Antiferromagnetism and piezoelectricity in Janus PdXY monolayers

The structural, electronic, magnetic, mechanical, and piezoelectric properties of Janus PdXY ($X,Y=\text{F, Cl, Br}$) monolayers are investigated. Electron localization function (ELF) and charge density difference confirm that all PdXY Janus monolayers have ionic character. Non-uniform ELF in these monolayers is attributed to the breakdown of inversion and reflection symmetry. Elastic constants and phonon calculations reveal the mechanical and dynamic stability of these monolayers . With non-zero piezoelectric stress tensors, the maximum magnitude of $d_{22}$ (9.90 pmV⁻¹) is found in the PdFBr monolayer, whereas the in-plane piezoelectric coefficient $e_{22}$ has the largest value of $2.15\times 10^{-10}$ C/m in Janus PdFBr. All these Janus monolayers are magnetic semiconductors with magnetic moments of 2 ${\mu }_B$, which are mainly contributed by the $E_2$ orbitals of Pd. PdBrCl shows an in-plane easy axis of magnetization, whereas monolayers PdBrF and PdClF show an out-of-plane easy axis of magnetization. The Curie temperatures, using Monte Carlo simulations, for PdBrCl, PdBrF, and PdClF are 660 K, 102 K, and 111 K, respectively.