We have obtained low resolution optical spectra of 15 isolated planetary mass objects (IPMOs) in the sigma Orionis cluster, and derived spectral types by comparison with nearby M and L dwarfs. The spectral types are in the range late M - mid L, in agreement with our expectations based on colors and magnitudes for bona fide members. Therefore, most of these objects have masses below the deuterium burning limit. About 2/3 show Hα in emission at our spectral resolution. From our spectroscopic and photometric data, we infer that three IPMOs in this sample may be binaries with components of similar masses. These results confirm that the substellar mass function of the sigma Orionis cluster, in the form dN/dM, keeps rising in the planetary domain. These observations were collected at the VLT of the European Southern Observatories.