Tunable magnetocrystalline anisotropy and valley polarization in an intrinsic ferromagnetic Janus $2H$-VTeSe monolayer

Two-dimensional Janus monolayers with specular asymmetry exhibit excellent physicochemical properties and are a good candidate for optoelectronic, valley electronic, and nanoelectronics devices. Based on the density functional theory, the Janus $2H$-VTeSe monolayer is an intrinsic ferromagnetic semiconductor with an indirect band gap of 0.324 eV and exhibits a good thermodynamic and kinetic stability, in-plane magnetocrystal anisotropy, large spontaneous valley polarization of 155 meV, and high Curie temperature ($T_c$) of 380 K. The biaxial strain ($-6\%<\varepsilon <6\%$) can effectively tune the Janus $2H$-VTeSe monolayer from the bipolar magnetic semiconductor phase to half-semiconductor, spin gapless semiconductor, and half-metallic phases. Moreover, the magnetocrystal anisotropy energy (MAE) is modulated by the strain from 0.54 meV ($\varepsilon =-6\%$) to 1.32 meV ($\varepsilon =-2\%$), and the easy [100] and hard [001] magnetic axes could be switched from each other by charge carrier doping. The calculated valley optical response of the Janus $2H$-VTeSe monolayer exhibits a valley-selective circular dichroism. Due to the broken inversion and time-reversal symmetry, the valley polarization and Berry curvature can be continuously tuned by applying biaxial strains (modulation range 24.2%), external electric field (modulation range 2%), and varying the magnetization angle (0 to 180 degrees). The Janus $2H$-VTeSe monolayer possesses intrinsic ferromagnetic ordering, large spontaneous valley polarization, high $T_c$ of 380 K, and considerable MAE of 1.15 meV, giving it a potential application in the two-dimensional spintronic devices.

Figure 1

(a) Top and side views of the Janus $2H$-VTeSe monolayer. Purple, red, and green spheres represent Te, V, and Se atoms, respectively. (b) The evaluation of total free energy and magnetic moment during the 9 ps AIMD simulation for the $6\times 6\times 1$ Janus $2H$-VTeSe monolayer. The inset is the initial (0 ps) and final (9 ps) supercells at 300 K. (c) The phonon spectrum of the Janus $2H$-VTeSe monolayer. (d) Evolution of magnetic moment (red) and specific heat capacity (blue) for the Janus $2H$-VTeSe monolayer in the $16\times 16\times 1$ superlattice based on the Monte Carlo simulation. The inset is the exchange path for the first (J1) and second (J2) nearest-neighbor V (red) pairs.

Figure 2

(a) The spin polarization band structure of the Janus $2H$-VTeSe monolayer. The red and blue lines indicate spin-up $(\alpha$) and spin-down ($\beta$) electrons, respectively. (b) The band structure of the Janus $2H$-VTeSe monolayer, considering SOC along the [001] direction in $\mathrm{DFT}+U$ and MLWFs, respectively. (c) The band structure with the projection of spin operator ${\widehat{S}}_{\mathrm{z}}$ (color map). The red and blue colors indicate the spin-up and spin-down states, respectively. The Fermi level is set to zero.

Figure 3

(a) The dependence of band gap energy on biaxial strain. The red, blue, and black lines indicate $E_{\mathrm{G}-\alpha }$ (spin up), $E_{\mathrm{G}-\beta }$ (spin down), and $E_{\mathrm{G}}$ (total), respectively. The (b) total and (c) atomic-layer-resolved magnetocrystal anisotropy energies (MAEs) of the Janus $2H$-VTeSe monolayer under various biaxial strains.

Figure 4

(a) V $d$, (b) Te $p$, and (c) Se $p$ orbital-resolved MAE for the Janus $2H$-VTeSe monolayer at the strain of $-6\%$, 0%, and 6%.

Figure 5

(a) The circular polarization ${\eta }^{C,V}\left(k\right)$ of the optical transition between the VBM and CBM in the first Brillouin zone. The color scale indicates the values of ${\eta }^{C,V}\left(k\right)$ over the Brillouin zone. Calculated Berry curvature ${\mathrm{\Omega }}_n\left(k\right)$ of the Janus $2H$-VTeSe monolayer along (b) high-symmetry lines and (c) over the 2D Brillouin zone. (d) Calculated anomalous Hall conductivity of the Janus $2H$-VTeSe monolayer. The two parallel lines indicate the two valley extremes. The magnetization vector along the out-of-plane [001] direction is considered for the above calculations.

Figure 6

The biaxial strain modulated (a) band structure, (b) valley gaps $\mathrm{\Delta }K(\mathrm{\Delta }{K}^{\prime }$) and valley polarization (${\mathrm{\Delta }}_{{KK}^{\prime }}$), and (c) Berry curvature along high-symmetry lines of the Janus $2H$-VTeSe monolayer.

Figure 7

The modulation of (a) band structures, (b) valley gaps $\mathrm{\Delta }K(\mathrm{\Delta }{K}^{\prime }$) and (the inset) valley polarization (${\mathrm{\Delta }}_{{KK}^{\prime }}$), and (c) Berry curvature along high-symmetry lines of the Janus $2H$-VTeSe monolayer by changing the magnetization angles $\theta$ between the magnetic moment and the $z$ direction. The inset indicates the polar angle and the rotation plane of the magnetization direction.

Figure 8

The external electric-field dependence of (a) band structure, (b) valley gaps $\mathrm{\Delta }K(\mathrm{\Delta }{K}^{\prime }$) and (the inset) valley polarization (${\mathrm{\Delta }}_{{KK}^{\prime }}$), and (c) Berry curvature along high-symmetry lines for the Janus $2H$-VTeSe monolayer.