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).