Spin waves in decorated lattices

Abstract The X X Z Heisenberg model is used to study the dispersion relation of spin waves propagating in decorated planar square and triangular lattices. A superposition of interpenetrating lattices will be used to generate the composed systems. The decorations are introduced in order to generate systems with more than one atom per unit cell. The formalism applied here allows us to study different types of decorated lattices according to the relative position between each other controlled by the parameters α and β . By using the Holstein–Primakoff transformation we obtained the SW dispersion relation for the decorated lattices considered here. The obtained numerical results show the effects of both (i) the relative position of the interpenetrating lattices and (ii) the intra-lattice and inter-lattice exchange couplings on the spin waves dispersion relation.