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-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 ).

Large Piezoelectric Response in Ferroelectric/Multiferroelectric Metal Oxyhalides MOX2 (M = Ti, V and X = F, Cl and Br) Monolayers

“…Note that e 11 of MOX 2 monolayers is signicantly (about 610 times) larger than that of well-known 1H-type piezoelectric monolayers e.g., 1H-MoS 2 [4,6,8]. We notice that e ion 11 of MOX 2 monolayers is an order of magnitude larger than that of 1H-MoS 2 or 1H-VS 2 [17], although their electronic part is quite comparable [17]. Because both Z 11 and du1 dη1 of MOX 2 monolayers are remarkably higher than those of 1H-MoS 2 or 1H-VS 2 [17].…”

“…We notice that e ion 11 of MOX 2 monolayers is an order of magnitude larger than that of 1H-MoS 2 or 1H-VS 2 [17], although their electronic part is quite comparable [17]. Because both Z 11 and du1 dη1 of MOX 2 monolayers are remarkably higher than those of 1H-MoS 2 or 1H-VS 2 [17]. Our e 11 is quite comparable with that of group-IV monochalcogenide monolayers such as SnS [14], although dierence between e 11 and e 12 in group-IV monochalcogenides is not as pronounce as in MOX 2 monolayers.…”

“…e ion 11 of TiOCl 2 and TiOBr 2 monolayers is almost twice larger than that of VOX 2 . Interestingly, we notice that both ionic and electronic parts of e 11 are positive (see Table III), thus they contribute positively to the total e 11 same like 1H-MoS 2 [17]. That is why TiOCl 2 or TiOBr 2 monolayer has signicantly large e 11 , compared to that of VOX 2 , although e elc 11 of TiOCl 2 and TiOBr 2 monolayers is slightly smaller than that of VOX 2 .…”

“…We see that because of their small positive e elc 12 but large negative e ion 12 , TiOCl 2 and TiOBr 2 monolayers have quite small e 12 (see Table III). We further decompose the ionic part [17,39,40]:…”

“…A moderate out-of-plane piezo-response is also observed in ferroelectric buckled monolayers and In 3 Se 3 nanoakes [15]. Furthermore, co-existence of piezoelectricity and magnetism and their coupling in 2D materials namely vanadium dichalcogenide monolayers [16] and 1H-LaBr 2 monolayer [17] have been investigated. Any strong coupling between piezoelectricity and magnetism can be utilized for making piezoelectric-based multifunctional nano-devices.…”