  The formation of binary stars is highly influenced by magnetic fields, which
play a crucial role in transporting angular momentum. We conducted
three-dimensional numerical simulations of binary star accretion via a
circumbinary disk, taking into account a magnetic field perpendicular to the
disk and an infalling envelope. Our simulations reproduce the following
phenomena: (1) spiral arms associated with circumstellar disks, (2) turbulence
in the circumbinary disk, induced by magneto-rotational instability (MRI), (3)
a fast outflow launched from each circumstellar disk, and (4) a slow outflow
from the circumbinary disk. The binary models exhibit a higher
$\alpha$-parameter than the corresponding single star models, indicating that
the binary stars enhance MRI turbulence. Moreover, an infalling envelope also
enhance the turbulence, leading to a high $\alpha$-parameter. While the spiral
arms promotes radial flow, causing transfer of mass and angular momentum within
the circumbinary disk, the MRI turbulence and outflows are main drivers of
angular momentum transfer to reduce the specific angular momentum of the
system.
