  (Abridged) We aim at identifying the least massive population of the solar
metallicity, young (120 Myr), nearby (133.5 pc) Pleiades star cluster with the
ultimate goal of understanding the physical properties of intermediate-age,
free-floating, low-mass brown dwarfs and giant planetary-mass objects, and
deriving the cluster substellar mass function across the deuterium-burning mass
limit at ~0.012 Msol. We performed a deep photometric and astrometric J- and
H-band survey covering an area of ~0.8 deg^2. The images with completeness and
limiting magnitudes of J,H ~ 20.2 and ~ 21.5 mag were acquired ~9 yr apart
(proper motion precision of +/-6 mas/yr). J- and H-band data were complemented
with Z, K, and mid-infrared magnitudes up to 4.6 micron coming from UKIDSS,
WISE, and follow-up observations of our own. Pleiades member candidates were
selected to have proper motions compatible with that of the cluster, and colors
following the known Pleiades sequence in the interval J = 15.5-8.8 mag, and
Z_UKIDSS - J > 2.3 mag or Z nondetections for J > 18.8 mag. We found a neat
sequence of astrometric and photometric Pleiades substellar member candidates
in the intervals J = 15.5-21.2 mag and ~0.072-0.008 Msol. The faintest objects
show very red near- and mid-infrared colors exceeding those of field
high-gravity dwarfs by >0.5 mag. The Pleiades photometric sequence does not
show any color turn-over because of the presence of photospheric methane
absorption down to J = 20.3 mag, which is about 1 mag fainter than predicted by
the color-computed models. Pleiades brown dwarfs have a proper motion
dispersion of 6.4-7.5 mas/yr and are dynamically relaxed at the age of the
cluster. The Pleiades mass function extends down to the deuterium burning-mass
threshold, with a slope fairly similar to that of other young star clusters and
stellar associations.
