First-principles calculations and a tight-binding analysis predict that the iron-pnictide BaCrFeAs2 is a promising candidate for half-metallic material with fully compensated magnetization. The transition metal ions Cr and Fe prefer the three-dimensional intervening lattice, which yields the antiferromagnetic order of spin orientations. Due to the difference between Cr and Fe in the electronegativity, a band gap is opened at the Fermi level in the spin channel in which Fe provides the majority carriers. The selective hybridization between 3d orbitals of Cr and As:4p states due to the peculiar lattice structure of the iron-pnictide is shown to be crucial for the novel properties.

•Vortex states in three-component superconductor are investigated theoretically.•Superconducting state with broken time-reversal symmetry at zero field is focused.•In parameter regime derived analytically a vortex-cluster state is observed.•Superconductor with frustrated phases cannot be categorized to type-I and -II.Time-dependent Ginzburg–Landau (TDGL) approach is used to investigate vortex states at the vicinity of Tc in three-component superconductors with time-reversal symmetry breaking (TRSB). When the nucleation field Hn is slightly larger than the thermodynamic field Htc, vortices form a cluster indicating clearly that this is an exotic superconducting state which cannot be categorized to type-I and type-II.