Spin Waves in a Surface-Diluted Quant um Spin system

A theoretical investigation of the effects of surface dilution on spin waves in a semi-infinite transverse Ising model (TIM) is presented. Within the framework of the double-time Green's function theory, the loctl density of spin-wave states is obtained by the application of the cluster-Bethe-lattice (CBL) method. Numerical calculations of paramagnetic phases reveal that surface dilution will lead to appearance of the localized spin-wave states whose frequencies are bulk independent while the corresponding density of states is a function of the exchange interactions. Increase of the bulk exchange interactions between the surface and the bulk spins tends to diminish the localized spin-wave states. Dependence of the local density of states on the concentration p of the magnetic atoms is similar with that in a three-dimensional infinite TIM which has been discussed in our previous paper.