  We present a long-term study of the 2011 outburst of the magnetar Swift
J1834.9-0846 carried out using new Chandra observations, as well as all the
available Swift, RXTE, and XMM-Newton data. The last observation was performed
on 2011 November 12, about 100 days after the onset of the bursting activity
that had led to the discovery of the source on 2011 August 07. This long time
span enabled us to refine the rotational ephemeris and observe a downturn in
the decay of the X-ray flux. Assuming a broken power law for the long-term
light curve, the break was at ~46 d after the outburst onset, when the decay
index changed from alpha ~ 0.4 to ~4.5. The flux decreased by a factor ~2 in
the first ~50 d and then by a factor ~40 until November 2011 (overall, by a
factor ~70 in ~100 d). At the same time, the spectrum, which was well described
by an absorbed blackbody all along the outburst, softened, the temperature
dropping from ~1 to ~0.6 keV. Diffuse X-ray emission extending up to 20" from
the source was clearly detected in all Chandra observations. Its spatial and
spectral properties, as well as its time evolution, are consistent with a
dust-scattering halo due to a single cloud located at a distance of
$\approx$200 pc from Swift J1834.9-0846, which should be in turn located at a
distance of ~5 kpc. Considering the time delay of the scattered photons, the
same dust cloud might also be responsible for the more extended emission
detected in XMM-Newton data taken in September 2011. We searched for the radio
signature of Swift J1834.9-0846 at radio frequencies using the Green Bank Radio
Telescope and in archival data collected at Parkes from 1998 to 2003. No
evidence for radio emission was found, down to a flux density of 0.05 mJy (at 2
GHz) during the outburst and ~0.2-0.3 mJy (at 1.4 GHz) in the older data.
