Green’s lattice function and local oscillations in a semibounded crystal

An analytic expression for Green’s function is derived in the k-representation for a simple model of a semibounded fcc crystal with an interaction of nearest and next nearest neighbors. The earlier dispersion relations for surface waves in cubic crystals are confirmed. The threshold of local oscillation generation near a defect (isotope) is calculated. It is shown that the peculiarities of the density of states which are important for the solution of similar problems can be analyzed by using two-dimensional projections of isofrequency surfaces. The obtained results describe, to within a redesignation, the peculiarities of spin excitation dynamics in a Heisenberg ferromagnet in the one-magnon approximation.

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