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The structural, mechanical, and magnetic properties of square-lattice 3d transition metal dihalide monolayers MX2 have been systematically investigated via crystal structure analysis by particle swarm optimization and density functional theory calculations. We identified 17 stable monolayers (MX2 for M=Mn, Fe, Co, Cu, Zn with X=Cl, Br, I, plus NiBr2 and NiI2). Among these stable systems, 13 monolayers (MnCl2, MnBr2, FeX2, CoCl2, CoBr2, NiBr2, NiI2, CuCl2, and ZnX2) exhibit in-plane auxetic effects, with CuCl2, NiI2, ZnCl2, and ZnBr2, showing superior auxetic performance compared to many typical 2D auxetic materials. FeI2 displays a near-zero Poisson's ratio, making it suitable for high geometric stability applications. All these monolayers also feature strong elastic anisotropy and low Young's moduli, favorable for strain engineering in flexible devices. Our spin-polarized calculations demonstrate that the ground magnetic state of MX2 monolayers can be effectively tuned by the Hubbard U, the halogen species, and the 3d electron count of M atom. The magnetocrystalline anisotropy energies of these monolayers are significantly dependent on the transition metal element M and effective Hubbard U value. An increase in the U value results in an orientation switch between an in-plane and an out-of-plane easy axis in some MX2 monolayers. This work enriches the family of 2D auxetic and nanomagnetic materials and provides a theoretical basis for their applications in next-generation flexible and spin-based nanodevices.
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