Ferromagnetic 1H-LaBr2 monolayer: a promising 2D piezoelectric

The discovery of two dimensional (2D) materials that have excellent piezoelectric response along with intrinsic magnetism is promising for nanoscale multifunctional piezoelectric or spintronic devices. Piezoelectricity requires non-centrosymmetric structures with an electric band-gap, whereas magnetism demands broken time-reversal symmetry. Most of the well-known 2D piezoelectric materials – e.g., 1H-MoS2 monolayer – are not magnetic. Being intrinsically magnetic, semiconducting 1H-LaBr2and 1H-VS2 monolayers can combine magnetism and piezoelectricity. We compare piezoelectric properties of 1H-MoS2, 1H-VS2 and 1H-LaBr2 using density functional theory. Our results show that ferromagnetic 1H-LaBr2 2D monolayer displays a larger piezoelectric strain co-efficient (d_{11}= -4.527 pm/V, which is close to d_{11}= 4.104 pm/V of 1H-VS2 monolayer) compared to that of well-known 1H-MoS2 monolayer (d_{11}= 3.706 pm/V), while 1H-MoS2 monolayer has a larger piezoelectric stress co-efficient (e_{11}= 370.675 pC/m) than the 1H-LaBr2 monolayer (e_{11}= -94.175 pC/m, which is also lower than e_{11}= 298.100 pC/m of 1H-VS2 monolayer). These in-plane piezoelectric d_{11} coefficients are quite comparable with piezo-response of bulk wurtzite nitrides – e.g., d_{33} of GaN is about 3.1 pm/V. The large d_{11} for 1H-LaBr2 monolayer originates from the low elastic constants, C_{11}= 30.338 N/m and C_{12} = 9.534 N/m. Interestingly, the sign of the piezoelectric co-coefficients for 1H-LaBr2 monolayer is different to that of the 1H-MoS2 or 1H-VS2 monolayers. The negative sign arises from the negative ionic contribution of e_{11}, which dominates in the 1H-LaBr2 monolayer, whereas the electronic part of e_{11} dominates in 1H-MoS2 and 1H-VS2. Furthermore, we explain the origin of this large ionic contribution of e_{11} for 1H-LaBr2 in terms of the Born effective charges (Z_{11}) and the sensitivity of the atomic positions to the strain (\frac{du}{d\eta}). Surprisingly, we observe a sign reversal in the Z_{11} of Mo and S compared to the nominal oxidation states, which makes both the electronic and ionic parts of e_{11} positive, and results in the high value of e_{11}. Additionally, our interatomic bond analysis using crystal orbital Hamilton populations indicates that the weaker covalent bond in 1H-LaBr2 monolayer is responsible for large \frac{du}{d\eta} and elastic softening (lower elastic constants).

Flexoelectric and Piezoelectric Coupling in a Bended MoS2 Monolayer

Low-dimensional (LD) transition metal dichalcogenides (TMDs) in the form of nanoflakes, which consist of one or several layers, are the subject of intensive fundamental and applied research. The tuning of the electronic properties of the LD-TMDs are commonly related with applied strains and strain gradients, which can strongly affect their polar properties via piezoelectric and flexoelectric couplings. Using the density functional theory and phenomenological Landau approach, we studied the bended 2H-MoS2 monolayer and analyzed its flexoelectric and piezoelectric properties. The dependences of the dipole moment, strain, and strain gradient on the coordinate along the layer were calculated. From these dependences, the components of the flexoelectric and piezoelectric tensors have been determined and analyzed. Our results revealed that the contribution of the flexoelectric effect dominates over the piezoelectric effect in both in-plane and out-of-plane directions of the monolayer. In accordance with our calculations, a realistic strain gradient of about 1 nm−1 can induce an order of magnitude higher than the flexoelectric response in comparison with the piezoelectric reaction. The value of the dilatational flexoelectric coefficient is almost two times smaller than the shear component. It appeared that the components of effective flexoelectric and piezoelectric couplings can be described by parabolic dependences of the corrugation. Obtained results are useful for applications of LD-TMDs in strain engineering and flexible electronics.