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The low-frequency linearly-polarised radio source population is largelyunexplored. However, a renaissance in low-frequency polarimetry has beenenabled by pathfinder and precursor instruments for the Square Kilometre Array.In this second paper from the POlarised GaLactic and Extragalactic All-SkyMurchison Widefield Array (MWA) Survey -- the POlarised GLEAM Survey, or POGS-- we present the results from our all-sky MWA Phase I Faraday Rotation Measuresurvey. Our survey covers nearly the entire Southern sky in the Declinationrange $-82^{\circ}$ to $+30^{\circ}$ at a resolution between around three andseven arcminutes (depending on Declination) using data in the frequency range169$-$231 MHz. We have performed two targeted searches: the first covering25,489 square degrees of sky, searching for extragalactic polarised sources;the second covering the entire sky South of Declination $+30^{\circ}$,searching for known pulsars. We detect a total of 517 sources with 200 MHzlinearly-polarised flux densities between 9.9 mJy and 1.7 Jy, of which 33 areknown radio pulsars. All sources in our catalogues have Faraday rotationmeasures in the range $-328.07$ rad m$^{-2}$ to $+279.62$ rad m$^{-2}$. TheFaraday rotation measures are broadly consistent with results fromhigher-frequency surveys, but with typically more than an order of magnitudeimprovement in the precision, highlighting the power of low-frequencypolarisation surveys to accurately study Galactic and extragalactic magneticfields. We discuss the properties of our extragalactic and known-pulsar sourcepopulation, how the sky distribution relates to Galactic features, and identifya handful of new pulsar candidates among our nominally extragalactic sourcepopulation.

The POlarised GLEAM Survey (POGS) II: Results from an All-Sky Rotation Measure Synthesis Survey at Long Wavelengths