The electronic and magnetic structure, including the Heisenberg model exchange interaction parameters, was explored for the recently proposed novel cuprate Cu$_2$F$_5$. Using the DFT+U calculation, it is shown that the compound is formed by two types of copper ions with $d^9$ and $d^8$ electronic configurations. We have found a very stable antiferromagnetic ordering with strong anisotropy of exchange interaction that results in the appearance of an unusual 2D-magnetism: within the (100)-plane the exchange between the S=1 and S=1/2 Cu ions has almost the same strength as between the two S=1 ions. The interplane magnetic interaction is five times weaker than the in-plane one.
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