  We present model constraints on the atmospheric structure of HD 106906 b, a
planetary-mass companion orbiting at a ~700 AU projected separation around a 15
Myr-old stellar binary, using the APOLLO retrieval code on spectral data
spanning 1.1-2.5 $\mu$m. C/O ratios can provide evidence for companion
formation pathways, as such pathways are ambiguous both at wide separations and
at star-to-companion mass ratios in the overlap between the distributions of
planets and brown dwarfs. We benchmark our code against an existing retrieval
of the field L dwarf 2M2224-0158, returning a C/O ratio consistent with
previous fits to the same JHKs data, but disagreeing in the thermal structure,
cloud properties, and atmospheric scale height. For HD 106906 b, we retrieve
C/O $=0.53^{+0.15}_{-0.25}$, consistent with the C/O ratios expected for HD
106906's stellar association and therefore consistent with a stellar-like
formation for the companion. We find abundances of H$_2$O and CO near chemical
equilibrium values for a solar metallicity, but a surface gravity lower than
expected, as well as a thermal profile with sharp transitions in the
temperature gradient. Despite high signal-to-noise and spectral resolution,
more accurate constraints necessitate data across a broader wavelength range.
This work serves as preparation for subsequent retrievals in the era of JWST,
as JWST's spectral range provides a promising opportunity to resolve
difficulties in fitting low-gravity L dwarfs, and also underscores the need for
simultaneous comparative retrievals on L dwarf companions with multiple
retrieval codes.
