  We report results of infrared imaging and spectroscopic observations of the
SN 1006 remnant, carried out with the Spitzer Space Telescope. The 24 micron
image from MIPS clearly shows faint filamentary emission along the northwest
rim of the remnant shell, nearly coincident with the Balmer filaments that
delineate the present position of the expanding shock. The 24 micron emission
traces the Balmer filaments almost perfectly, but lies a few arcsec within,
indicating an origin in interstellar dust heated by the shock. Subsequent
decline in the IR behind the shock is presumably due largely to grain
destruction through sputtering. The emission drops far more rapidly than
current models predict, however, even for a higher proportion of small grains
than would be found closer to the Galactic plane. The rapid drop may result in
part from a grain density that has always been lower -- a relic effect from an
earlier epoch when the shock was encountering a lower density -- but higher
grain destruction rates still seem to be required. Spectra from three positions
along the NW filament from the IRS instrument all show only a featureless
continuum, consistent with thermal emission from warm dust. The dust-to-gas
mass ratio in the pre-shock interstellar medium is lower than that expected for
the Galactic ISM -- as has also been observed in the analysis of IR emission
from other SNRs but whose cause remains unclear. As with other SN Ia remnants,
SN 1006 shows no evidence for dust grain formation in the supernova ejecta.
