Study of the hyperfine fields in the BaFe${}_2$As${}_2$ family and its relation to the magnetic moment

Abstract

The hyperfine field $B_{\text{hf}}$ and the magnetic properties of the BaFe${}_2$As${}_2$ family are studied using the fully relativistic Dirac formalism for different types of substitution. The study covers electron doped Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ and Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$, hole doped (Ba${}_{1-x}$K${}_x$)Fe${}_2$As${}_2$ and also isovalently doped Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ and BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ for a wide range of the concentration $x$. For the substituted compounds the hyperfine fields show a very strong dependence on the dopant type and its concentration $x$. Relativistic contributions were found to have a significantly stronger impact for the iron pnictides when compared to bulk Fe. As an important finding, we demonstrate that it is not sensible to relate the hyperfine field $B_{\text{hf}}$ to the average magnetic moment $\hat{I}¼$ of the compound, as it was done in earlier literature.