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    Two-dimensional ferromagnetic MoSeX (X = F, Cl, Br, I) with large out-of-plane piezoelectricity exhibiting an electronegativity difference ratio effect

    Gui-Juan Du1, Xiao Shang1, Dan-Yang Zhu1, Min Tao1, Fu-Chun Liu1,*, Shou-Xin Cui2, Zeng-Tao Lv2,†, and Xiao-Chun Wang1,2,‡

    • 1Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China
    • 2School of Physics Science and Information Technology, Liaocheng University, Liaocheng 252000, China

    • *Contact author: lfc@jlu.edu.cn
    • †Contact author: lvzengtao@lcu.edu.cn
    • ‡Contact author: wangxiaochun@tsinghua.org.cn

    Phys. Rev. B 113, 085411 – Published 6 February, 2026

    DOI: https://doi.org/10.1103/gn9s-smrb

    Abstract

    The coexistence of ferromagnetic (FM) state, out-of-plane piezoelectricity, and multiple channels for energy exchange in two-dimensional (2D) materials is highly advantageous for multifunctional ultrathin electronic devices. We predict the stable MoSeX (X = F, Cl, Br, I) semiconductor monolayers by first principles calculation. The Ueff values of Mo atoms are obtained via linear fitting GGA+(U) band gaps to match with HSE results. The magnetic configuration with the lowest energy is the FM state for the four monolayers. Among these monolayers, MoSeI exhibits the largest absolute value of out-of-plane piezoelectric strain coefficient d31 (−0.55 pm/V). The absolute value is greater than those of the majority of 2D materials. Such as it is 4.2 times higher than d31 of h-BN (0.13 pm/V) and 18.3 times higher than Janus TMD monolayers (0.03 pm/V). The d31 of MoSeF and MoSeCl are 0.40 and 0.43 pm/V, respectively. Furthermore, there exists a positive correlation between the out-of-plane piezoelectric stress coefficient e31 and the electronegativity difference ratio (red), which conforms to the electronegativity difference ratio effect. Intriguingly, MoSeF has multiple channels for energy exchange of holes and electrons in the bands due to the quasiequal extreme point defined in this work. This work presents four multifunctional monolayers that exhibit ferromagnetism, large out-of-plane piezoelectricity, and multiple energy exchange channels. It provides a possible approach for the design of multifunctional energy materials.

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