Results are presented for spin-wave dispersions in geometrically frustrated stacked triangular antiferromagnets with a thin film or semi-infinite geometry having either zero, easy-plane, or easyaxis anisotropy. Surface effects on the equilibrium spin configurations and excitation spectrum are investigated for the case of antiferromagnetically coupled films, serving to extend previous results on ferromagnetically coupled layers [E. Meloche et al., Phys. Rev. B 74, 094424 (2006)]. An operator equation of motion formalism is applied to systems which are quasi-one and quasi-two dimensional in character. In contrast to the case of ferromagnetically coupled films the new results show surface modes that are well separated in frequency from bulk excitations. Magnetic excitations in thin films with an even or an odd number of layers show qualitatively different behavior. These results are relevant for a wide variety of stacked triangular antiferromagnetics materials. PACS numbers: 75.30.Ds, 75.70.-i I. INTRODUCTION The significant amount of research effort devoted to the discovery and understanding of new aspects of geometrically frustrated magnetic systems in recent decades has been almost exclusively focused on the study of bulk properties. 1 Among such systems, a large number of materials have been identified which are realizations of the prototype frustrated triangular antiferromagnet (AF). In addition to the AF near-neighbor in-plane coupling, the vast majority of these systems are also characterized by AF coupling between stacked triangular layers, such as in most of the ABX 3 compounds. 2 Theoretical and experimental studies of magnetic excitations in these model materials have revealed important information on the nature of the fundamental interactions and exposed new types of spin-wave modes in the bulk systems. 3,4,5,6 Interest in surface effects on frustrated magnetic systems has been enhanced recently with where J i,j > 0 represents the intralayer nearest-neighbor AF exchange coupling and J ′ i,i ′ > 0 represents the interlayer AF exchange coupling. The effects of anisotropic exchange coupling are included through the parameters σ and σ ′ , and D i represents the strength of the single-ion anisotropy at a magnetic site labelled i. The Hamiltonian in Eq. (1) can used to describe systems characterized with easy-plane (D i > 0) and easy-axis (D i < 0) single-ion anisotropy.where the position vector ρ = (x, y) and the amplitudes S ± A1,n (k ) depend on the z coordinate through the layer index n. Similar expressions are defined for sites on sublattices B 1 , C 1 , A 2 , B 2 and C 2 . For a semi-infinite system the set of finite difference equations connecting the Fourier amplitudes may be expressed in supermatrix form as Mb = 0, where M is an ∞ × ∞ block-tridiagonal matrix defined as are considered. For simplicity, we outline the calculation of Q A (k , n). This quantity can be written in terms of the transverse spin-correlation functions S − A,n (t)S + A,n (t ′ ) k and S + A,n (t)S − A,n (t ′ ) k evaluated at equa...
