  Spin-1 condensed matter systems characterized by the combination of a
Dirac-like dispersion and flat bands are ideal for realizing high-temperature
electronics and spintronic technologies in the absence of external magnetic
field. In this study, we propose a three-band tight binding model, with
spin-polarized Haldane-like next-nearest-neighbour tunnelling, on dice lattice
and show that spin-1 Dirac half-metal, spin-1 Dirac spin-gapless semiconductor,
and spin-polarized spin-1 massive Dirac dispersion with nontrivial topology can
exist in two-dimensional ferromagnetic condensed matter systems with electron
spin polarization P = 1. The proposed spin-polarized spin-1 phases can be
realized in ferromagnetic transition metal dihalides MX2 monolayers
effectively. By using first principle calculations, we show that a small
compressive strain leads MX2 monolayers to be spin-one Dirac half-metal for M =
Fe and X = Br, Cl while spin-one Dirac spin-gapless semiconductor for M = Co
and X = Br, Cl. Spin-one Dirac spin-gapless semiconductors CoBr2 and CoCl2
embeds flat band ferromagnetism where spin-orbit coupling opens a topologically
non-trivial Dirac gap between dispersing valance and conduction band while
leaving flat band unaffected. The intrinsic flat-band ferromagnetism in
spin-polarized spin-1 massive Dirac dispersion plays key role in materializing
quantum anomalous Hall state with Chern number C = -2.

Mesoscale and Nanoscale Physics;Materials Science