The integrated Spectral Energy Distributions ( SED ) of the Large Magellanic Cloud ( LMC ) and Small Magellanic Cloud ( SMC ) appear significantly flatter than expected from dust models based on their far-infrared and radio emission .
The origin of this millimetre excess is still unexplained , and is here investigated using the Planck data .
The integrated SED of the two galaxies before subtraction of the foreground ( Milky Way ) and background ( CMB fluctuations ) emission are in good agreement with previous determinations , confirming the presence of the millimetre excess .

The background CMB contribution is subtracted using an Internal Linear Combination ( ILC ) method performed locally around the galaxies .
The foreground emission from the Milky Way is subtracted as a Galactic H i template and the dust emissivity is derived in a region surrounding the two galaxies and dominated by Milky Way emission .
After subtraction , the remaining emission of both galaxies correlates closely with the atomic and molecular 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 IRAS-IRIS data at 100 \thinspace { \upmu m } 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 dust optical depth maps are used to constrain the thermal dust emissivity power law index ( \beta ) .
The average spectral index is found to be consistent with \beta = 1.5 and \beta = 1.2 below 500 \thinspace { \upmu m } 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 , unlike for the LMC where the SED remains consistent with \beta = 1.5 .
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 .