At high-energy gamma-rays (>100 MeV) the Large Area Telescope (LAT) on the Fermi satellite already detected more than 145 rotation-powered pulsars (RPPs), while the number of pulsars seen at soft gamma-rays (20 keV - 30 MeV) remained small. We present a catalogue of 18 non-recycled RPPs from which presently non-thermal pulsed emission has been securely detected at soft gamma-rays above 20 keV, and characterize their pulse profiles and energy spectra. For 14 of them we report new results, (re)analysing mainly data from RXTE, INTEGRAL, XMM-Newton and Chandra. The soft gamma-pulsars are all fast rotators and on average ~9.3x younger and ~ 43x more energetic than the Fermi LAT sample. The majority (11 members) exhibits broad, structured single pulse profiles, and only 6 have double (or even multiple, Vela) pulses. Fifteen soft gamma-ray pulsar show hard power-law spectra in the hard X-ray band and reach maximum luminosities typically in the MeV range. For only 7 of the 18 soft gamma-ray pulsars pulsed emission has also been detected by the LAT, but 12 have a pulsar wind nebula (PWN) detected at TeV energies. For six pulsars with PWNe, we present also the spectra of the total emissions at hard X-rays, and for IGR J18490-0000, associated with HESS J1849-000 and PSR J1849-0001, we used our Chandra data to resolve and characterize the contributions from the point-source and PWN. Finally, we also discuss a sample of 15 pulsars which are candidates for future detection of pulsed soft gamma-rays, given their characteristics at other wavelengths.
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