Competition and coexistence of magnetic and quadrupolar ordering

The large number of low-lying states of d- and f-shells supports a variety of order parameters. The effective dimensionality of the local Hilbert space depends on the strength, and kind, of intersite interactions. This gives rise to complicated phase diagrams, and an enhanced role of frustration and fluctuation effects. The general principles are illustrated on the example of the effect of a magnetic field on quadrupolar phase transitions in some Pr-based skutterudite compounds.