Negative Piezoelectric Coefficient in Ferromagnetic 1H-LaBr2 Monolayer

Abstract

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, d11 = −4.527 pm/V for 1H-LaBr2 and d11 = 4.104 pm/V for 1H-VS2, compared to 1H-MoS2 (d11 = 3.706 pm/V). 1H-MoS2 has a larger piezoelectric stress coefficient (e11 = 370.675 pC/m) than 1H-LaBr2 (e11 = −94.175 pC/m) and 1H-VS2 (e11 = 298.100 pC/m). The large d11 for 1H-LaBr2 originates from the low elastic constants, C11 = 30.338 N/m and C12 = 9.534 N/m. The sign of the piezoelectric coefficients for 1H-LaBr2 is negative, and this arises from the negative ionic contribution of e11, which dominates in 1H-LaBr2, whereas the electronic part of e11 dominates in 1H-MoS2 and 1H-VS2. We explain the origin of this large ionic contribution of e11 for 1H-LaBr2 through Born effective charges (Z11) and the sensitivity of the atomic positions to the strain (du/dη). We observe a sign reversal in the Z11 values of Mo and S compared to the nominal oxidation states, which makes both the electronic and ionic parts of e11 positive and results in the high value of e11. We also show that a change in magnetic order can enhance (reduce) the piezoresponse of 1H-LaBr2 (1H-VS2).