  We present the results of simultaneous 450 $\mu$m and 850 $\mu$m polarization
observations toward the massive star forming region NGC 2071IR, a target of the
BISTRO (B-fields in Star-Forming Region Observations) Survey, using the POL-2
polarimeter and SCUBA-2 camera mounted on the James Clerk Maxwell Telescope. We
find a pinched magnetic field morphology in the central dense core region,
which could be due to a rotating toroidal disk-like structure and a bipolar
outflow originating from the central young stellar object, IRS 3. Using the
modified Davis-Chandrasekhar-Fermi method, we obtain a plane-of-sky magnetic
field strength of 563$\pm$421 $\mu$G in the central $\sim$0.12 pc region from
850 $\mu$m polarization data. The corresponding magnetic energy density of
2.04$\times$10$^{-8}$ erg cm$^{-3}$ is comparable to the turbulent and
gravitational energy densities in the region. We find that the magnetic field
direction is very well aligned with the whole of the IRS 3 bipolar outflow
structure. We find that the median value of polarization fractions, 3.0 \%, at
450 $\mu$m in the central 3 arcminute region, which is larger than the median
value of 1.2 \% at 850 $\mu$m. The trend could be due to the better alignment
of warmer dust in the strong radiation environment. We also find that
polarization fractions decrease with intensity at both wavelengths, with
slopes, determined by fitting a Rician noise model, of $0.59 \pm 0.03$ at 450
$\mu$m and $0.36 \pm 0.04$ at 850 $\mu$m, respectively. We think that the
shallow slope at 850 $\mu$m is due to grain alignment at the center being
assisted by strong radiation from the central young stellar objects.
