Comparing hastatic and quadrupolar order in cubic Pr-1-2-20 systems

Non-Kramers doublet materials can host a variety of interesting phases including quadrupolar order, superconductivity, and hastatic order. The latter state is a symmetry-breaking heavy Fermi liquid or Kondo insulator arising from valence fluctuations of the non-Kramers level to an excited Kramers doublet. We use a slave boson mean-field analysis of a simple yet realistic two-channel Anderson lattice model to contrast the experimental signatures of the spatially uniform hastatic state with those of ferroquadrupolar order, noting the challenges in distinguishing the two states experimentally. In particular, measurements of time-reversal symmetry breaking are found to be essential. These issues are exemplified by the PrT₂Al₂₀ (T=Ti, V) materials. In PrTi₂Al₂₀, ferroquadrupolar ordering was observed without evidence of hastatic order. The situation is more complicated for PrV₂Al₂₀, where a suspected antiferroquadrupolar phase undergoes a first order transition in magnetic field below 2 T. We discuss the possibility that this feature represents the development of the hastatic ordered state, and how this scenario may be experimentally tested.