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Considering the next-nearest neighbor hopping interaction of the electrons, we investigate the magnon excitation of a theoretical model proposed for quasi-one-dimensional pi-conjugated organic ferromagnetic polymer. By employing the random-phase approximation (RPA), the magnon excitation spectrum is obtained. It is found that the lowest branch-the acoustic mode in excitation spectrum displays the characteristic of the ferromagnetic magnon, and with the increase of the next-nearest neighbor hopping interaction, the ferromagnetic correlation in the system will be weakened.

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