Giant valley polarization and perpendicular magnetocrystalline anisotropy energy in monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math> (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mi>Ru</mml:mi><mml:mo>,</mml:mo><mml:mi>Os</mml:mi></mml:mrow></mml:math>; <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>Cl</mml:mi><mml:mo>,</mml:mo><mml:mi>Br</mml:mi></mml:mrow></mml:math>)
Weifeng Xie, Long Zhang, Yunliang Yue, Min Li, Hui Wang
Abstract
Large valley polarization and perpendicular magnetocrystalline anisotropy energy (PMAE) in room-temperature ferrovalley materials has been pursued for a long time because PMAE not only stabilizes long-range ferromagnetic (FM) order but also ensures spontaneous valley polarization. Herein, valley polarization and MAE of monolayer $M{X}_{2}$ ($M=\mathrm{Ru},\mathrm{Os}$; $X=\mathrm{Cl},\mathrm{Br}$) are investigated based on first-principles calculations, Wannier functions, and Monte Carlo simulations. It is found that $\mathrm{Os}{\mathrm{Br}}_{2}$ has a giant valley polarization of 327.158 meV and PMAE of 10.354 meV, ascribing to the strong spin-orbital coupling. The physical mechanism of valley polarization and PMAE are analyzed both qualitatively and quantitatively on the basis of perturbation theory, which shows that the valley polarization induces the distribution of MAE at $K$ and ${K}^{\ensuremath{'}}$ valley points with opposite signs, and the couplings between ${d}_{{z}^{2}}$ and ${d}_{yz}, {d}_{xz}$ and ${d}_{xy}$, and ${d}_{{x}^{2}\text{\ensuremath{-}}{y}^{2}}$ and ${d}_{yz}$ in opposite spin channels through orbital angular momentum operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{L}}_{x}$ have a dominant contribution to the total MAE. Moreover, doping of a few holes and biaxial compressive strain both remarkably improve the PMAE of $\mathrm{Os}{\mathrm{Br}}_{2}$. Meanwhile, the compressive strain can enhance FM exchange coupling of $\mathrm{Os}{\mathrm{Br}}_{2}$, increasing the Curie temperature ${T}_{c}$ far beyond the room temperature. Additionally, doping of a few electrons can significantly increase the PMAE of room-temperature ferrovalley $\mathrm{Os}{\mathrm{Cl}}_{2}$ to reach \ensuremath{\sim}40 meV. In this paper, we elucidate the physical mechanism of the valley polarization and MAE and indicate that monolayer $\mathrm{Os}{\mathrm{Cl}}_{2}$ and $\mathrm{Os}{\mathrm{Br}}_{2}$ are promising for application in valleytronic and magnetic storage devices at room-temperature condition.