Theoretical realization of fully spin-polarized nodal box with traversing Brillouin zone surface state

Magnetic topological materials have attracted much attention because of their exotic topological quantum physics arising from the interplay between spintronics, crystallography, magnetism, and topology. Based on first-principles calculations and crystal symmetry analysis, we present a lot of materials with fully spin-polarized nodal boxes in a ferromagnetic cubic structure. This nodal box is formed by six butterflylike nodal lines in the Brillouin zone when neglecting the weak spin-orbit coupling (SOC) mainly from F atoms. Such a fully spin-polarized nodal box is reported here. The ${M}_{110}$ mirror symmetry is not broken in [110] magnetization direction, thus leaving a symmetrically protected butterflylike nodal line on the (110) surface when the SOC is present. The band gaps of the nodal box induced by SOC are less than 1 meV due to the weak SOC effect. Our discovery fills the gap in the study of a fully spin-polarized nodal box in the magnetic system and provides a good research platform for studying the combination of new topological states and spintronics. Such a fully spin-polarized nodal box with unique Fermi surfaces and surface states traversing the Brillouin zone holds great promise for applications in catalysis and spin transport.