Half-metallic magnetism and electronic structures of CrPSe<sub>3</sub> monolayers with multiple Dirac cones<span style="background-color: rgb(255, 255, 255);"><span style="color:#ff0000;">（withdraw）</span></span>

Abstract

According to the first-principles calculation within PBE+<em>U</em> method and tight-binding model, the magnetic properties and electronic structures of two-dimensional (2D) CrPSe<sub>3</sub> monolayer were investigated. Constructed by a Cr-honeycomb hexagonal lattice, 2D CrPSe<sub>3</sub> was predicted to be in a half-metallic ferromagnetic state with dynamic stability, confirmed by the phonon spectrum with no imaginary dispersion. The Curie temperature was estimated as 224 K by Monte Carlo simulation within the Metropolis algorithm under the periodic boundary condition. The thermal stability of CrPSe<sub>3</sub> monolayer was estimated at 300 K by a first-principles molecular dynamics simulation. It is found that the magnetic ground state of CrPSe<sub>3</sub> monolayer is determined by a competition between the antiferomagnetic d-d direct exchange interactions and the Se-p orbitals mediated ferromagnetic p-d superexchange interactions. Most interestingly, in the half-metallic state the band structure exhibits multiple Dirac cones in the first Brillouin zone: two cones at <em>K</em> point showing a very high Fermi velocity<inline-formula><tex-math id="M6">\begin{document}${v_{\rm F}{(K)}} = 15.8 \times 10^5 \;{\rm m \!\cdot\! s^{-1}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M6.jpg"></graphic><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M6.png"></graphic></alternatives></inline-formula> about twice larger than the <inline-formula><tex-math id="M7">\begin{document}$ v_{\rm F} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M7.jpg"></graphic><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M7.png"></graphic></alternatives></inline-formula> of graphene in the vicinity of Fermi level, and six cones at <inline-formula><tex-math id="M8">\begin{document}$ K'/2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M8.jpg"></graphic><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M8.png"></graphic></alternatives></inline-formula> points with <inline-formula><tex-math id="M9">\begin{document}${ v_{\rm F} {(K'/2)}} = 10.1 \times 10^5\;{\rm m \!\cdot\! s^{-1}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M9.jpg"></graphic><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M9.png"></graphic></alternatives></inline-formula> close to the graphene's value. These spin-polarized Dirac cones are mostly composed of Cr <inline-formula><tex-math id="M10">\begin{document}${\rm d}_{xz}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M10.jpg"></graphic><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M10.png"></graphic></alternatives></inline-formula> and <inline-formula><tex-math id="M11">\begin{document}${\rm d}_{yz}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M11.jpg"></graphic><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20200960_M11.png"></graphic></alternatives></inline-formula> orbitals. The novel electronic structure of CrPSe<sub>3</sub> monolayer is also confirmed by the HSE06 functional. A tight-binding model was built based on the Cr-honeycomb structure with two Cr-d orbitals as the basic with the first, second and third nearest-neighboring interactions, further demonstrating that the multiple Dirac cones are protected by the Cr-honeycomb lattice symmetry. Our findings indicate that 2D CrPSe<sub>3</sub> monolayer is a candidate with potential applications in the low-dimensional, high speed and temperature spintronics.