Staggered Hastatic order: the role of magnetic field and relevance to PrV₂Al₂₀

Materials with a non-Kramers doublet ground state exhibit valence fluctuations to an excited Kramers doublet, realizing the two channel Kondo effect and requiring that any heavy Fermi liquid breaks some symmetry. PrV₂Al₂₀, which has a cubic Γ₃ 4f² non-Kramers doublet ground state and displays strong conduction and f electron coupling, serves as a promising candidate. However, its phase diagram in magnetic field is still a puzzle. Here, we explore the channel symmetry breaking heavy Fermi liquid, also known as hastatic order, within a simple two-channel Kondo-Heisenberg model. Particularly, we investigate the competition or cooperation among a uniform or staggered hastatic order and magnetism, and how that is affected by magnetic field. We show that, with reasonable parameters, one can roughly reproduce the PrV₂Al₂₀ in-field phase diagram. We find that as the magnetic field increases, the system undergoes a first order transition from staggered into uniform hastatic order, which then is also suppressed by higher field. We also discuss possible experimental measurements are to test these results.