Theory of spin excitations in Fe(110) monolayers

We present theoretical studies of short-wavelength spin excitations in ferromagnetic Fe(110) monolayers either adsorbed on a W(110) substrate or free standing. We use an itinerant model of electrons as the basis for our analysis, with nine bands (the five $3d$ bands and the $4sp$ complex) included. The bands are described within an empirical tight-binding scheme, and the ferromagnetic ground state is generated from on-site intraatomic Coulomb interactions, described in mean-field theory. The random phase approximation (RPA) is employed to describe the spin excitations through analysis of the wave vector and frequency dependence of the dynamic transverse susceptibility. Several issues are explored. We compare the spin-wave stiffness and other features of the spin-wave spectrum for the free standing film and that adsorbed on the substrate to find substantial quantitative differences with origin in spin-spin interactions mediated by the substrate. We also compare the spin-wave spectrum calculated through use of the RPA, an approximate theory, but a scheme that does not invoke the adiabatic approximation, with results generated within the framework of the adiabatic approach. While the spin-wave exchange stiffnesses produced by the two methods are in agreement, there are substantial differences between excitation spectra at short wavelengths. We argue that effective interspin exchange couplings generated within the framework of the adiabatic approximation fail to provide a description of the spin-wave spectrum in the itinerant ferromagnets, beyond the low-frequency, long-wavelength regime where the spin-wave exchange stiffness suffices to describe the spectrum. We also discuss apparent hybridization gaps in the spin-wave spectrum. We show that in some cases they can be artifact of a poorly converged numerical analysis and, in one instance, on use of an inappropriate form for the intra-atomic Coulomb interaction.