Question: Magnon dispersion relation derive the magnon dispersion relation (24) for a spin S on a simple cubic lattice, z = 6 is replaced by where

Magnon dispersion relation derive the magnon dispersion relation (24) for a spin S on a simple cubic lattice, z = 6 is replaced by where the central atom is at p and the six nearest neighbors arc connected to it by six vectors δ. Look for solutions of the equations for dS^x_p/dt and dS^y_p/dt of the form exp (ik ∙ p – iwt).

ds;jdt = (2]S/k)(6S% – S.) .

ds;jdt = (2]S/k)(6S% S.) .

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