The adiabatic magnetization of a superconductor is a cooling principle proposed in the 1930s, which has remained mostly unexploited so far. Here we present a detailed dynamic description of the effect, computing the achievable final temperatures as well as the process time scales for different superconductors in various regimes. We show that, although in the experimental conditions explored so far the method is in fact inefficient, a suitable choice of initial temperatures and metals can lead to unexpectedly large cooling effect, even in the presence of dissipative phenomena. Our results suggest that this principle can be re-envisaged today as a performing refrigeration method to access the μK regime
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