Structural and antiferromagnetic properties of Ba(Fe$_{\mathrm{1-}}_{x}_{\mathrm{-}}_{y}$Co$_{x}$Rh$_{y})_{\mathrm{2}}$As$_{\mathrm{2}}$ compounds*

We present a systematic investigation of the electrical, structural, and antiferromagnetic properties for the series of Ba(Fe$_{\mathrm{1-}}_{x}_{\mathrm{-}}_{y}$Co$_{x}$Rh$_{y})_{\mathrm{2}}$As$_{\mathrm{2}}$ compounds with fixed $x \quad =$ 0.027 and 0 \textless $y$ \textless 0.035. We compare our results for the Co-Rh doped Ba(Fe$_{\mathrm{1-}}_{x}_{\mathrm{-}}_{y}$Co$_{x}$Rh$_{y})_{\mathrm{2}}$As$_{\mathrm{2}}$ compounds with Ba(Fe$_{\mathrm{1-}}_{x}$Co$_{x})_{\mathrm{2}}$As$_{\mathrm{2}}$ compounds. We demonstrate that the electrical, structural, antiferromagnetic, and superconducting properties of the Co-Rh doped compounds are similar to the properties of the Co doped compounds. We find that the overall behaviors of Ba(Fe$_{\mathrm{1-}}_{x}_{\mathrm{-}}_{y}$Co$_{x}$Rh$_{y})_{\mathrm{2}}$As$_{\mathrm{2}}$ and Ba(Fe$_{\mathrm{1-}}_{x}$Co$_{x})_{\mathrm{2}}$As$_{\mathrm{2}}$ compounds are very similar when the total number of the extra electrons per Fe/\textit{TM} (\textit{TM} $=$ transition metal) site is considered, which is consistent with the rigid band model. Despite the similarity, we find that the details of the transitions are different in between Ba(Fe$_{\mathrm{1-}}_{x}_{\mathrm{-}}_{y}$Co$_{x}$Rh$_{y})_{\mathrm{2}}$As$_{\mathrm{2}}$ and Ba(Fe$_{\mathrm{1-}}_{x}$Co$_{x})_{\mathrm{2}}$As$_{\mathrm{2}}$ compounds.