Surface spin waves and surface spin arrangements in helical magnets

In order to investigate the nature of the spin arrangement in the surface of a semi-infinite helical magnet, we calculate both the surface spin-wave frequency spectra and the classical spin-ordering energies. We present detailed calculations for a (100) surface of a body-centered tetragonal lattice with nearest neighbor and next nearest neighbor exchange interactions (J₁ and J₂, which are both negative). The possibility that the exchange interactions in the surface (J^s₂) may differ from those in the bulk (J₂) is taken into account. We find the following: In the case 0≳J^s₂≳J₂, the surface spin-wave frequencies are real and positive, and hence the uniform helical spin arrangement is stable. On the other hand, in the case J^s ₂<J₂, there exist soft surface spin-wave modes, which indicate that the uniform helical spin arrangement is not stable. In the latter case, it is shown that a nonuniform spin arrangement, characterized by a rearrangement of spins in the surface, has a lower classical spin-ordering energy than the uniform state and hence is stable.