  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.
