  Ferromagnetism (FM) is the cornerstone of permanent magnets, data storage and
other technologies that directly impact our everyday life by their
implementation in standard applications and devices. When downscaling bulk
materials into their two-dimensional (2D) magnetic isotropic form, the
Mermin-Wagner theorem precludes this collective state mediated by short-range
exchange interactions at finite temperatures. Interestingly, this prediction
fails when significant magnetic anisotropy is present in the material, as
recently demonstrated in single layered van der Waals crystals. Before the
latter, single layer metal-organic frameworks (MOFs) grown on metallic supports
were one of the earliest candidates for achieving 2D-FM. Such high expectations
were based on the chemical and spacing control of the 2D-MOF magnetic centers,
the tunability of the organic linkers and the rich self-assembled architectures
displayed. However, despite many attempts, extended FM in 2D-MOFs has been
experimentally elusive. In this work, we demonstrate that extended, cooperative
FM takes place in an atom thick 2D-MOF consisting of 9,10-dicyanoanthracene
(DCA) molecules and Fe adatoms grown on Au(111). We show this by means of an
experimental multitechnique approach that is endorsed by state-of-the art
first-principles calculations. Particularly, this 2D ferromagnet follows a
first order transition with TC ~ 35 K, which is driven by exchange interactions
mainly through the molecular linkers (J=2 meV) and exhibits an out-of-plane
square-like hysteresis loop. The strict periodicity of our 2D-MOF allows us to
envision the fabrication of ultra-dense single atom magnetic memories and opens
the way to explore periodic magnetic 2D-models that could considerably increase
the fundamental superparamagnetic limit.
