  Using high-contrast imaging with the SPHERE instrument at the VLT, we report
the first images of a cold brown dwarf companion to the exoplanet host star
HD4113A. The brown dwarf HD4113C is part of a complex dynamical system
consisting of a giant planet, stellar host and a known wide M-dwarf companion.
Its separation of $535\pm3$mas and H-band contrast of $13.35\pm0.10$mag
correspond to a projected separation of 22AU and an isochronal mass estimate of
$36\pm5$M$_J$ based on COND models. The companion shows strong methane
absorption, and through atmospheric model fitting we estimate a surface gravity
of $\log g$=5 and an effective temperature of ~500-600K. A comparison of its
spectrum with observed T dwarfs indicates a late-T spectral type, with a T9
object providing the best match. By combining the observed astrometry from the
imaging data with 27 years of radial velocities, we use orbital fitting to
constrain its orbital and physical parameters, as well as update those of the
planet HD4113Ab, discovered by previous radial velocity measurements. The data
suggest a dynamical mass of $66\pm5$M$_J$ and moderate eccentricity of
$0.44\pm0.08$ for the brown dwarf. This mass estimate appears to conflict with
the isochronal estimate and that of similar objects, which may be caused by the
newly detected object being an unresolved binary brown dwarf system or the
presence of an additional object in the system. Through dynamical simulations
we show that the planet may undergo strong Lidov-Kozai cycles, raising the
possibility that it formed on a quasi-circular orbit and gained its currently
observed high eccentricity through interactions with the brown dwarf. Follow-up
observations combining radial velocities, direct imaging and Gaia astrometry
will be crucial to precisely constrain the dynamical mass of the brown dwarf
and allow for in-depth comparison with evolutionary and atmospheric models.
