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 \sim 46 d after the outburst onset , when the decay index changed from \alpha \sim 0.4 to \sim 4.5 . The flux decreased by a factor \sim 2 in the first \sim 50 d and then by a factor \sim 40 until November 2011 ( overall , by a factor \sim 70 in \sim 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 \sim 1 to \sim 0.6 keV . Diffuse X-ray emission extending up to 20 ^ { \prime \prime } 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 \sim 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 \sim 0.2-Ð0.3 mJy ( at 1.4 GHz ) in the older data .