The equations of motion for the dynamic properties of spin waves in three dimensions were obtained using Heisenberg model and solved for two and three dimensional lattices analytically up to an exponential operator representation. The second order Suzuki Trotter decomposition method was extended to incorporate second nearest interaction parameters into the numerical solution. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for two dimensional lattice as well as three dimensional simple cubic and bcc lattices. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor presenting the variation of energy transfer with respect to momentum transfer of spin waves. Second order Suzuki Trotter algorithm used conserved the energy.
International Letters of Chemistry, Physics and Astronomy (Volume 49)
H.S. Wijesinhe and K.A.I.L. Wijewardena Gamalath, "Spin Waves in Two and Three Dimensional Magnetic Materials", International Letters of Chemistry, Physics and Astronomy, Vol. 49, pp. 35-47, 2015