Non-linear shock acceleration models predict a flattening of synchrotron radiation spectrum at higher frequencies .
For Cassiopeia A a synchrotron spectral flattening was previously reported for a small part of the remnant in the mid-infrared regime .
Here we present new measurements for spectral flattening using the archival radio ( 4.72 GHz ) and mid-infrared ( 3.6 \mu m ) data , and produce a complete spectral index map to investigate the spatial variations within the remnant .
Our result shows overall spectral flattening across the remnant ( \alpha \sim - 0.5 to -0.7 ) , with the flattest values coinciding with the locations of most recent particle acceleration .
In addition to overall flattening , we also detect a relatively steeper region in the Southeast of the remnant ( \alpha \sim - 0.67 ) .
We argue that this could be a signature of a cooling break , and estimate the lower limit of magnetic field to be B \sim 420 \mu G , consistent with other magnetic-field strength estimates .