Re: What is adiabatic nuclear demagnetization?

Dear Sue!

Adiabatic demagnetization is an ingenious method to achieve very low temperatures. It depends on a simple thermodynamical fact: If one blocks all heat flow to and from a system, the overall entropy in the system cannot change (change in entropy is heat flow devided by temperature). Entropy is a measure for the disorder in a system, and is thus a statistical concept.

The systems used for such experiments are so-called spin systems. The most well-known spin system is a magnet: Imagine a magnetic material as being a collection of very tiny elementary magnets (the spins) which can align in an external magnetic field. It might even be possible than when the external field is switched off, some magnetism remains because the spins align due to the fields of their neighbours (that would be a ferromagnet then), but let's disregard this effect for now.

The next step is to understand how such a system behaves at a temperature above absolute zero. If there is an external magnetic field, the spins will tend to align themselves to it, but the temperature will try to reverse that effect: temperature means that the spins tend to `jitter' around the direction they try to maintain due to the external magnetic field. Now imagine the following process: Apply a low temperature to a spin system (maybe that of liquid Helium, about 1K) together with a magnetic field. The spins will more or less align with the field. Let the whole thing settle to equlibrium and then disconnect the system from the liquid He. It is now thermally insulated, which means that the system's entropy cannot change any more: Any changes are adiabatic, in physicist's speak. Nothing will happen so far. Then lower the magnetic field gradually down to zero, and the temperature will drop. Why? Because the entropy in the system depends solely on the quotient between B/T the magnetic field and the temperature. If the entropy stays constant while the magntic field gets weaker, the temperature must drop!

A physical, intuitive explanation of this process is not easy to get. When switching off the magnetic field, the spins would like to get back into some more chaotic, disordered state. But this is impossible because the entropy cannot change due to thermal insulation! The only way out is a drop in temperature. There is actually a simpler system in which the process is entirely clear: Imagine a container with some gas in it. Put the container in thermal contact with a heat bath of constant temperature T. There is a piston which can compress the gas inside. Compress the gas to some amount and wait till everything is equlibrated again (i.e. the gas has assumed the temperature of the heat bath, T). This situation is now equivalent to the magnetic system with liquid He and magnetic field applied. Now disconnect the container from the heat bath ( <-> pump off the liquid He) and let the gas expand freely, pushing the piston out ( <-> lower the magnetic field to zero). The temperature of the gas will drop, because the work that is done on the piston must be applied by the gas alone. As there is no thermal contact with anything, the energy needed must come from the kinetic energy of the gas molecules and the temperature must go down. The microscopic situation (gas molecules pushing the piston, losing energy etc.) is not quite in analogy with the spin system, but the statistical picture is: When the piston moves outward, there is now more room for the gas molecules. If the system weren't thermally insulated, there would thus be more disorder. But due to the insulation the gain in space must be compensated by a loss in energy in order to leave the entropy constant. In the case of the magnetic system lowering the magnetic field also, in a sense, gives more `room' to the spins (due to some effects I cannot explain in detail here), and due to the adiabaticity the temperature goes down.

Now there are some remaining questions I have not addressed but which may come to your mind:

1. Why does the temperature not drop to absolute zero? If B/T stays constant while B is lowered to zero, T must surely vanish as well! That this is not the case is due to the fact that the picture I have sketched above is a little bit too simplified. In reality, the spins are not completely independent from each other but their magnetic fields influence neighbouring spins. So when the external field is zero, each individual spin still `feels' a small magnetic field that comes from the neighbouring spins, and so there is a `residual' temperature below which this procedure can not take us. One can of course attempt to select materials in which this mutual interaction (also called coupling) is especially low. Usually the spins are carried by the electrons in the atom. But the coupling between nuclear spins is much weaker. So if it is possible to find a material in which electron spins do not contribute significantly to magnetism, nuclear adiabatic demagnetization can be used to reach temperatures in the microkelvin range.
2. Why does the magnetic field have to be switched off gradually? This is because the spins are not the only objects in a material which can carry thermal energy. There is also the atomic lattice, in which the individual atoms or molecules can vibrate around their rest positions. At room temperature, lattice vibrations do indeed form the predominant `storage' for thermal energy, and the spins are completely unimportant. At low T, one has to make sure that changes of external conditions (like the magnetic field) take place slowly enough to let the spin system and the lattice equlibrate at every moment.