Abstract
The influence of next-nearest neighbor interaction on the dispersion characteristics of simple cubic, bcc, and fcc lattices is studied. It is shown that the next-nearest neighbor interaction affects significantly the dynamic characteristics of the above systems. In the scalar model describing the one-magnon excitations in magnetically ordered Heisenberg systems, the inclusion of the second coordination sphere can lead to the emergence of a minimum and an additional peak on the dispersion curves inside the Brillouin zone and to the disappearance of divergence of the density of states. In some cubic lattice models, the inclusion of next-nearest neighbor interaction may lead to a significant variation of the “anisotropy parameter:” in the longwave limit, two transverse branches may coincide or differ sharply from each other, depending on the relation between the force constants characterizing the interaction between the nearest and next-nearest neighbors.
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