\documentclass[border=10pt]{standalone}
\usepackage{pgfplots, tikz, amsmath}
\usepackage{filecontents}

\usepgfplotslibrary{colorbrewer}
\usepgfplotslibrary{fillbetween, external}

\begin{document}
\begin{tikzpicture}
\begin{axis}[xlabel=$k$,
ylabel= $\Re(\hat{r})$,
width = 4.5 cm,
height = 3.5 cm,
transpose legend,
legend columns=-1,
%grid = both,
ylabel near ticks,
xlabel near ticks,
%xmin=0.0,
%xmax = 1.0,
%cycle list/RdGy-11,
%cycle list/Paired-10,
cycle list name=Paired-10,
%cycle list name=linestyles*,
]
\addplot+[thick] table[x index=0,y index=1] {./data/rhat.txt};
\addplot+[thick] table[x index=0,y index=2] {./data/rhat.txt};
\addplot+[thick] table[x index=0,y index=3] {./data/rhat.txt};
\addplot+[thick] table[x index=0,y index=4] {./data/rhat.txt};
\addplot+[thick] table[x index=0,y index=5] {./data/rhat.txt};
\addplot+[thick] table[x index=0,y index=6] {./data/rhat.txt};
\addplot+[thick] table[x index=0,y index=7] {./data/rhat.txt};
\addplot+[thick] table[x index=0,y index=8] {./data/rhat.txt};
\addplot+[thick] table[x index=0,y index=9] {./data/rhat.txt};
\end{axis}
\end{tikzpicture}

%\input{rTNew.tex}
\end{document}