M G Cottam

Theory of surface modes in ferroelectrics

A theoretical investigation is made of the possible occurrence of surface modes in semi-infinite ferroelectric materials. Three different approaches are used: (1) a microscopic pseudo-spin theory based on the Ising model in a transverse field, (2) a macroscopic Landau theory in which surface effects can be introduced phenomenologically, and (3) a polariton model appropriate to the very long wavelength region. Existence conditions and dispersion relations are deduced for the localised surface modes, which are predicted by all three methods. The results are illustrated by means of numerical examples. Methods (1) and (2) are found to give rise to similar results in certain limits, and the authors are able to establish a formal relationship between the two approaches. The applicability of the theoretical models to real ferroelectrics is discussed, and some experimental techniques by which the surface modes might be detected are suggested.

General linear response theory of polaritons in binary superlattices

A general fully retarded theory of polaritons in a two-component (binary) dielectric superlattice is developed using linear response techniques. The polariton Green functions of the superlattice are derived explicitly assuming arbitrary forms for the isotropic dielectric functions of the superlattice components. From these Green functions the dispersion relations and spectral intensities for transverse electric and transverse magnetic polariton models in the superlattice may be deduced. Some numerical illustrations are included. The results of the general theory are verified to yield correct forms in various known special cases. The authors also deduce the form of the Green functions in the nonretarded approximation, anticipating subsequent application of the theory to light scattering by low-frequency plasmon-polaritons in semiconductor superlattices.

The spin correlation functions of a finite-thickness ferromagnetic slab

Explicit expressions are derived for the Green functions between a pair of spin operators at any two sites within a Heisenberg ferromagnetic slab of finite thickness. These Green functions are found to contain a description of the bulk spin waves and surface spin waves, together with their spectral weighting factors. The results are employed to evaluate the magnetisation in the ferromagnet as a function of temperature and distance from the surfaces.

The spin correlation functions of a semi-infinite Heisenberg ferromagnet

Results are derived for the dynamic correlation functions between a pair of spin operators at any two sites within a semi-infinite Heisenberg ferromagnet at low temperatures, T<<Tc. The correlation functions are found to contain terms describing the effects of the bulk spin-wave modes and the surface spin-wave modes, together with appropriate weighting factors. The results are employed to evaluate the spin deviation in the ferromagnet as a function of temperature and distance from the surface.

Green-function theory of light scattering from plasmons in a superlattice with electron-gas layers

Abstract Linear response theory is employed to calculate the Green functions describing the plasma modes in a superlattice of two-dimensional electron-gas layers separated by an isotropic dielectric medium. Applications are made to inelastic light scattering from the plasma modes, and we give expressions for the spectral lineshape and integrated intensity. Numerical results are obtained for GaAs Al x Ga 1 − x As superlattices,allowing comparison with experimental data.

Bulk and surface plasmon modes in a superlattice of alternating layered electron gases

Calculations are presented for the collective plasmon modes of a superlattice consisting of two-dimensional electron gas layers separated by media of alternating thickness and/or dielectric constant. The theory is developed for bulk plasmon modes in an infinite superlattice, and for bulk and surface modes in a semi-infinite superlattice. Applications are made to layered electron gases in semiconductor heterojunctions (such as GaAs/AlxGa1-xAs), and in particular to light scattering from the plasmons.

Theory of spin-wave interactions in s=1 two-sublattice uniaxial magnets

A semi-invariant diagrammatic perturbation formalism is employed to study spin-wave interaction effects in S=1 Heisenberg magnets with single-ion uniaxial anisotropy and in an applied magnetic field. A general two-sublattice model is assumed with both intra-sublattice and inter-sublattice exchange interactions. The theory takes account of the optical branches to the spin-wave spectrum (arising due to the single-ion anisotropy) as well as the usual spin-wave excitations. Expressions are derived for the renormalised energy and damping of all these modes as a function of temperature and applied field in the ordered regime, but excluding the spin-flop phase. Numerical application is given to the metamagnetic system FeCl2 in its zero-applied-field antiferromagnetic phase. The results are found to be in good agreement with recent one-magnon Raman scattering measurements for this material.

Effects of finite charge-layer thickness in Raman scattering by plasmons in semiconductor superlattices

Abstract A response-function theory of light scattering by plasmons in the bulk of semiconductor superlattices is employed to study effects due to the finite thickness of the charge layers. It is shown that in the non-retarded limit of this theory there may be two low-frequency plasmon peaks in the light scattering spectrum, compared with only one bulk plasmon peak in the two-dimensional charge sheets model of semiconductor superlattices. The spectral lineshapes and intensities corresponding to the plasmon excitations are calculated. This theory is applied in particular to GaAs/ AlxGa1-xAs superlattices, allowing comparison with experimental data.

A magnetostatic theory of the response functions for a finite-thickness ferromagnetic slab and the application to Brillouin scattering

Calculations are given for the spin-dependent response functions (or Green functions) of a finite-thickness ferromagnetic slab using magnetostatic theory. The results are employed to obtain expressions for the integrated intensities for Brillouin scattering from the surface (magnetostatic) modes and bulk spin-wave modes of a ferromagnetic slab. Numerical estimates are made to compare the theory with recent experimental measurements for Fe and EuO, and it is found that many of the experimental observations can be satisfactorily explained.

Surface excitations for the Ising model in a transverse field

Abstract We employ a microscopic theory to discuss the excitation spectrum of a semi-infinite spin system (or pseudo-spin system) described by the Ising model in a transverse field. It is shown that under certain conditions localised surface spin waves may exist, as well as the usual bulk spin waves.