  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 1 Bohr
magneton per formula unit. 2D K2CuF4 unites ferromagnetic and insulating
properties and is a demonstration of principles for nanoelectronics such as
novel 2D-based heterostructures.
