Adiabatic Demagnetization

Suppose that we take the spin-1/2 paramagnetic system discussed in the previous section, and thermally isolate it from its surroundings. In this case, the numbers of atoms in the spin-up and spin-down states cannot change, because the system is unable to get rid of excess energy. In other words, the ratio of the number of atoms in the spin-up state to the number of atoms in the spin-down state,

$$\frac{N_+}{N_-} = \frac{P_+}{P_-} = \exp\left(\frac{2\,\mu\,B}{k_B\,T}\right),$$ (5.351)

is fixed. Under these so-called adiabatic conditions, we find that $T\propto B$. This is known as the magnetocaloric effect.

The magnetocaloric effect is the basis of a method of cooling atomic systems down to very low temperatures that is known as adiabatic demagnetization. In this scheme, the sample is initially in thermal contact with liquid helium at $0.8$ K. The sample is then magnetized. In the process, heat is given off by the sample, and is conducted away by the liquid helium. Next, the sample is thermally isolated by pumping out the liquid helium. Finally, the sample is demagnetized, leading to a reduction in its temperature via the magnetocaloric effect. Temperatures as low as $10^{-8}$ K have been achieved by this method.