Abstract
A mechanism of the high temperature ferromagnetism in polymerized fullerenes is suggested. It is assumed that some of the C$_{60}$ molecules in the crystal become magnetically active due to spin and charge transfer from the paramagnetic impurities (atoms or groups), such as hydrogen, fluorine, hydroxyl group OH, amino group NH$_2$, or methyl group CH$_3$, dispersed in the fullerene matrix. The exchange interaction between the spins localized on the magnetically active fullerenes is evaluated using \textit{ab initio} calculations. The nearest neighbour and next nearest neighbour exchange interaction is found to be in the range $0.1\div 0.3 $ eV, that is, high enough to account for the room temperature ferromagnetism.
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