Negative Piezoelectric Coefficient in Ferromagnetic 1H-LaBr ₂ Monolayer

The discovery of two-dimensional (2D) magnetic materials that have excellent piezoelectric response is promising for nanoscale multifunctional piezoelectric or spintronic devices. Piezoelectricity requires a noncentrosymmetric structure with an electronic band gap, whereas magnetism demands broken time-reversal symmetry. Most of the well-known 2D piezoelectrics, e.g., 1H-MoS₂ monolayer, are not magnetic. Being intrinsically magnetic, semiconducting 1H-LaBr₂ and 1H-VS₂ monolayers can combine magnetism and piezoelectricity. We compare piezoelectric properties of 1H-MoS₂, 1H-VS₂, and 1H-LaBr₂ using density functional theory. The ferromagnetic 1H-LaBr₂ and 1H-VS₂ monolayers display larger piezoelectric strain coefficients, namely, d ₁₁ = -4.527 pm/V for 1H-LaBr₂ and d ₁₁ = 4.104 pm/V for 1H-VS₂, compared to 1H-MoS₂ (d ₁₁ = 3.706 pm/V). 1H-MoS₂ has a larger piezoelectric stress coefficient (e ₁₁ = 370.675 pC/m) than 1H-LaBr₂ (e ₁₁ = -94.175 pC/m) and 1H-VS₂ (e ₁₁ = 298.100 pC/m). The large d ₁₁ for 1H-LaBr₂ originates from the low elastic constants, C ₁₁ = 30.338 N/m and C ₁₂ = 9.534 N/m. The sign of the piezoelectric coefficients for 1H-LaBr₂ is negative, and this arises from the negative ionic contribution of e ₁₁, which dominates in 1H-LaBr₂, whereas the electronic part of e ₁₁ dominates in 1H-MoS₂ and 1H-VS₂. We explain the origin of this large ionic contribution of e ₁₁ for 1H-LaBr₂ through Born effective charges (Z ₁₁) and the sensitivity of the atomic positions to the strain (du/dη). We observe a sign reversal in the Z ₁₁ values 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. We also show that a change in magnetic order can enhance (reduce) the piezoresponse of 1H-LaBr₂ (1H-VS₂).