  We present late-time ($200-400$ days) near-infrared spectral evolution for
the Type Ia supernova SN 2005df. The spectra show numerous strong emission
features of [CoII], [CoIII], and [FeII] throughout the $0.8-1.8$\mu m region.
As the spectrum ages, the cobalt features fade as would be expected from the
decay of $^{56}$Co to $^{56}$Fe. We show that the strong and isolated [FeII]
emission line at $1.644$\mu m provides a unique tool to analyze near-infrared
spectra of Type Ia supernovae. Normalization of spectra to this line allows
separation of features produced by stable versus unstable isotopes of iron
group elements. We develop a new method of determining the initial central
density, $\rho_c$, and the magnetic field, $B$, of the white dwarf using the
width of the $1.644$\mu m line. The line width is sensitive because of electron
capture in the early stages of burning, which increases as a function of
density. The sensitivity of the line width to $B$ increase with time and the
effects of the magnetic field shift towards later times with decreasing
$\rho_c$. The initial central density for SN 2005df is measured as
$\rho_c=0.9(\pm0.2)$ (in $10^9$g/cm$^3$), which corresponds to a white dwarf
close to the Chandrasekhar mass ($\rm M_{Ch}$) with $\rm
M_{WD}=1.313(\pm0.034)$M$_{\odot}$ and systematic error less than
$0.04$M$_{\odot}$. Within $\rm M_{Ch}$ explosions, however, the central density
found for SN 2005df is very low for a H-accretor, possibly suggesting a helium
star companion or a tidally-disrupted white dwarf companion. As an alternative,
we suggest mixing of the central region. We find some support for high initial
magnetic fields of strength $10^6$G for SN 2005df, however, $0$G cannot be
ruled out because of noise in the spectra combined with low $\rho_c$.
