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

TL;DR

This paper proposes a model for spin-1 Dirac systems in 2D ferromagnetic monolayers, predicting novel topological phases and flat-band ferromagnetism relevant for spintronics and quantum Hall effects.

Contribution

It introduces a three-band tight binding model on dice lattice showing new spin-1 Dirac phases in ferromagnetic monolayers with first-principles validation.

Findings

FeBr2 and FeCl2 are spin-1 Dirac half-metals under strain.

CoBr2 and CoCl2 are spin-1 Dirac spin-gapless semiconductors.

Flat-band ferromagnetism leads to quantum anomalous Hall state with Chern number -2.

Abstract

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.