Low-frequency dynamics of cubic crystals with next-nearest neighbor interaction

The influence of next-nearest neighbor interaction on the dispersion charac teristics of simple cubic, bcc, and fcc lattices is studied. It is shown th at the next-nearest neighbor interaction affects significantly the dynamic characteristics of the above systems. In the scalar model describing the on e-magnon excitations in magnetically ordered Heisenberg systems, the inclus ion of the second coordination sphere can lead to the emergence of a minimu m 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 c ubic lattice models, the inclusion of next-nearest neighbor interaction may lead to a significant variation of the "anisotropy parameter:" in the long wave limit, two transverse branches may coincide or differ sharply from eac h other, depending on the relation between the force constants characterizi ng the interaction between the nearest and next-nearest neighbors. (C) 1999 American Institute of Physics. [S1063-777X(99)01111-1].