  Theoretical simulations and observations at different angular resolutions
have shown that magnetic fields have a central role in massive star formation.
Like in low-mass star formation, the magnetic field in massive young stellar
objects can either be oriented along the outflow axis or randomly. Measuring
the magnetic field at milliarcsecond resolution (10-100 au) around a
substantial number of massive young stellar objects permits determining with a
high statistical significance whether the direction of the magnetic field is
correlated with the orientation of the outflow axis or not. In late 2012, we
started a large VLBI campaign with the European VLBI Network to measure the
linearly and circularly polarized emission of 6.7 GHz methanol masers around a
sample of massive star-forming regions. This paper focuses on the first seven
observed sources, G24.78+0.08, G25.65+1.05, G29.86-0.04, G35.03+0.35,
G37.43+1.51, G174.20-0.08, and G213.70-12.6. For all these sources, molecular
outflows have been detected in the past. We detected a total of 176 methanol
masing cloudlets toward the seven massive star-forming regions, 19% of which
show linearly polarized emission. The methanol masers around the massive young
stellar object MM1 in G174.20-0.08 show neither linearly nor circularly
polarized emission. The linear polarization vectors are well ordered in all the
other massive young stellar objects. We measured significant Zeeman splitting
toward both A1 and A2 in G24.78+0.08, and toward G29.86-0.04 and G213.70-12.6.
By considering all the 19 massive young stellar objects reported in the
literature for which both the orientation of the magnetic field at
milliarcsecond resolution and the orientation of outflow axes are known, we
find evidence that the magnetic field (on scales 10-100 au) is preferentially
oriented along the outflow axes.
