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Spin-1 condensed matter systems characterized by the combination of aDirac-like dispersion and flat bands are ideal for realizing high-temperatureelectronics and spintronic technologies in the absence of external magneticfield. In this study, we propose a three-band tight binding model, withspin-polarized Haldane-like next-nearest-neighbour tunnelling, on dice latticeand show that spin-1 Dirac half-metal, spin-1 Dirac spin-gapless semiconductor,and spin-polarized spin-1 massive Dirac dispersion with nontrivial topology canexist in two-dimensional ferromagnetic condensed matter systems with electronspin polarization P = 1. The proposed spin-polarized spin-1 phases can berealized in ferromagnetic transition metal dihalides MX2 monolayerseffectively. By using first principle calculations, we show that a smallcompressive 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 = Coand X = Br, Cl. Spin-one Dirac spin-gapless semiconductors CoBr2 and CoCl2embeds flat band ferromagnetism where spin-orbit coupling opens a topologicallynon-trivial Dirac gap between dispersing valance and conduction band whileleaving flat band unaffected. The intrinsic flat-band ferromagnetism inspin-polarized spin-1 massive Dirac dispersion plays key role in materializingquantum anomalous Hall state with Chern number C = -2.

Spin-1 Dirac half-metal, spin-gapless semiconductor, and spin-polarized massive Dirac dispersion in transition metal dihalide monolayers