We report on the discovery of gamma-ray pulsations from five millisecond pulsars (MSPs) using the Fermi Large Area Telescope (LAT) and timing ephemerides provided by various radio observatories. We also present confirmation of the gamma-ray pulsations from a sixth source, PSR J2051-0827. Five of these six MSPs are in binary systems: PSRs J1713+0747, J1741+1351, J1600-3053 and the two black widow binary pulsars PSRs J0610-2100 and 2051-0827. The only isolated MSP is the nearby PSR J1024-0719, which is also known to emit X-rays. We present X-ray observations in the direction of PSRs J1600-3053 and J2051-0827. While the latter is firmly detected, we an only give upper limits for the X-ray flux of the former. There are no dedicated X-ray observations available for the other 3 objects. The MSPs mentioned above, together with most of the MSPs detected by Fermi, are used to put together a sample of 30 gamma-ray MSPs which is used to study the morphology and phase connection of radio and gamma-ray pulse profiles. We show that MSPs with pulsed gamma-ray emission which is phase aligned with the radio emission present the steepest radio spectra and the largest magnetic fields at the light cylinder among all MSPs. As well, we also observe a trend towards very low, or undetectable, radio linear polarisation levels. These properties could be attributed to caustic radio emission produced at a range of different altitudes in the magnetosphere. We note that most of these characteristics are also observed in the Crab pulsar, the only other radio pulsar known to exhibit phase-aligned radio and gamma-ray emission.
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