Introduction

Since the discovery of graphene1,2, two-dimensional (2D) nanostructures have attracted extensive attention because of their unusual physical, mechanical and chemical properties1,2,3,4,5,6,7,8. Among these 2D nanostructures, transition metal dichalcogenide (MX2) monolayers, where M is a transition metal element from group IV, group V, or group VI and X is a chalcogen (S, Se or Te), have been widely investigated because of their easy fabrication, distinctive electronic, optical and catalytic properties and multi-functional applications6,7,8,9,10,11,12,13,14. Particularly, the physical and chemical properties of transition metal dichalcogenide monolayers can be easily tuned by controlling the composition, functionalizing and applying external fields due to the abundant configurations of MX2, mechanic flexibility and surface activity15,16,17,18,19,20,21,22. As one of important physical properties, the magnetism of these 2D monolayers has been a hot research area for their applications into quantum devices, such as spintronics. Ferromagnetism had been reported to be present in perfect VX2 (X = S, Se and Te) monolayer23,24,25,26, NbS2 monolayers16 and zigzag MoS2 nanoribbons5,15. It was also reported that the ferromagnetism of 2D MX2 nanostructures can be efficiently enhanced by applying strain15,16,17 and controlled by hydrogenation26. For example, the magnetic properties of hydrogenated MoS2 monolayer can be tuned from non-magnetism, to ferromagnetism and further to non-magnetism with the increase of tension17. The switching between the antiferromagnetic and ferromagnetic ground states, however, has not been realized in two-dimensional nanostructures. Here, we report the realization of the switching on hydrogenated vanadium telluride (VTe2-H) monolayer by applying tension on the basis of first-principles calculations. We find that VTe2-H monolayer can be tuned from antiferromagnetic state to paramagnetic state and further to ferromagnetic state as tension increases. Accompanying with the magnetic evolution, we also show that its electrical character switches from semiconductor, to metal and further to half-metal with tension increasing.

Results and Discussion

The VTe2 monolayer with trigonal prismatic (2H) coordination and hydrogenation at one side (Figure 1) is first optimized to obtain the lattice parameters. A supercell with 4 unit cells (2 × 2 × 1) (Figure 1) is used to study its magnetic property. The ferromagnetic and anti-ferromagnetic spin alignments are shown in Figures 1c and 1d, respectively. The original lattice (c0 = 2a) is referring to its supercell's lattice under zero strain (7.462 Å). VTe2-H monolayer with extended lattice (c) is realized by stretching (see Figure 1a). The tension is defined as . A tension range of 0 to 15% is used in our calculations. The optimized structure shows that Te-V bond (Te without hydrogen cover) extends from 2.746 to 2.931 Å as the tension increasing from 0 to 15%, Te-V bond (Te with hydrogen cover) is 2.639 Å at zero tension and increases by 0.016 Å/1% tension and Te-H bond is 1.721 Å at zero tension and increases by 0.001 Å/1% tension.

Figure 1
figure 1

Representative structures of hydrogenated vanadium telluride (VTe2-H) monolayer.

(a) top view with uniform static tension, (b) tilted view, (c) ferromagnetic spin-alignment and (d) antiferromagnetic spin alignment.

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To find out the magnetic evolution of VTe2-H monolayer under tension, the exchange energy (ΔEAFM-FM), defined as ΔEAFM–FM = (EAFM – EFM)/N (where EFM and EAFM are the energies at ferromagnetic and anti-ferromagnetic states and N ( = 4) is the number of units in the supercell.), is calculated. We see that VTe2-H monolayer is anti-ferromagnetic with Eex = −13 meV under zero tension (Figure 2). The exchange energy (negative) initially decreases with the tension increasing and goes sharply down to bottom peak (−186 meV) at a tension of 2%. Then, the exchange energy (negative) increases with the tension increasing and reaches zero at a tension of ~8.6%, indicating that VTe2-H monolayer is anti-ferromagnetic with the tension less than 8.6%. Further increasing tension, the exchange energy becomes positive and increases with the applied tension, indicating that VTe2-H monolayer is ferromagnetic with the tension larger than 8.6%. To confirm the ground and metastable states of VTe2-H monolayer under tension, the energy difference between magnetic states (EFM and EAFM) and non-magnetic state (ENM), including ΔEFM-NM ( = (EFM – ENM)/N) and ΔEAFM-NM ( = (EAFM – ENM)/N), are calculated. The calculated energy difference between anti-ferromagnetic and non-magnetic states of VTe2-H monolayer shows that the anti-ferromagnetic state is more stable than non-magnetic state in the whole range of considered tension because its energy at anti-ferromagnetic state is lower than that at non-magnetic state (Figure 3). However, its ferromagnetic state is equivalent to its non-magnetic state when tension is less than 2%. At the tension of 2%, its ferromagnetic state becomes unstable as indicated by the larger positive ΔEFM-NM. Then, ΔEFM-NM decreases with tension increasing and is negative after ε > 4%, indicating that ferromagnetic state is more stable than non-magnetic state when ε > 4%. We see that the ground state of VTe2-H monolayer is anti-ferromagnetic and its metastable state is no-magnetic at the tension range of 0 < ε < 5%, because ΔEAFM-NM < 0 and ΔEFM-NM ≥ 0. At the tension range of 4% < ε < 8.5%, both ΔEAFM-FM and ΔEFM-NM are negative (Figure 3), indicating that anti-ferromagnetic and ferromagnetic states of VTe2-H monolayer are ground and metastable states, respectively. At ε ~ 8.6%, ΔEAFM-FM is equal to zero, but both of the energies of anti-ferromagnetic and ferromagnetic states are lower than that of non-magnetic state. So, we predict that VTe2-H monolayer is paramagnetic at ε ~ 8.6%. With further increasing tension, the energy of its ferromagnetic state is lower than that of anti-ferromagnetic states (positive ΔEAFM-FM in Figure 2) and ΔEAFM-NM keeps negative (Figure 3), confirming that the ground state of VTe2-H monolayer is ferromagnetic when ε > 8.6%, as well as its metastable anti-ferromagnetism. The calculated exchange energy and energy differences clearly show that the VTe2-H monolayer switches from anti-ferromagnetic state to ferromagnetic state via a paramagnetic state with the increment of applied tension (Figures 2&3). At its ferromagnetic ground state, the exchange energy (ΔEAFM-FM) can be up to 65 meV at a tension of 15%. On the basis of mean field theory and Heisenberg model with long-range interaction, the Curie temperature (TC) can be estimated from 27. We see that the Curie temperature increases with the increase of tension (ε > 8.6%) because of the increased exchange energy (Figure 2). The estimated Curie temperature is 500 K for VTe2-H monolayer at a tension of 15%, indicating that they can be used in spintroincs at high temperature. The theoretically estimated Curie temperature should be confirmed experimentally.

Figure 2
figure 2

The calculated exchange energy of VTe2-H monolayer as function of tension.

The regions with the evolution of magnetism and conductivity as tension are highlighted.

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Figure 3
figure 3

The calculated energy differences of VTe2-H monolayer between magnetic (antiferromagnetic/ferromagnetic) and non-magnetic states as function of tension.

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To reveal the origin of the magnetic evolution with applied tension, the electronic structure of VTe2-H monolayer under tension is calculated. The calculated band structures show that VTe2-H monolayer under a tension up to 4% is a semiconductor (Figures 4a–e). The VTe2-H monolayer at zero tension is a direct band semiconductor with both of conduction band bottom (CBB) and valence band top (VBT) at M point and a gap of 0.48 eV (Figure 4a). As the tension increases, the conduction band and valence band at Γ point are pulled down and pushed up, respectively and gradually become the CBB and VBT (Figures 4b–e), leading to the narrowing of band gap. At the tension of 4%, the direct band gap at Γ points is only 0.13 eV (Figure 4e). With further increasing the tension (>4%), CBB continuously moves down and VBT up reversely (Figures 4f–j). At a tension of 5%, CBB and VBT cross each other at the Fermi level (0 eV in Figure 4), leading to the metallic conductivity of VTe2-H monolayer (Figure 4f). Its conductivity is further improved with the tension increasing up to 8.5%, because the overlap between conduction and valence bands increases in the same trend (Figures 4f–j). We can see that the conductivity of anti-ferromagnetic ground state of VTe2-H monolayer is continuously improved (from narrow-band semiconductor, to ultra-narrow-band semiconductor, further to metal) with the tension increasing from 0 to 8.5% (Figures 2&4). However, the conductivity of VTe2-H monolayer is changed as its magnetic ground state switches from anti-ferromagnetism to ferromagnetism under a tension above 8.6%. The calculated band structures of VTe2-H monolayers under a tension ranging from 8.8 to 15% clearly show that spin-up states are metallic, while spin-down states are semiconducting, resulting in half-metallic and ferromagnetic ground states (Figure 5). The change of conductivity (or carrier density) may provide evidence to find the mechanism on the magnetic evolution of VTe2-H monolayer with tension.

Figure 4
figure 4

The calculated band structures of VTe2-H monolayers with anti-ferromagnetic ground states at a tension of 0% (a), 1% (b), 2% (c), 3% (d), 4% (e), 5% (f), 6% (g), 7% (h), 8% (i) and 8.5% (j).

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Figure 5
figure 5

The calculated band structures of VTe2-H monolayers with ferromagnetic ground states under a tension of 8.8% (a), 9% (b), 10% (c), 11% (d), 12% (e), 13% (f), 14% (g) and 15% (h).

Black line: spin-up; red line: spin-down.

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Further analysis on the partial density of states (PDOSs) shows that the coupling between d electrons of V atoms (V_d) and p electrons of Te atoms (Te_d) of VTe2-H monolayer and their contribution to spin-polarized states and carrier near the Fermi level change as tension increasing from 0 to 15% (Figures 6&7), because of the charge redistribution. The PDOSs show that the hybridization between Te_p and V_d orbitals in semiconducting VTe2-H monolayer is strong under weak strain (Figures 6a~ d ), where these orbitals strongly couple below the Fermi level in a range of −0.8 to 0 eV and the covalent bonding is dominant. Under medium strain, the covalent-coupling between Te_p and V_d orbitals weakens, especially near the Fermi level (Figures 6e ~ h), leading to equivalent ionic and covalent bonding. Further increasing strain, the hybridization is weakened and ionic bonding becomes dominant (Figure 7). The H_s orbital hybridizes with Te_p orbitals around −2.0 eV below the Fermi level at a strain of 1%, which increases to around −1.3 eV with the strain increasing up to 15% (Figures 6&7). The calculated magnetic moments of V atom and Te atom are 0.79 and 0.02 μB at zero tension, respectively and increase with tension, confirming the redistribution of charge (Figure 8). The moments of V atoms of VTe2-H monolayer under a tension ranging from 0 to 4% are anti-parallel because of its anti-ferromagnetic ground states (Figure 9a). Importantly, we see that the moments of Te atoms are also anti-parallel among neighboring cells (Figure 9a). From the anti-parallel alignment of magnetic moments between V and Te atoms and its semiconducting character, we see that super-exchange among V atoms, the mechanism of anti-ferromagnetic oxide insulators26,28,29, is achieved via Te atoms and plays a dominant role on the anti-ferromagnetism of VTe2-1H monolayer in tension range of 0 to 4%. The alignments of magnetic moments keep unchanged in metallic VTe2-H monolayer in tension range of 5 to 8.5% (Figure 9a). The metallic anti-ferromagnetic ground state is also attributed to super-exchange, because the mobile carriers with high density can enhance the super-exchange interaction of anti-ferromagnetic metals30. Increasing tension from 8.6 to 15%, the VTe2-1H monolayer is half-metallic and ferromagnetic (Figure 5). We see that the magnetic moments of V and Te atoms jump up at the turning-point with a tension of ~8.8% (Figure 8). The magnetic moments of V and Te atoms are contributed to d and p electrons, respectively (Figure 7) and increase as tension (Figure 8). The magnetic moment of V atom can be up to 2.08 μB at a tension of 15%. The magnetic moments of Te atoms without and with H functionalization at a tension of 15% are 0.23 and 0.14 μB, respectively. The PDOSs analysis shows that the moments of V atoms of VTe2-H monolayer at ε > 8.5% are parallel to each other because of its ferromagnetic ground states and those of Te atoms are also parallel (Figure 9b). However, the moment alignment between V and Te atoms is anti-parallel (Figure 9b). The anti-parallel alignment between the magnetic moments of V and Te atoms and the half-metallic character of VTe2-H monolayer at ε > 8.6% demonstrate that double exchange is the dominant mechanism for the ferromagnetism31,32,33,34,35, where the exchange interaction is realized by the hopping of mobile carriers. That is, given the incomplete filling of bands (only spin-down bands are filled) (Figure 5), the band energy of the ferromagnetic state is lower than that of the antiferromagnetic state if a sufficient (usually rather small) number of carriers exist36. We see that the band gap of spin-up band structure of ferromagnetic VTe2-H monolayer increases with the increment of tension, resulting in the enhancement of spin-polarized electrons and larger magnetic moments due to the extended ionic bond strength of V-Te, which further confirms the dominant role of double-exchange for their ferromagnetism.

Figure 6
figure 6

The calculated partial densities of states of VTe2-H monolayers with anti-ferromagnetic ground states at a tension of 1% (a) and (b), 2% (c) and (d), 5% (e) and (f) and 8.5% (g) and (h).

Te1 and Te2 are Te atoms without and with H attachment, respectively.

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Figure 7
figure 7

The calculated partial densities of states of VTe2-H monolayers with ferromagnetic ground states at a tension of 8.8% (a) and (b), 11% (c) and (d) and 15% (e) and (f).

Te1 and Te2 are Te atoms without and with H attachment, respectively.

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Figure 8
figure 8

The calculated magnetic moments of VTe2-H monolayers as a function of tension.

(a) V atom and (b) Te atoms (Te-1 andTe-2 are Te atoms without and with H attachment, respectively.).

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Figure 9
figure 9

Alignment configurations of magnetic moments.

(a) antiferromagnetic ground state and (b) ferromagnetic ground state.

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From the band structures, PDOSs and spin-alignment of VTe2-H monolayer under tension, we see that magnetic and conducting properties can be controlled by external strain and the magnetic switching is contributed to the change of its conducting character and the hybridization between Te_p and V_d orbitals under tension. According to the conducting character of VTe2-H monolayer under tension, there are three regions: semiconductor (ε ≤ 4%), metal (4% < ε < 8.6%) and half-metal (ε > 8.6%) (Figure 2). According to the magnetic property of VTe2-H monolayer under tension, there are two regions: anti-ferromagnetism (ε ≤ 8.5%) and ferromagnetism (ε > 8.6%) (Figure 2). Under low tension, the semiconducting or metallic VTe2-H monolayer is anti-ferromagnetic due to the super-exchange interaction or carrier-enhanced super-exchange. At high tension, the half-metallic VTe2-H monolayer is ferromagnetic due to carrier-mediated double exchange.

To further confirm the origin of magnetic evolution of VTe2-H monolayer under tension, we investigate the electronic and magnetic properties of hydrogenated vanadium disulfide (VS2-H) and diselenide (VSe2-H) monolayers under tension. Similar to VTe2-H monolayer, the calculated exchange energies demonstrate that VS2-H and VSe2-H monolayers switch from anti-ferromagnetism to ferromagnetism via paramagnetic turning points as tension increases (Figure 10). Differently, VS2-H and VSe2-H monolayers are non-magnetic at tension ranges of ε ≤ 4% and ε ≤ 2%, respectively, because the exchange energies and energy differences between magnetic and non-magnetic states are zero (Figure 10). The VS2-H monolayer is an intrinsic semiconductor with a direct band gap of 0.75 eV at zero tension (Figure 11a), which becomes indirect with a reduced gap of 0.2 eV when ε = 4% (Figure 11c). Within the tension range of 4% < ε < 10%, VS2-H monolayer is a semiconductor with anti-ferromagnetic ground state because the exchange energy is negative (Figures 10a, 11d & 11e). The anti-ferromagnetic VS2-H monolayer is metallic when 10% ≤ ε ≤ 16% (Figures 11f ~ i). When ε > 16%, VS2-H monolayer is ferromagnetic and half-metallic (Figures 10a & 11j). The evolutions of magnetism and conductivity of VSe2-H monolayer with tension (Figures 10b & 12) are similar to those of VS2-H monolayer (Figures 10a & 11). VS2-H monolayer is semiconducting and no-magnetic when ε ≤ 2%, semiconducting and anti-ferromagnetic when 2% < ε < 6%, metallic and anti-ferromagnetic when 6% ≤ ε ≤ 12% and ferromagnetic and half-metallic when ε > 12% (Figures 10b & 12). According to the evolutions of conducting characters of VS2-H and VSe2-H monolayers, their anti-ferromagnetism under low tension is contributed to super-exchange for narrow-band semiconductor or carrier-enhanced super-exchange for metal and their ferromagnetism under high tension is dominated by carrier-mediated double exchange in half-metal. The strong covalent bond between V and S/Se atoms in VS2-H and VSe2-H monolayers under zero or lower tension results in large band gap and less charge redistribution, contributing to their non-magnetic and semiconducting characters (Figures 10, 11a–c, & 12a–b). Comparing the exchange energies of hydrogenated vanadium dichalcogenides (VX2-H) monolayers (Figures 2&10), we see that the required tension at the turning point (magnetic or conducting switching) decrease with X in V-X bond changing as S → Se → Te because of its covalent bond weakening in the same trend and enhancement of charge redistribution.

Figure 10
figure 10

The calculated exchange energies and energy differences between magnetic (antiferromagnetic/ferromagnetic) and non-magnetic states as function of tension.

(a) VS2-H and (b) VSe2-H monolayers.

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Figure 11
figure 11

The calculated band structures of VS2-H monolayers under tension ranging from 0 to 18%.

In (j), black line: spin-up; red line: spin-down.

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Figure 12
figure 12

The calculated band structures of VSe2-H monolayers under tension ranging from 0 to 16%.

In (h) and (i), black line: spin-up; red line: spin-down.

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Conclusions

We present a first-principles study on the magnetic and electronic evolutions of hydrogenated vanadium dichalcogenides (VX2-H) monolayers under tension. Our calculations show that VTe2-H monolayer switches from anti-ferromagnetism to ferromagnetism via paramagnetic turning point accompanying with electronic evolution from semiconductor to metal, further to half-metal as tension increases. The anti-ferromagnetism of VTe2-H monolayer under low tension is contributed to the super-exchange in narrow-band semiconductor or mobile-carrier enhanced super-exchange in metal. The carrier-mediated double exchange in half-metal is attributed to the origin of ferromagnetism observed in VTe2-H monolayer under high tension. VS2-H and VSe2-H monolayers under lower tension are non-magnetic and semiconducting because the strong covalent bonds result in less charge redistribution. After tension exceeding a certain value, their magnetic and electronic evolutions under tension are similar to those of VTe2-H monolayer because of the charge redistribution and carrier-mediated interaction. We show that strain engineering, as a simple method, can efficiently control the magnetic and electronic properties of VX2-H monolayers. These monolayers with controllable functions can be applicable in mechanical sensors, functional nanodevices and spintronics.

Methods

The first-principles calculations are carried out to investigate the electronic and magnetic properties of vanadium dichalcogenide monolayer under tension. The calculations are based on the density functional theory (DFT)36 and the Perdew-Burke-Eznerhof generalized gradient approximation (PBE-GGA)37. The projector augmented wave (PAW) scheme38,39 as incorporated in the Vienna ab initio simulation package (VASP)40 is used in the study. The Monkhorst and Pack scheme of k point sampling is used for integration over the first Brillouin zone41. A 15 × 15 × 1 grid for k-point sampling for geometry optimization of unit cells and an energy cut-off of 450 eV are consistently used in our calculations. Sufficiently large supercells are used so that the monolayers in neighboring cells in the vertical direction are separated by a vacuum region of at least 20 Å. A 2 × 2 × 1 cell is used to study the spin alignments. Spin-polarized calculations are employed. Full structural optimization is carried out for all the systems with tension before investigating their physical properties. Good convergence is obtained with these parameters and the total energy was converged to 2.0 × 10−5 eV/atom.