Magnon localization in one-dimensional disordered XYZ Heisenberg ferromagnets

Abstract

Disordered one-dimensional XYZ Heisenberg ferromagnets with substitutional impurities are studied. The substitutional spins give rise to a random distribution of the exchange couplings. By introducing a new transformation for spin operators, the XYZ Heisenberg Hamiltonian can be exactly diagonalized and expressed by Bose operators. Being restricted by the spin wave approximation, the Hamiltonian obtained is shown to be similar to the Anderson Hamiltonian for electronic systems. We have shown that the magnon localization should be destroyed at the middle of the band due to the effects of commensurability of the magnon wavelength and lattice constant. The magnon density of states and the localization length are shown to have singularities at the middle of the band irrespective of the strength of disorder. The middle of the magnon band can be reached not only by changing the magnon energy but also by varying the external magnetic field which facilitates the observation of the phenomenon.