Critical points and the two-magnon spectrum

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Abstract
The spectrum of two noninteracting magnons in a simple-cubic Heisenberg ferromagnet is examined for representative values of the next-nearest-neighbor exchange interaction. The critical points of the two-magnon continuum for total wave vectors in the [111] direction are analyzed and are found to be of two kinds: (i) isolated critical points which give rise to Van Hove type singularities and (ii) lines of critical points leading to logarithmic divergencies in the density of states. The critical-point structure is more complicated than the nearest-neighbor case and the number and positions of the critical points depend on the ratio of the next-nearest- to nearest-neighbor interactions. Finally, the Ising levels are obtained and their relationship to the continuum and two-magnon bound states discussed.