  We address a number of issues regarding solid state electron electric dipole
moment (EDM) experiments, focusing on gadolinium iron garnet (abbreviated GdIG,
chemical formula Gd$_3$Fe$_5$O$_{12}$) as a possible sample material. GdIG
maintains its high magnetic susceptibility down to 4.2 K, which enhances the
EDM-induced magnetization of a sample placed in an electric field. We estimate
that lattice polarizability gives rise to an EDM enhancement factor of
approximately 20. We also calculate the effect of the demagnetizing field for
various sample geometries and permeabilities. Measurements of intrinsic GdIG
magnetization noise are presented, and the fluctuation-dissipation theorem is
used to compare our data with the measurements of the imaginary part of GdIG
permeability at 4.2 K, showing good agreement above frequencies of a few hertz.
We also observe how the demagnetizing field suppresses the noise-induced
magnetic flux, confirming our calculations. The statistical sensitivity of an
EDM search based on a solid GdIG sample is estimated to be on the same level as
the present experimental limit. Such a measurement would be valuable, given the
completely different methods and systematics involved. The most significant
systematics in such an experiment are the magnetic hysteresis and the
magneto-electric effect. Our analysis shows that it should be possible to
control these at the level of statistical sensitivity.
