  The M{\o}ller polarimeter in Hall A at Jefferson Lab in Newport News, VA, has
provided reliable measurements of electron beam polarization for the past two
decades reaching the typically required $\pm$1\% level of absolute uncertainty.
However, the upcoming proposed experimental program including MOLLER and SoLID
have stringent requirements on beam polarimetry precision at the level of 0.4\%
\cite{MOLLER2014, SoLID2019}, requiring a systematic re-examination of all the
contributing uncertainties.
  M{\o}ller polarimetry uses the double polarized scattering asymmetry of a
polarized electron beam on a target with polarized atomic electrons. The target
is a ferromagnetic material magnetized to align the spins in a given direction.
In Hall A, the target is a pure iron foil aligned perpendicular to the beam and
magnetized out of plane parallel or antiparallel to the beam direction. The
acceptance of the detector is engineered to collect scattered electrons close
to 90$^{\circ}$ in the center of mass frame where the analyzing power is a
maximum (-7/9).
  One of the leading systematic errors comes from determination of the target
foil polarization. Polarization of a magnetically saturated target foil
requires knowledge of both the saturation magnetization and $g^\prime$, the
electron $g$-factor which includes components from both spin and orbital
angular momentum from which the spin fraction of magnetization is determined.
This paper utilizes the existing world data to provide a best estimate for
target polarization for both nickel and iron foils including uncertainties in
magnetization, high-field and temperature dependence, and fractional
contribution to magnetization from orbital effects. We determine the foil
electron spin polarization at 294~K to be 0.08020$\pm$0.00018 (@4~T applied
field) for iron and 0.018845$\pm0.000053$ (@2~T applied field) for nickel.

Instrumentation and Detectors;Nuclear Experiment