Magnetic and Electronic Evolutions of Hydrogenated VTe2 Monolayer under Tension

Two-dimensional nanostructures with controllable magnetic and electronic properties are desirable for their versatile applications in quantum devices. Here, we present a first-principles design on their magnetic and electronic switching controlled by tension. We find that hydrogenated VTe2 monolayer experiences a transfer from anti-ferromagnetism to ferromagnetism via a turning-point of paramagnetism, and switches from semiconductor, to metal, further to half-metal as tension increases. We show that its anti-ferromagnetism with semiconducting or metallic character under low tension is contributed to super-exchange or mobile-carrier enhanced super-exchange, while the ferromagnetism with half-metallic character under high tension is induced by carrier-mediated double exchange. We further show that the magnetic and electronic evolutions of hydrogenated VS2 and VSe2 monolayers under tension follow the same trend as those of hydrogenated VTe2 monolayer. We predict that tension is efficient and simple to control the magnetic and electronic properties of hydrogenated vanadium dichalcogenides monolayers. The monolayers with controllable magnetism and conductivity may find applications in multi-functional nanodevices.


e~c
{c 0 c 0 |100%. A tension range of 0 to 15% is used in our calcula- tions. 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.
To find out the magnetic evolution of VTe 2 -H monolayer under tension, the exchange energy (DE AFM-FM ), defined as DE AFM -FM 5 (E AFM -E FM )/N (where E FM and E AFM are the energies at ferromagnetic and anti-ferromagnetic states, and N (54) is the number of units in the supercell.), is calculated. We see that VTe 2 -H monolayer is anti-ferromagnetic with E ex 5 213 meV under zero tension ( Figure 2). The exchange energy (negative) initially decreases with the tension increasing and goes sharply down to bottom peak (2186 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 VTe 2 -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 VTe 2 -H monolayer is ferromagnetic with the tension larger than 8.6%. To confirm the ground and metastable states of VTe 2 -H monolayer under tension, the energy difference between magnetic states (E FM and E AFM ) and non-magnetic state (E NM ), including DE FM-NM (5 (E FM -E NM )/N) and DE AFM-NM (5 (E AFM -E NM )/N), are calculated. The calculated energy difference between anti-ferromagnetic and non-magnetic states of VTe 2 -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 DE FM-NM . Then, DE FM-NM decreases with tension increasing and is negative after e . 4%, indicating that ferromagnetic state is more stable than non-magnetic state when e . 4%. We see that the ground state of VTe 2 -H monolayer is anti-ferromagnetic and its metastable state is no-magnetic at the tension range of 0 , e , 5%, because DE AFM-NM , 0 and DE FM-NM $ 0. At the tension range of 4% , e , 8.5%, both DE AFM-FM and DE FM-NM are negative (Figure 3), indicating that antiferromagnetic and ferromagnetic states of VTe 2 -H monolayer are ground and metastable states, respectively. At e , 8.6%, DE AFM-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 VTe 2 -H monolayer is paramagnetic at e , 8.6%. With further increasing tension, the energy of its ferromagnetic state is lower than that of anti-ferromagnetic states (positive DE AFM-FM in Figure 2), and DE AFM-NM keeps negative (Figure 3), confirming that the ground state of VTe 2 -H monolayer is ferromagnetic when e . 8.6%, as well as its metastable anti-ferromagnetism. The calculated exchange energy and energy differences clearly show that the VTe 2 -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 (DE AFM-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 (T C ) can be estimated     27 . We see that the Curie temperature increases with the increase of tension (e . 8.6%) because of the increased exchange energy ( Figure 2). The estimated Curie temperature is 500 K for VTe 2 -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.
To reveal the origin of the magnetic evolution with applied tension, the electronic structure of  Figure 4), leading to the metallic conductivity of VTe 2 -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 VTe 2 -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 VTe 2 -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 VTe 2 -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     (Figures 6a, d ), where these orbitals strongly couple below the Fermi level in a range of 20.8 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 22.0 eV below the Fermi level at a strain of 1%, which increases to around 21.3 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 m B at zero tension, respectively, and increase with tension, confirming the redistribution of charge (Figure 8). The moments of V atoms of VTe 2 -H monolayer under a tension ranging from 0 to 4% are antiparallel because of its anti-ferromagnetic ground states (Figure 9a). Importantly, we see that the moments of Te atoms are also antiparallel 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 insulators 26,28,29 , is achieved via Te atoms, and plays a dominant role on the antiferromagnetism of VTe 2 -1H monolayer in tension range of 0 to 4%. The alignments of magnetic moments keep unchanged in metallic VTe 2 -H monolayer in tension range of 5 to 8.5% (Figure 9a). The metallic anti-ferromagnetic ground state is also attributed to superexchange, because the mobile carriers with high density can enhance the super-exchange interaction of anti-ferromagnetic metals 30 . Increasing tension from 8.6 to 15%, the VTe 2 -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 m B 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 m B , respectively. The PDOSs analysis shows that the moments of V atoms of VTe 2 -H monolayer at e . 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 antiparallel alignment between the magnetic moments of V and Te atoms and the half-metallic character of VTe 2 -H monolayer at e . 8.6% demonstrate that double exchange is the dominant mechanism for the ferromagnetism [31][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 exist 36 . We see that the band gap of spin-up band structure of ferromagnetic VTe 2 -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.
From the band structures, PDOSs, and spin-alignment of VTe 2 -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 VTe 2 -H monolayer under tension, there are three regions: semiconductor (e # 4%), metal (4% , e , 8.6%), and half-metal (e . 8.6%) (Figure 2). According to the magnetic property of VTe 2 -H monolayer under tension, there are two regions: anti-ferromagnetism (e # 8.5%) and ferromagnetism (e . 8.6%) (Figure 2). Under low tension, the semiconducting or metallic VTe 2 -H monolayer is anti-ferromagnetic due to the superexchange interaction or carrier-enhanced super-exchange. At high tension, the half-metallic VTe 2 -H monolayer is ferromagnetic due to carrier-mediated double exchange.
To further confirm the origin of magnetic evolution of VTe 2 -H monolayer under tension, we investigate the electronic and magnetic properties of hydrogenated vanadium disulfide (VS 2 -H) and diselenide (VSe 2 -H) monolayers under tension. Similar to VTe 2 -H monolayer, the calculated exchange energies demonstrate that VS 2 -H and  VSe 2 -H monolayers switch from anti-ferromagnetism to ferromagnetism via paramagnetic turning points as tension increases ( Figure 10). Differently, VS 2 -H and VSe 2 -H monolayers are nonmagnetic at tension ranges of e # 4% and e # 2%, respectively, because the exchange energies and energy differences between magnetic and non-magnetic states are zero ( Figure 10). The VS 2 -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 e 5 4% (Figure 11c). Within the tension range of 4% , e , 10%, VS 2 -H monolayer is a semiconductor with anti-ferromagnetic ground state because the exchange energy is negative (Figures 10a, 11d & 11e). The anti-ferromagnetic VS 2 -H monolayer is metallic when 10% # e # 16% (Figures 11f , i). When e . 16%, VS 2 -H monolayer is ferromagnetic and half-metallic (Figures 10a & 11j). The evolutions of magnetism and conductivity of VSe 2 -H monolayer with tension (Figures 10b & 12) are similar to those of VS 2 -H monolayer (Figures 10a & 11). VS 2 -H monolayer is semiconducting and no-magnetic when e # 2%, semiconducting and anti-ferromagnetic when 2% , e , 6%, metallic and anti-ferromagnetic when 6% # e # 12%, and ferromagnetic and half-metallic when e . 12% (Figures 10b & 12). According to the evolutions of conducting characters of VS 2 -H and VSe 2 -H monolayers, their antiferromagnetism under low tension is contributed to super-exchange for narrow-band semiconductor or carrier-enhanced superexchange 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 VS 2 -H and VSe 2 -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 (VX 2 -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 R Se R Te because of its covalent bond weakening in the same trend and enhancement of charge redistribution.

Conclusions
We present a first-principles study on the magnetic and electronic evolutions of hydrogenated vanadium dichalcogenides (VX 2 -H) monolayers under tension. Our calculations show that VTe 2 -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 VTe 2 -H monolayer under low tension is contributed to the super-exchange in narrow-band semi-

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) scheme 38,39 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 zone 41 . A 15 3 15 3 1 grid for k-point sampling for geometry optimization of unit cells, and an energy cutoff 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 3 2 3 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 3 10 25 eV/atom.