Negative Piezoelectric Coefficient in Ferromagnetic 1H-LaBr(2) Monolayer

[Image: see text] 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-MoS(2) monolayer, are not magnetic. Being intrinsically magnetic, semiconducting 1H-LaBr(2) and 1H-VS(2) monolayers can combine magnetism and piezoelectricity. We compare piezoelectric properties of 1H-MoS(2), 1H-VS(2), and 1H-LaBr(2) using density functional theory. The ferromagnetic 1H-LaBr(2) and 1H-VS(2) monolayers display larger piezoelectric strain coefficients, namely, d(11) = −4.527 pm/V for 1H-LaBr(2) and d(11) = 4.104 pm/V for 1H-VS(2), compared to 1H-MoS(2) (d(11) = 3.706 pm/V). 1H-MoS(2) has a larger piezoelectric stress coefficient (e(11) = 370.675 pC/m) than 1H-LaBr(2) (e(11) = −94.175 pC/m) and 1H-VS(2) (e(11) = 298.100 pC/m). The large d(11) for 1H-LaBr(2) 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-LaBr(2) is negative, and this arises from the negative ionic contribution of e(11), which dominates in 1H-LaBr(2), whereas the electronic part of e(11) dominates in 1H-MoS(2) and 1H-VS(2). We explain the origin of this large ionic contribution of e(11) for 1H-LaBr(2) 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-LaBr(2) (1H-VS(2)).