Elliptical spin textures in two-dimensional semimetals with spatially anisotropic Dzyaloshinskii-Moriya interaction

Elliptical skyrmions within epitaxial bulk materials have been intensively studied due to their intriguing dynamics behaviors. In two-dimensional materials, however, elliptical spin textures are rarely explored. In this paper, we investigate various properties of ${\text{V}X}_2$ via first-principles calculations and Monte Carlo simulations. At zero external field, the $\text{sub}\text{−}10\mathrm{nm}$ circular antiskyrmions are obtained in the monolayer ${\mathrm{VTe}}_2$. Interestingly, these antiskyrmions can be transformed into bimerons and elliptical antiskyrmions under biaxial and uniaxial strains. More importantly, even without strains and external fields, the intrinsic elliptical antiskyrmions and bimerons are discovered in monolayer $\text{V}XY$ ($X,Y=$ S, Se, Te), which present rather high Curie temperatures. These spin textures exhibit stability over a wide temperature range. Our results provide a very feasible approach to realizing elliptical spin textures in two-dimensional materials.

Figure 1

Top and side views of monolayer (a) ${\text{V}X}_2$ and (b) $\mathrm{V}XY$, where $X/Y$ represents different chalcogen atoms (S, Se, and Te). Red: V atom; black yellow: $X$ atom; green: $Y$ atom. (c) Highlights the tetrahedral coordination of the V atom with nearest-neighbor $X$ atoms and the scheme of V tetrahedron molecular orbitals of atomic $d$ orbitals. (d) The charge density difference and projected density of states (PDOS) of the monolayer ${\mathrm{VTe}}_2$ and VSeTe, where the yellow (blue) area represents the net charge gain (loss).

Figure 2

Calculated phonon dispersions of (a)–(c) ${\text{V}X}_2$ and (d)–(f) $\text{V}XY$ systems.

Figure 3

(a)–(c) The band structures of ${\text{V}X}_2$ under biaxial strain. Black and red markers represent spin-up and spin-down orbitals respectively. The Fermi levels are set to be zero. (d)–(f) The electronic band structures of monolayer ${\text{V}X}_2$ with considering the effect of spin-orbit coupling. The blue and red dashed lines represent the band structures with the magnetic moment along the out-of-plane $z$ axis and the in-plane $x$ axis, respectively.

Figure 4

(a) Left: The calculated anisotropic DMI of the monolayer ${\text{V}X}_2$. Yellow and red bars indicate the DMI components of nearest-neighboring magnetic atoms along $x$ and $y$ directions, respectively. Here, $d_{\parallel }>0$ ($d_{\parallel }<0$) represents the anticlockwise (clockwise) chirality. Right: Atomic-resolved localization of the DMI associated spin-orbit coupling energy difference between clockwise and anticlockwise chiralities in the monolayer ${\text{V}X}_2$. (b) The exchange couplings $J_1, J_2$, the magnetic anisotropy $K$, the criterion $k$ (in set) for the systems with the magnetic atom arranging in the 2D square lattice and the DMI component $d_{\parallel }$ as a function of the biaxial strain in the monolayer ${\mathrm{VTe}}_2$. Strain $\%<0$(strain $\%>0$) represent compressive strain (tensile strain). (c) The PDOS of the Te atom as a function of the biaxial strain in the monolayer ${\mathrm{VTe}}_2$. (d) The phase of spin textures under biaxial strain for the monolayer ${\mathrm{VTe}}_2$ quenched to 0.001 K from a high temperature state. (e)–(f) The magnetic topological charge $Q$, the specific heat $C_v$ and the spin texture of ${\mathrm{VTe}}_2$ as functions of the temperature at the biaxial strain of $-5\%$ and $-3\%$.

Figure 5

(a) The exchange couplings $J_1, J_2$, the magnetic anisotropy $K$, and the DMI component $d_{\parallel }$ as a function of the uniaxial strain in the monolayer ${\mathrm{VTe}}_2$. (b) Phase of spin textures under uniaxial strain and temperature for the monolayer ${\mathrm{VTe}}_2$. (c) Atomic-resolved localization of the DMI associated spin-orbit coupling energy difference between clockwise and anticlockwise chirality as a function of the uniaxial strain in monolayer ${\text{V}X}_2$. (d) The magnetic topological charge $Q$, the specific heat $C_v$ and the spin texture of ${\mathrm{VTe}}_2$ versus temperature at the uniaxial strain of $-3\%$.

Figure 6

(a) The magnetic anisotropy $K$ of monolayer $\text{V}XY$. (b) The orbital-resolved MAE of Se-p and Te-p orbitals of the monolayer VSeTe. (c) The calculated anisotropic DMI and the atomic-resolved localization of the DMI associated SOC energy difference of monolayer $\text{V}XY$. (d)–(e) The average magnetization $M$, the magnetic topological charge $Q$ and the specific heat $C_v$ of VSSe and VSeTe under increasing temperature.