2D to 1D magnetic interactions evolution in Cu$_2$F$_{5-x}$ through electron doping by fluoride non-stoichiometry

The copper fluoride Cu$_2$F$_5$ is a compound with 2D-magnetic exchange interactions between the Cu ions in the $S=1$ and $S=\frac{1}{2}$ spin-states. Using ab-initio calculations, we predict that the existence of 5% vacancies in the fluoride sublattice of Cu$_2$F$_5$ results in the drastic transformation of the spin-state of all copper ions and the final spin-states are $S=\frac{1}{2}$ and $S=0$. Consequently, the anisotropy of magnetic interactions increases, and the 1D linear chains of the Cu $d^9$, $S=\frac{1}{2}$ ions appear. We also propose a microscopic mechanism of such exchange interaction transformation via CuO$_6$ octahedra elongation.