Landau Theory of Multipolar Order in Pr(TM)2X20 Kondo materials

A series of Pr(TM)2X20 (with TM=Ti,V,Rh,Ir and X=Al,Zn) Kondo materials exhibits exotic behavior such as quadrupolar order, superconductivity and non-Fermi liquid behavior. In particular, non-Kramers Pr3+ 4f2 moments show interesting magnetic field dependence with multipolar orderings.
In this paper, by taking into account both quadrupolar and octupolar moments of non-Kramers doublet in Pr3+, we study magnetic field effect of multipolar orderings based on a simple Landau theory. We discuss the unique features of two different cases with fields; pure ferroquadrupolar order, antiferroquadrupolar order coexisting with octupolar ordering. Based on our theory, we also provide understanding of experimental results on a series of Pr(TM)2X20 materials.