Jianhui
Yang
^{ab},
Anping
Wang
^{a},
Shaozheng
Zhang
^{a},
Jia
Liu
^{a},
Zhicheng
Zhong
^{bc} and
Liang
Chen
*^{b}
^{a}Quzhou University, Quzhou 324000, P. R. China
^{b}Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo, Zhejiang, 315201, P. R. China. E-mail: chenliang@nimte.ac.cn
^{c}Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
First published on 28th November 2018
Akin to three dimensional (3D) multiferroics, two dimensional (2D) piezoelectric materials with intrinsic magnetic properties are promising applications in nanoscale spintronic devices. In this study, 2D magnetic transition metal dichalcogenides (VS_{2}, VSe_{2}, and Janus-VSSe) have been investigated by the first principles method for their structural, magnetic, electronic, and piezoelectric properties. H type Janus-VSSe has been shown to be more stable than the T type, and dynamically stable through phonon frequency analysis. Our calculations show that H type Janus-VSSe is not only a magnetic semiconductor but also exhibits appreciable in-plane and vertical piezoelectricity. Additionally, H type VS_{2} and VSe_{2} also show high in-plane piezoelectricity. The calculated values of in-plane piezoelectricity for these magnetic materials are higher than traditional 3D piezoelectric materials such as α-quartz. The coexistence of magnetism and piezoelectricity in H type VS_{2}, Janus-VSSe, and VSe_{2} makes them promising piezoelectric materials in nanoscale spin devices.
2D piezoelectric materials with intrinsic tunable magnetic properties can have extended applications in spin electronic devices similar to 3D multiferroics. In the case of 3D materials, multiferroics have magnetic ordering with simultaneous ferroelectric properties.^{17} The magneto–electric coupling makes them promising materials in sensors and spin electronic devices with atomic-level scales. More importantly, the properties of 2D piezoelectric magnetic materials can be tuned easily through epitaxial strain or magnetic field. As a result, there is a growing need to investigate the piezoelectricity and magnetic properties of 2D materials.
Until now, a few types of 2D magnetic materials have been studied, such as VS_{2}, Cr_{2}Ge_{2}Te_{6}, CrI_{3}, Cr or Mn-based MXene, and transition metal doped MXene.^{18–22} For example, Gong et al. showed that Cr_{2}Ge_{2}Te_{6} is an intrinsic ferromagnetic 2D material.^{20} Previous work from our group also showed that Cr-based double metal MXenes can be antiferromagnetic or ferromagnetic depending on their terminations and compounds.^{2,3} 2D vanadium dichalcogenides such as VS_{2} and VSe_{2} have also been experimentally demonstrated to be magnetic by Guo et al. and studied theoretically by Ma et al.^{19,23} From a structural standpoint, theoretical results have shown that 2D VS_{2} and VSe_{2} energetically prefer to be H type rather than T type.^{19} However, until now, VS_{2} and VSe_{2} have been synthesized in the T type.^{23,24} Through harmonic approximation, Liu et al. showed that bulk VS_{2} prefers to exhibit the T type at room temperature, whereas monolayer VS_{2} prefers to exhibit the H type below or at room temperature.^{18}
Due to the inversion symmetry along the z-direction, piezoelectricity of H type TMDs has been restricted in the xy-plane along the armchair direction.^{15} In order to possess piezoelectricity along the vertical direction, breaking-symmetry along the z-direction is necessary. Interestingly, H type Janus-TMDs have the required breaking-symmetry along z-directions, which explains their large piezoelectricity along the vertical direction.^{15} Hence, theoretical study on the piezoelectricity of Janus-VSSe can generate insights and promote the application of TMDs in spin electronics. In fact, experimental studies have shown that Janus phase of TMDs is an effective approach to tune the physical and chemical properties of TMDs.^{16,25} For example, Janus phase with different compounds on its two sides has distinct features and promising applications due to its structural breaking-symmetry, which has been extensively implemented on nano-particles and some 2D materials.^{26,27} Calculations and experimental results have indicated that Janus 2D materials can be synthesized and their piezoelectricity is quite distinct from pure TMDs.
Taking all these factors into account, the structural and magnetic properties of VS_{2}, VSe_{2} and Janus-VSSe in T and H types are investigated through density functional theory (DFT) in this study. The band structures of H type VS_{2}, VSe_{2} and Janus-VSSe are analyzed, and used to calculate their piezoelectricity and elasticity. The corresponding values of piezoelectricity (d_{11}) in the xy-plane along the armchair direction for H type VS_{2}, VSe_{2} and Janus-VSSe are calculated to be 2.34, 2.30, and 2.97 pm V^{−1}, respectively. Finally, the piezoelectricity along the vertical direction of multilayer Janus-VSSe is studied. The value of e_{33} is calculated to be 0.49 C m^{−2}, corresponding to a d_{33} of 4.92 pm V^{−1}.
The lattice parameters of T type VS_{2} and VSe_{2} are 3.18 and 3.33 Å, respectively, which are in good agreement with the experimental results of 3.22 and 3.35 Å.^{35,36} The lattice parameters of H types are similar to the corresponding T types. For T and H type Janus-VSSe, the lattice parameters are 3.26 and 3.25 Å, respectively, which are larger than VS_{2} but smaller than VSe_{2}. The bond lengths of V–S (L_{V–S}) in VS_{2} and Janus-VSSe are 2.34 and 2.36 Å, respectively, while the bond length of V–Se (L_{V–Se}) is about 2.50 Å, which is larger than that of L_{V–S}.
The magnetic moment of V atoms in T type VS_{2} and VSe_{2} are 0.54 and 0.68 μ_{B}, respectively, in accordance with earlier experimental and theoretical results.^{35} The magnetic moments of V atoms in H types are higher than those of T types (∼1.0 μ_{B}) and a similar trend is obtained for Janus-VSSe. Note that the calculation results by the PBE functional here are similar to that of the GGA+U method conducted by Popov and coworkers.^{37} This is mainly due to the localization and correlations of 3d electrons in the V atoms are weaker than other 3d elements such as Mn, Co, Fe, and Ni. For the ground states of all 2D vanadium dichalcogenides, the spin directions of V atoms are in-plane along the x-axis. When a spin up channel is fixed along the z axis (out-of-plane), the energy of all 2D vanadium dichalcogenides increases with an order of 10^{−3} eV.
Due to inversion symmetry in T type, no piezoelectric properties can be expected. As a result, H type VS_{2}, VSe_{2}, and Janus-VSSe are investigated for piezoelectricity in this study. The lattice parameters, bond lengths and magnetic moments of the constituent V, S, and Se atoms are summarized in Table 1.
H-VS_{2} | T-VS_{2} | H-VSSe | T-VSSe | H-VSe_{2} | T-VSe_{2} | |
---|---|---|---|---|---|---|
E (eV) | −39.49 | −39.40 | −37.78 | −37.69 | −36.06 | −35.97 |
a (Å) | 3.18 | 3.18 | 3.25 | 3.26 | 3.33 | 3.33 |
L _{V–S} (Å) | 2.36 | 2.35 | 2.36 | 2.34 | — | — |
L _{V–Se} (Å) | — | — | 2.51 | 2.50 | 2.50 | 2.49 |
M _{V} (μ_{B}) | 1.02 | 0.54 | 1.02 | 0.67 | 1.08 | 0.68 |
M _{S} (μ_{B}) | −0.05 | −0.03 | −0.02 | −0.02 | — | — |
M _{Se} (μ_{B}) | — | — | −0.08 | −0.05 | −0.07 | −0.05 |
Since, energetically favorable configurations obtained through ionic relaxations based on DFT may not be stable in their equilibrium positions, the stability of H type Janus-VSSe is further probed by phonon dispersions. The corresponding top and side views of H type Janus-VSSe are shown in Fig. 1(a and b). As shown in Fig. 1(c), all phonon frequencies of H type Janus-VSSe are positive, indicating that H type Janus-VSSe is dynamically stable. The highest phonon frequencies are around 400 cm^{−1}, which is close to VS_{2} and VSe_{2}.^{38}
Since the electronegativity of S is larger than that of Se, there are more electrons assembling near S. As show in Table 2, for H type VS_{2}, there are 6.90 electrons on S atoms, as compared to 6.81 electrons on Se atoms in H type VSe_{2}. For H type Janus-VSSe, there are also more electrons on S atoms as compared to Se atoms, as shown in Fig. 1(d). This induces an asymmetry of Janus-VSSe along the vertical direction, thereby significantly influencing the piezoelectricity.
H-VS_{2} | H-VSSe | H-VSe_{2} | |
---|---|---|---|
e _{V} | 3.20 | 3.28 | 3.37 |
e _{S} | 6.90 | 6.96 | — |
e _{Se} | — | 6.75 | 6.81 |
Piezoelectric materials also can act as semiconductors, so the band structures of H type VS_{2}, Janus-VSSe, and VSe_{2} structures were calculated using the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional, which has been shown to be effective in studying semiconductors.^{39} The calculation results show that H type VS_{2}, Janus-VSSe, and VSe_{2} are semiconductors with band gaps of 0.43, 0.91 and 0.88 eV, respectively (Fig. 2). Specifically, H type VS_{2} and VSSe are indirect semiconductors, while H type VSe_{2} is a direct semiconductor.
Fig. 2 Band structures of H type VS_{2}, Janus-VSSe, and VSe_{2}. The red and blue lines represent the spin-up and spin-down bands. |
e_{ijk} = əP_{i}/əε_{j} = əε_{jk}/əE_{i} | (1) |
d_{ijk} = əP_{i}/əσ_{jk} = əσ_{jk}/əE_{i} | (2) |
e_{ik} = d_{ij}C_{jk} | (3) |
For 2D materials, C_{ij} and e_{ij} are multiplied by the length of the z-axis. For nonmagnetic single TMDs, earlier studies have shown that e_{11} = −e_{12} and e_{26} = −e_{11}, which is caused by their 3m point-group symmetry.^{40} However, spin directions may lead to the absence of such symmetry in magnetic TMDs.
An orthorhombic unit cell was used for the calculation of piezoelectricity, as shown in Fig. 1(a). The calculated values of e_{11} for H type VS_{2}, VSSe, and VSe_{2} are 311.46, 282.87 and 322.83 pC m^{−1}, respectively. The corresponding values of d_{11} for H type VS_{2}, VSSe, and VSe_{2} are 2.34, 2.30, and 2.97 pm V^{−1}, respectively. These results are comparable with earlier reported values for other transition metal dichalcogenides such as WS_{2} obtained from DFT calculations.^{11,15,40} The values of d_{11} for these H type VS_{2}, VSSe, and VSe_{2} are higher than α-quartz (d_{11} = 2.27 pm V^{−1}), which is a common 3D piezoelectric material.^{41} This indicates that H type VS_{2}, Janus-VSSe, and VSe_{2} show potential in atomic in-plane piezoelectric devices.
Due to the inversion symmetry along the z-direction, e_{31} and d_{31} of monolayer H type VS_{2} and VSe_{2} are zero, and their piezoelectric polarizations are restricted in the xy-plane along the armchair direction. However, for the H type Janus-VSSe monolayer, e_{31} is obtained as 76.95 pC m^{−1}. Such a non-zero value is attributed to the structural breaking-symmetry along the z-direction. Thus, extensile strain can cause both vertical and in-plane piezoelectric polarizations in Janus-VSSe monolayers. All the obtained piezoelectric coefficients are summarized in Table 3.
e _{11} (pC m^{−1}) | e _{31} (pC m^{−1}) | C _{11} (N m^{−1}) | C _{12} (N m^{−1}) | d _{11} (pm V^{−1}) | |
---|---|---|---|---|---|
H type VS_{2} | 311.46 | 0 | 102.46 | 31.20 | 2.34 |
H type VSSe | 282.87 | 76.95 | 93.10 | 28.71 | 2.30 |
H type VSe_{2} | 322.83 | 0 | 84.12 | 26.65 | 2.97 |
Additionally, the polarization along the x-axis (arm-chair direction) and magnetic moment were calculated under different extensile strains. The strain was realized by stretching or compressing the optimized orthorhombic unit cell along the x axis by ±1 and ±0.5% with y-axis. As shown in Fig. 3, the polarizations for VS_{2} and VSSe increased linearly with extensile strain, while a non-linear variation is observed for VSe_{2} under ±1% strain. Similarly, the magnetic moment of Cr atoms also increased monotonically with extensile strain. The bond lengths of V–V, V–S, and V–Se increase with extensile strain, weakening the covalence interaction between V and nearby atoms. This leads to an increase in the number of unpaired electrons for V atoms, which results in the enhanced magnetic moment of V atoms. The inverse piezoelectric effect means that application of an electric field will lead to a deformation or strain of these materials along the corresponding direction. The induced deformation or strain will also cause the variation of magnetic moment. As a result, the magnetic moment can be varied by an electric field, which is a kind of magnetoelectric effect. Such a characteristic will promote the applications of two-dimensional vanadium dichalcogenides in spin electronic nano-devices.
Fig. 3 Polarization along the x-axis (top panel) and the magnetic moment of V atoms (down panel) for monolayer VS_{2}, VSSe, and VSe_{2} with uniaxial strain along the x-axis. |
Since Janus-VSSe possesses vertical piezoelectricity, a multilayer Janus-VSSe comprising of stacked monolayers can yield a large vertical piezoelectricity. Five different stacking models (Fig. 4) with high symmetry were considered to ascertain the energetically favorable configuration. The second model as shown in Fig. 4(b) was found to be the most stable stacking models with 2.89 Å interlayer distance and 0.36 eV binding energy. For this structure, the value of e_{33} is 0.49 C m^{−2}, corresponding to a d_{33} of 4.92 pm V^{−1}. The vertical piezoelectricity value for H type Janus-VSSe is close to Janus-MoSSe and AlN.^{15} This suggests that H type Janus-VSSe is applicable to piezoelectric devices while maintaining its magnetic properties.
Although the in-plane piezoelectric coefficients of H type VS_{2}, Janus-VSSe, and VSe_{2} and the vertical piezoelectric coefficients of multilayer Janus-VSSe are smaller than other transition metal dichalcogenides, having a similar magnetic property makes them interesting 2D materials for applications in nanoscale devices.
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