Effect of correlations and doping on the spin susceptibility of iron pnictides: the case of KFe$_{2}$As$_{2}$

The temperature dependence of the paramagnetic susceptibility of the iron pnictide superconductor KFe$_{2}$As$_{2}$ and its connection with the spectral properties of that material is investigated by a combination of density functional theory (DFT) in the local density approximation and dynamical mean-field theory (DMFT). Unlike other iron pnictide parent compounds where the typical oxidation state of iron is 2, the formal valence of Fe in KFe$_{2}$As$_{2}$ is 2.5, corresponding to an effective doping with 0.5 hole per iron atom compared to, for example, BaFe$_{2}$As$_{2}$. This shifts the chemical potential and thereby reduces the distance between the peaks in the spectral functions of KFe$_{2}$As$_{2}$ and the Fermi energy as compared to BaFe$_{2}$As$_{2}$. The shift, which is clearly seen on the level of DFT as well as in DMFT, is further enhanced by the strong electronic correlations in KFe$_{2}$As$_{2}$. In BaFe$_{2}$As$_{2}$ the presence of these peaks results (Phys. Rev. B 86, 125124 (2012)) in a temperature increase of the susceptibility up to a maximum at ${\sim}\,1000$ K. While the temperature increase was observed experimentally the decrease at even higher temperatures is outside the range of experimental observability. We show that in KFe$_{2}$As$_{2}$ the situation is different. Namely, the reduction of the distance between the peaks and the Fermi level due to doping shifts the maximum in the susceptibility to much lower temperatures, such that the decrease of the susceptibility becomes visible in experiment.