  Although, from a theoretical point of view, magnetic fields are believed to
have a significant role during the early stages of star formation, especially
during the main accretion phase, the magnetic field strength and topology is
poorly constrained in the youngest accreting Class 0 protostars that lead to
the formation of solar-type stars. We carried out observations of the polarized
dust continuum emission with the SMA interferometer at 0.87mm, in order to
probe the structure of the magnetic field in a sample of 12 low-mass Class 0
envelopes, including both single protostars and multiple systems, in nearby
clouds. Our SMA observations probe the envelope emission at scales of 600-5000
au with a spatial resolution ranging from 600 to 1500 au depending on the
source distance. We report the detection of linearly polarized dust continuum
emission in all of our targets, with average polarization fractions ranging
from 2% to 10% in these protostellar envelopes. The polarization fraction
decreases with the continuum flux density, which translates into a decrease
with the H2 column density within an individual envelope. Our analysis show
that the envelope-scale magnetic field is preferentially observed either
aligned or perpendicular to the outflow direction. Interestingly, our results
suggest for the first time a relation between the orientation of the magnetic
field and the rotational energy of envelopes, with a larger occurrence of
misalignment in sources where strong rotational motions are detected at
hundreds to thousands of au scales. We also show that the best agreement
between the magnetic field and outflow orientation is found in sources showing
no small-scale multiplicity and no large disks at about 100 au scales.
