Voltage-controllable colossal magnetocrystalline anisotropy in single-layer transition metal dichalcogenides

Materials with large magnetocrystalline anisotropy and strong electric field effects are highly needed to develop new types of memory devices based on electric field control of spin orientations. Instead of using modified transition metal films, we propose that certain monolayer transition metal dichalcogenides are the ideal candidate materials for this purpose. Using density functional calculations, we show that they exhibit not only a large magnetocrystalline anisotropy (MCA), but also colossal voltage modulation under an external field. Notably, in some materials such as ${\mathrm{CrSe}}_2$ and ${\mathrm{FeSe}}_2$, where spins show a strong preference for in-plane orientation, they can be switched to an out-of-plane direction. This effect is attributed to the large band character alteration that the transition metal $d$ states undergo around the Fermi energy due to the electric field. We further demonstrate that strain can also greatly change MCA, and can help to improve the modulation efficiency when combined with an electric field.

Figure 1

Atomic structures of single-layer $A{X}_2$. (a) and (c) are the top and side views of the $H$ phase, and (b) and (d) are top and side views of the $T$ phase. The shaded areas show the primitive unit cells with Bravais lattice vectors $\vec{a}$ and $\vec{b}$ ($|\vec{a}|=|\vec{b}|$). $h$ is the vertical distance between the chalcogen atom and transition metal atom and $\theta$ is the $X-A-X$ bond angle across the top and the bottom layers. Magenta spheres represent transition metal atoms ($A$) while blue and yellow spheres represent the top and the bottom layer chalcogen atoms ($X$), respectively.

Figure 2

The calculated MCA (in units of $\mathrm{erg}/{\mathrm{cm}}^2$) as a function of electric field ($F=0$, 0.25, 0.5, and 0.75 V/Å) for $T-{\mathrm{FeI}}_2$ (black lines), $T-{\mathrm{CrSe}}_2$ (red lines), $H-{\mathrm{FeSe}}_2$ (cyan lines), $H-{\mathrm{FeTe}}_2$ (yellow lines), $H-{\mathrm{TaS}}_2$ (blue lines), and $H-{\mathrm{TaSe}}_2$ (green lines) ($H-{\mathrm{FeTe}}_2$ is unstable when $F=0.75$ V/Å). Inset: Schematic diagrams for two magnetic orientations. The upper and lower ones represent the magnetization aligned along the out-of-plane [001] and in-plane [100] directions, respectively.

Figure 3

Energy- and $k$-resolved distribution of orbital character for electronic structures along high-symmetry lines for Fe $d$ orbitals in ${\mathrm{FeSe}}_2$ compound under an electric field of (a) 0, (b) 0.25, (c) 0.5, and (d) 0.75 V/Å, respectively. The left and right subpanels are majority- and minority-spin bands, respectively. The thickness represents the amplitude of the orbital character. Numerals refer to points on high-symmetry lines ($\mathrm{HSL}n, n=1$–5) where there are large changes in MCA.

Figure 4

Variation of relevant structural parameters vs electric field for the ${\mathrm{FeSe}}_2$ system. $h$ (Å) and $\theta$ (deg) represent, respectively, the vertical distance between the chalcogen atom and the transition metal atom, and the $X-A-X$ bond angles, while $\mathrm{\Delta }{M}_{\mathrm{orb}}$ (in units of ${\mu }_B$) is the orbital moment anisotropy.