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We propose that stable two-dimensional (2D) ferromagnets can be made of regular single-layered lattices of single-molecule nanomagnets with enough uniaxial magnetic anisotropy on appropriate substrates by controlling the inter-nanomagnet magnetic interaction. Our Monte Carlo simulated results show that such ideal 2D ferromagnets are thermodynamically stable when the anisotropy is strong enough. If the anisotropy energy equals 80 K, approximately that of the Mn12, the T_c varies from zero to 15 K depending on different inter-nanomagnet coupling constants. Such stable spin systems, experimentally accessible, should be promising for information applications.

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