We present K-band photometry and low-resolution near-infrared spectroscopy from 1.44 to 2.45 micron of isolated planetary-mass candidate members in the sigma Orionis cluster found by Zapatero Osorio et al. The new data have been obtained with NIRC at the Keck I telescope. All of our targets, except for one, are confirmed as likely cluster members. Hence, we also confirm that the planetary-mass domain in the cluster is well populated. Using our deep K-band images we searched for companions to the targets in the separation range 0.3" to 10" up to a maximum faint limit of K=19.5 mag. One suspected companion seems to be an extremely red galaxy. The near-infrared colors of the sigma Orionis substellar members indicate that dust grains condense and settle in their atmospheres. We estimate that the surface temperatures range from 2500 K down to 1500 K. The spectroscopic sequence covers the full range of L subclasses, and the faintest object is tentatively classified as T0. These targets provide a sequence of substellar objects of known age, distance and metallicity, which can be used as benchmark for understanding the spectral properties of ultracool dwarfs.

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