Cubic hastatic order in the two-channel Kondo-Heisenberg model

Materials with non-Kramers doublet ground states naturally manifest the two-channel Kondo effect, as the valence fluctuations are from a non-Kramers doublet ground state to an excited Kramers doublet. Here, the development of a heavy Fermi liquid requires a channel symmetry breaking spinorial hybridization that breaks both single and double time-reversal symmetry, and is known as hastatic order. Motivated by cubic Pr-based materials with $\Gamma_3$ non-Kramers ground state doublets, this paper provides a survey of cubic hastatic order using the simple two-channel Kondo-Heisenberg model. Hastatic order necessarily breaks time-reversal symmetry, but the spatial arrangement of the hybridization spinor can be either uniform (ferrohastatic) or break additional lattice symmetries (antiferrohastatic). The experimental signatures of both orders are presented in detail, and include tiny conduction electron magnetic moments. Interestingly, there can be several distinct antiferrohastatic orders with the same moment pattern that break different lattice symmetries, revealing a potential experimental route to detect the spinorial nature of the hybridization. We employ an SU(N) fermionic mean-field treatment on square and simple cubic lattices, and examine how the nature and stability of hastatic order varies as we vary the Heisenberg coupling, conduction electron density, band degeneracies, and apply both channel and spin symmetry breaking fields. We find that both ferrohastatic and several types of antiferrohastatic orders are stabilized in different regions of the mean-field phase diagram, and evolve differently in strain and magnetic fields.