Surface Magnons and Surface Spin Arrangements in Heisenberg Magnets with Two Kinds of Exchange Interactions

Acoustic surface-magnon spectra are calculated for semi-infinite ferro- and antiferromagnets, where spins are coupled via exchange interactions both with nearest neighbors (J₁) and with next-nearest neighbors (J₂). It is found that, when the parameter α=J₂/|J₁| lies in certain intervals, the surface-magnon frequency is negative or imaginary, although the bulk-magnon frequencies remain real and positive. This condition indicates that the uniform ferro- or antiferromagnetic spin arrangement is not stable. For several cases of this type, it is shown that a nonuniform spin arrangement, characterized by a rearrangement of spins in the surface region, has a lower classical spin-ordering energy than the uniform state, and hence is stable. In various cases, various different arrangements of surface spins are found to be stable, including a helical arrangement, in which spins in the surface region are ordered with helical symmetry while bulk spins are in an antiferromagnetic state.