that the linear in $T$ term appears to be due to the nonanalytic temperature dependence of $\chi (T)$ in a two-dimensional Fermi liquid. We show that the prefactor of the $T$ term is expressed via the square of the spin-density-wave (SDW) amplitude connecting nested hole and electron pockets. Because of an incipient SDW instability, this amplitude is large, which, along with a small value of the Fermi energy, makes the $T$ dependence of $\chi (T)$ strong. We demonstrate that this mechanism is in quantitative agreement with the experiment.

Figure 1

Second-order diagrams for the thermodynamic potential. Solid and dashed lines correspond to $f$ fermions (electrons) and to $c$ fermions (holes), respectively.

Figure 2

(a) $T$ dependence of the spin susceptibility $\chi (T)$, as given by Eq. (6), for perfect nesting ($\mu =0$) and for a range of couplings $u{N}_F$, as indicated in the plot. In a calculation, $\max (T,\mu )$ in Eq. (6) is approximated by $\sqrt{T^2+{\mu }^2}$. Inset: Calculated slope $d\chi (T)/dT$ as a function of $u{N}_F$ at $T=300\mathrm{K}$ (chosen to match Ref. 11). (b) Calculated $\chi (T)$ for $u{N}_F=0.5$ for a range of $\mu$, as shown in the plot. Inset: Same curves as in (a) normalized by ${\chi }_{\mathrm{extr}}$, obtained by extrapolating $\chi (T)$ down to $T=0$. (c) $\chi (T)$ in ${\mathrm{BaFe}}_{2-x}{\mathrm{Co}}_x{\mathrm{As}}_2$ from Ref. 12. Inset: Same data as in the main panel normalized by $\chi (0)$. (d) Calculated slope $d\chi (T=300\mathrm{K})/dT$ as a function of $\mu$. Inset: Measured slope as a function of doping (from Ref. 11).