In Praise of Praseodymium

Praseodymium is one of only a few elements in the periodic table that are regularly found in non-trivial but non-magnetic electronic configurations: i.e. having partially filled orbitals that do not possess a magnetic moment.  The resulting orbital degrees of freedom can give rise to novel properties. Examples include the quadrupolar Kondo effect and exotic superconductivity in the so-called 1-2-20 compounds (e.g. PrTi₂Al₂₀), and hyperfine-enhanced magnetism in Pr metal and in PrNi₅. Following an overview of this physics, I will discuss PrOs₄Sb₁₂, which has a magnetic-field-induced "antiferroquadrupolar" ordered phase, resulting from the crossing of singlet and triplet states at a quantum critical point. The simple, but rather fun, physics of this phase is enriched by hyperfine coupling to the nuclear moments of the Pr ion, which leads to unusual critical behaviour, at millikelvin temperatures, involving an admixture of nuclear and electronic degrees of freedom.