The integrated Spectral Energy Distributions of the Large and Small Magellanic Cloud appear significantly flatter than expected from dust models based on their FIR and radio emission. The origin of this millimetre excess is still unexplained, and is here investigated using the Planck data. The background CMB contribution is subtracted using an ILC method performed locally around the galaxies. The foreground emission from the Milky Way is subtracted. After subtraction, the emission of both galaxies correlates closely with the gas emission of the LMC and SMC. The millimetre excess in the LMC can be explained by CMB fluctuations, but a significant excess is still present in the SMC SED. The Planck and IRIS data at 100 micron are combined to produce thermal dust temperature and optical depth maps of the two galaxies. The LMC temperature map shows the presence of a warm inner arm already found with the Spitzer data, but also shows the existence of a previously unidentified cold outer arm. Several cold regions are found along this arm, some of which are associated with known molecular clouds. The average emissivity spectral index is found to be consistent with beta=1.5 and beta=1.2 below 500 microns for the LMC and SMC respectively, significantly flatter than the values observed in the Milky Way. Furthermore, there is evidence in the SMC for a further flattening of the SED in the sub-mm. The spatial distribution of the millimetre dust excess in the SMC follows the gas and thermal dust distribution. Different models are explored in order to fit the dust emission in the SMC. It is concluded that the millimetre excess is unlikely to be caused by very cold dust emission and that it could be due to a combination of spinning dust. emission and thermal dust emission by more amorphous dust grains than those present in our Galaxy.
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