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-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 (d u /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 ).