Spin excitations in exchange-dominated regime on (1 0 0) and (1 1 0) antiferromagnetic surfaces

Abstract

Theoretical investigations in the context of Heisenberg model have been made for (1 0 0) and (1 1 0) magnetic surface dynamics for a semi-infinite antiferromagnet geometry. The calculations apply to the exchange dominated regime and are based on a spin-wave operator and matching technique within the framework of non-interacting spin-wave theory. The theoretical formalism developed here does not include either relaxation or reconstruction at the surface and no electronic effects have been considered. Dispersion curves of surface spin-waves are obtained within a single framework by matching the evanescent and travelling solutions, respectively, obtained from the secular equation and satisfying the boundary conditions brought about by the surface. The excitation spectrum of the surface spin-waves has been obtained and compared with that for bulk spin-waves. The quantized bulk modes of the same energy travelling to and away from the surface are related to one another by reflection coefficients, for which sum rules are derived. The numerical results for the evolution of acoustic and optical modes are presented for two different surface planes, namely (1 0 0) and (1 1 0). The findings reported here show that: (i) the reduced coordination number for atoms near the surface as well as the surface orientation play an obvious and crucial part in the surface spin-wave spectra; (ii) the evolutions of bulk as well as surface modes undergo significant changes as a function of the bulk-surface exchange integrals for a given direction of propagation of the spin-wave modes along the surface.