Liquid 3He is amazing stuff. Below temperatures of a few hundred milliKelvin it forms a model (and the original inspiration for) Landau Fermi liquid. Furthermore, below about 1 mK it forms two different superfluid states, involving Cooper pairs in a spin triplet state. This is the model case for unconventional superconductivity.
Liquid 3He is actually of great practical use since it the crucial ingredient of dilution refrigerations that allow cooling from a few Kelvin to temperatures as low milliKelvin.
But where do labs get 3He from?
Well, it is a very useful by-product of nuclear weapons production.
Currently, the scientific community (which consumes only about 1% of the supply) is experience supply problems and dramatic price increases (a 15-fold increase between 2004 and 2010).
Why is this happening?
Thankfully, we are cutting back on nuclear weapons production!
One practical way to solve this problem is to develop alternative materials for ultra-low temperature refrigeration; one possibility is by adiabatic demagnetisation. Indeed, this is the method that was first developed in the 1930s using paramagnetic salts to achieve temperatures below about 0.3 K (and was the basis of the 1949 Nobel Prize in Chemistry) and is the basis for nice undergraduate problems in thermodynamics and statistical mechanics. Simply the entropy is a function of B/T (where B is the magnetic field and T the temperature). One cools the system down in a fixed magnetic field, then adiabatic isolates it and reduces the magnetic field slowly. In the last step the entropy must not change and so the temperature must decrease. (This is shown as the red horizontal arrow in the figure below). This is also known as the magnetocaloric effect. The problem is that most paramagnetic materials are insulators and one would prefer to have a metallic material that is a good thermal conductor and can be "machined".
I learnt some of this from an interesting paper (that I actually looked at in preparing an undergraduate thermodynamics lecture about Maxwell relations).
Large magnetocaloric effect and adiabatic demagnetization refrigeration with YbPt2Sn
Dongjin Jang, Thomas Gruner, Alexander Steppke, Keisuke Mitsumoto, Christoph Geibel and Manuel Brando
The authors mention some basic unanswered science questions about why this material is a good candidate. Specifically, why is the Kondo temperature (associated with interaction of the magnetic moments of the Yb3+ ions with the conduction electrons) and the inter-ion magnetic interactions so low? This ensures that the spins act essentially like non-interacting spins (with a large entropy) down to less than 1 K.
A key figure is below, showing the entropy versus temperature at several different magnetic fields.