What the researchers actually showed was that heat transmission rates could be changed with a magnetic field. That manipulates the response of the material to vibrations--not the same thing at all as showing that vibrations are magnetic.
Incidentally, the article cites an earlier finding that in graphene (effectively a 2-D material) sound propagated as phonons instead of random vibrations. Of course phonons are a form of vibration, and you could at least theoretically decompose any vibration into a large enough collection of phonons going different directions with different amplitudes and phases. That in a highly structured 2-D material like graphene the vibrations of heat can show up in a more structured way is a nice result, but not exactly earth-shattering news.
Their result is actually kind of fun. At nearly absolute zero, and in extremely small and uniform materials, the size and shape of the materials matters more. And then turning a 7 tesla field on dropped heat flow rate by about 12%.