Radio relics are patches of diffuse synchrotron radio emission that trace shock waves. Relics are thought to form when intra-cluster medium electrons are accelerated by cluster merger induced shock waves through the diffusive shock acceleration mechanism. In this paper, we present observations spanning 150 MHz to 30 GHz of the `Sausage and `Toothbrush relics from the Giant Metrewave and Westerbork telescopes, the Karl G. Jansky Very Large Array, the Effelsberg telescope, the Arcminute Microkelvin Imager and Combined Array for Research in Millimeter-wave Astronomy. We detect both relics at 30 GHz, where the previous highest frequency detection was at 16 GHz. The integrated radio spectra of both sources clearly steepen above 2 GHz, at the >6$sigma$ significance level, supports the spectral steepening previously found in the `Sausage and the Abell 2256 relic. Our results challenge the widely adopted simple formation mechanism of radio relics and suggest more complicated models have to be developed that, for example, involve re-acceleration of aged seed electrons.
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