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The hyperfine field $B_\text{hf}$ and the magnetic properties of theBaFe$_2$As$_2$ family are studied using the fully relativistic Dirac formalismfor different types of substitution. The study covers electron dopedBa(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 dopedBa(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ and BaFe$_2$(As$_{1-x}$P$_x$)$_2$ for a widerange of the concentration $x$. For the substituted compounds the hyperfinefields show a very strong dependence on the dopant type and its concentration$x$. Relativistic contributions were found to have a significantly strongerimpact for the iron pnictides when compared to bulk Fe. As an importantfinding, we demonstrate that it is not sensible to relate the hyperfine field$B_\text{hf}$ to the average magnetic moment $\mu$ of the compound, as it wasdone in earlier literature.

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