The successful isolation of graphene ten years ago has evoked a rapidly growing scientific interest in the nature of two-dimensional (2D) crystals. A number of different 2D crystals has been produced since then, with properties ranging from superconductivity to insulating behavior. Here, we predict the possibility for realizing ferromagnetic 2D crystals by exfoliating atomically thin films of K2CuF4. From a first-principles theoretical analysis, we find that single layers of K2CuF4 form exactly 2D Kosterlitz-Thouless systems. The 2D crystal can form a free-standing membrane, and exhibits an experimentally accessible transition temperature and robust magnetic moments of 1µB per formula unit. 2D K2CuF4 unites ferromagnetic and insulating properties and is a demonstration of principles for nanoelectronics such as novel 2D-based heterostructures.Introduction The large variety of two-dimensional (2D) atomic crystals which are available to us [1, 2] comprise into a very rich class of materials, which collectively covers a large diversity of properties. Also, the recent progress in creating heterostructures made from individual atomic crystals [3][4][5] allowed the investigation of such phenomena as Coulomb drag [6] and the Hofstadter butterfly [7][8][9], but also facilitated the creation of novel, often multifunctional devices, such as tunneling transistors [10,11] and photovoltaic devices [12][13][14].