Tunable magnetism in bilayer transition metal dichalcogenides

Twist between neighboring layers and variation of interlayer distance are two extra ways to control the physical properties of stacked two-dimensional van der Waals materials without alteration of chemical compositions or application of external fields compared to their monolayer counterparts. In this work, we explored the dependence of the magnetic states of the untwisted and twisted bilayer 1T-${\mathrm{VX}}_2$ ($X$ = S, Se) on the interlayer distance by density functional theory calculations. We find that, while a magnetic phase transition occurs from interlayer ferromagnetism to interlayer antiferromagnetism either as a function of decreasing interlayer distance for the untwisted bilayer 1T-${\mathrm{VX}}_2$ or after twist, richer magnetic phase transitions consecutively take place for the twisted bilayer 1T-${\mathrm{VX}}_2$ as interlayer distance is gradually reduced. Besides, the critical pressures for the phase transition are greatly reduced in twisted bilayer 1T-${\mathrm{VX}}_2$ compared with the untwisted case. We derived the Heisenberg model with intralayer and interlayer exchange couplings to comprehend the emergence of various magnetic states. Our results point out an easy access toward tunable two-dimensional magnets.

Figure 1

The energy difference between FM and LAFM $E_{FM}-E_{\mathrm{LAFM}}$ as a function of the interlayer distance for untwisted 1T-${\mathrm{VX}}_2$. The inset demonstrates the specific configurations of FM and LAFM, where the orange dot arrow and orange (black) line arrow denote the spin up in the bottom layer and the spin up (down) in the top layer, respectively.

Figure 2

The superexchange couplings in untwisted 1T-${\mathrm{VSe}}_2$ as functions of the interlayer distance. The nearest-neighbor intralayer coupling $J_0$, nearest-neighbor interlayer coupling $J_{1\perp }$, and next-nearest-neighbor interlayer coupling $J_{2\perp }$ are illustrated in the inset.

Figure 3

(a) The schematic diagram of magnetic phase transitions in the twisted bilayer 1T-${\mathrm{VS}}_2$ and 1T-${\mathrm{VSe}}_2$ as functions of interlayer distance. (b) The specific configurations of LAFM, FM, AFM1, and AFM2, where the orange (black) dot arrow and orange (black) line arrow denote the spin up (down) in the bottom layer and the spin up (down) in the top layer, respectively.

Figure 4

(a) The top view of twisted bilayer 1T-${\mathrm{VX}}_2$ with twisted angle $\theta =21.{79}^{\circ }$, where the red, blue, and green balls denote V atoms in the top layer, V atoms in the bottom layer, and X atoms, respectively. By treating the total magnetic moment of three nonoverlap V atoms with $C_3$ rotational symmetry [located at the vertexes of each triangle in (a)] in the supercell at each layer as an effective magnetic moment, twisted bilayer 1T-${\mathrm{VX}}_2$ can be mapped onto an effective AA stacking bilayer triangular lattice. The top view (b) and side view (c) of the effective AA stacking bilayer triangular lattice, where the intralayer nearest-neighbor coupling $J_0^{\prime }$ is shown in (b) and interlayer couplings $J_{\perp }, J_{AO1}, J_{AO2}, J_{11}, J_{OO}$, and $J_{22}$ are presented in (c). (d) The superexchange couplings $J_0^{\prime }, J_{\perp }, J_{AO1}, J_{AO2}, J_{11}, J_{OO}$, and $J_{22}$ as functions of interlayer distance. (e) The superexchange couplings of twisted bilayer 1T-${\mathrm{VS}}_2$ and 1T-${\mathrm{VSe}}_2$ at interlayer distance of 2.32 Å and 2.62 Å, respectively