  NLTT 5306 is a post-common envelope binary made up of a white dwarf host and
brown dwarf companion that has shown evidence of inflation and active mass
donation despite not filling its Roche lobe. Two proposed mechanisms for the
brown dwarf's inflation are magnetic interactions and a high metallicity,
cloudy atmosphere. We present moderate resolution ($R\lesssim2000$) $J$ band
Keck/NIRSPEC observations of this system. These phase-resolved data allow us to
constrain differences between atmospheric parameters of the day- and night-side
of the brown dwarf. Our day- and night-side effective temperature measurements
are consistent, in agreement with the brightness temperatures measurements from
Casewell et al. 2021a. The day-side favors a slightly lower surface gravity,
perhaps stemming from the material streaming between the two objects. Finally,
our data show a preference for low metallicity models. This would be expected
from the system's old age, but provides direct evidence that a high
metallicity, cloudy brown dwarf atmosphere is not responsible for the witnessed
inflation. These results strengthen the case for magnetic interactions leading
to inflation of NLTT 5306 B.

Solar and Stellar Astrophysics;Earth and Planetary Astrophysics