Adiabatic magnetization of superconductors as a high-performance cooling mechanism

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 $\mu \text{K}$ regime.

Figure 1

(Color online) Adiabatic magnetization of a superconductor. Solid curves describe the entropy $\mathcal{S}$ of a metal in the N state and in the S state as a function of the reduced temperature. When a magnetic field is applied on a thermally isolated superconductor at $T_i$, the metal is driven into the N state $\left(A\to B\right)$ and the temperature decreases down to $T_f$. Dashed lines refer to the entropy in the intermediate state.

Figure 2

(Color online) Final temperature $T_f$ vs initial temperature $T_i$ for several type-I superconductors in the absence of dissipative effects.

Figure 3

(Color online) (a) Time evolution of $T_f$ in the intermediate state calculated at $T_i=250\text{mK}$ for three values of $\tau$. The inset shows a scheme of the adiabatic magnetization cooler. (b) Full time evolution of $T_f$ calculated at three different $T_i$ for $\tau =1\text{h}$. Dashed curves refer to $P_{load}\ne 0$: from bottom to top, $P_{load}=10\text{pW}$, 1 nW, and 100 nW. All calculations were performed for Ta (see text).