Here's a link to a Scientific American story about a map of the magnetic field in the LMC.
Astronomers Map Chaotic Galaxy's Magnetic Field
The article is very brief, but says that it was a surprise that the overall magnetic field of this satellite galaxy of ours is very smooth and orderly... more so than the team doing the measurement expected, considering the LMC's recent episodes of starburst and supernova activities.
I wish these articles would point to the arXiv version of the original paper, but they don't. The paper quotes Bryan Gaensler of the Harvard-Smithsonian Center for Astrophysics.
I was surprised that Sarah Graham (whose writing I like) didn't seem to recognise M31 as our neighbor in Andromeda.