  [Full abstract in the paper] We aim to better constrain the atmospheric
properties of the directly imaged exoplanet 51~Eri~b by using a retrieval
approach on higher signal-to-noise data than previously reported. In this
context, we also compare the results of using the atmospheric retrieval code
\texttt{petitRADTRANS} vs a self-consistent model to fit atmospheric
parameters. We present a higher signal-to-noise $YH$ spectrum of the planet and
revised $K1K2$ photometry (M$_{K1} = 15.11 \pm 0.04$ mag, M$_{K2} = 17.11 \pm
0.38$ mag). The best-fit parameters obtained using an atmospheric retrieval
differ from previous results using self-consistent models. In general, we find
that our solutions tend towards cloud-free atmospheres (e.g. log $\tau_{\rm
clouds} = -5.20 \pm 1.44$). For our ``nominal'' model with new data, we find a
lower metallicity ([Fe/H] $= 0.26\pm$0.30 dex) and C/O ratio ($0.38\pm0.09$),
and a slightly higher effective temperature (T$_{\rm{eff}} = 807\pm$45 K) than
previous studies. The surface gravity (log $g = 4.05\pm0.37$) is in agreement
with the reported values in the literature within uncertainties. We estimate
the mass of the planet to be between 2 and 4 M$_{\rm{Jup}}$. When comparing
with self-consistent models, we encounter a known correlation between the
presence of clouds and the shape of the $P-T$ profiles. Our findings support
the idea that results from atmospheric retrievals should not be discussed in
isolation, but rather along with self-consistent temperature structures
obtained using the retrieval's best-fit parameters.
