Magnon properties of the one-dimensional quasiperiodic system

Abstract

At low excitations, the ferromagnetic spin-wave problem of the one-dimensional quasiperiodic system is converted into the one which is analogous to the electronic and phonon problems. The ferromagnetic magnon properties are studied by the transfer-matrix technique and it is concluded that the frequency spectrum is a Cantor set. It is also shown that, at low excitations, the antiferromagnetic spin-wave problem of the one-dimensional quasiperiodic system can be converted in a similar way to the ferromagnetic one, and the antiferromagnetic magnon properties can be studied by the transfer-matrix technique.