D. R. Tilley

Landau theory of phase transitions in thick films

Abstract A simple expression is used for the free energy density with a one-component order parameter, and the boundary conditions at the surfaces of a film of thickness L are given by means of an extrapolation length δ. Exact expressions are given for the critical temperature and the order parameter profile in terms of elliptic functions, and the nature of the phase transition is discussed.

Spin waves in a magnetic superlattice

Abstract A superlattice consisting of alternating layers of two simple-cubic Heisenberg ferromagnets is considered. The dispersion equation for spin waves propagating in a general direction in the superlattice is derived by the transfer-matrix method. The result is illustrated numerically; the curves are analogous to those found for phonons in a diatomic superlattice.

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.

Far-infrared spectroscopy of phonons and plasmons in semiconductor superlattices

Abstract Experimental far-infrared spectra of semiconductor superlattices and the related theory are reviewed. An account is given of Fourier-transform spectroscopy in various forms. In discussing superlattice spectra, a distinction is made between long- and short-period superlattices. In the former the constituent layers are many monolayers thick and can be described as slabs of the corresponding bulk material. A fairly simple account of the far-infrared optics can be based on this description, which is usually applied by treating the superlattice as a uniaxial effective medium in which the dielectric-tensor components are given by averages over the dielectric constants of the layer materials. Examples of spectra are shown for all the main experimental techniques. In short-period superlattices the effect of confinement on the dielectric function must be included; this review concentrates on the effect on phonon modes. Experimental measurements of confined-mode frequencies show significant shifts from values predicted by theories that assume perfect interfaces. This indicates that the effect of interface roughness must be included into phonon-confinement models. It is shown how this can be incorporated into a 1D lattice-dynamic model which leads to a generalised effective-medium description. Comparison with experimental results is presented. Possible future developments are discussed in a final section.

Landau theory for coupled ferromagnetic and ferroelectric films and superlattices

Abstract This Communication is concerned with the implications of a free energy expression for two media in contact; exchange coupling across interfaces is included. Exact implicit equations are derived for the critical temperatures of two semi-infinite media in contact, of a film of one medium embedded in another, and of a superlattice structure.

Transverse surface and slab modes in semiconductor superlattices

Abstract It is shown from the exact equations for transverse electromagnetic waves propagating in a superlattice that in the long-wavelength limit the superlattice has the optical properties of a conventional uniaxial medium. This result is used to derive the dispersion equations for polaritons at single and double interfaces between superlattices and ordinary media.

Thickness Transitions of Ferroelectricity in Thin Films

The disappearance of ferroelectricity in thin films is discussed in the framework of the Landau theory. The way in which ferroelectricity is lost with decreasing film thickness has the properties of a phase transition. The polarization profiles, the average energy density and the average polarization, which depend on the film thickness, are analytically obtained for various boundary conditions.

Hysteresis loops of ferroelectric bilayers and superlattices

A ferroelectric superlattice with an antiferroelectric interfacial coupling is considered; the same model describes a bilayer with antiferroelectric coupling. By mapping minimum points in the Landau free energy expression and plotting them against the applied electric field, a triple hysteresis loop pattern is obtained. The loop patterns vary between typically ferroelectric and typically antiferroelectric depending on the layer thicknesses and the magnitude of the interfacial-coupling constant. This work suggests the possibility of designing multilayer elements for computer memories with four or more different storage states.

Theory of far infrared properties of magnetic surfaces, films and superlattices

Abstract Many magnetic materials, particularly antiferromagnets and ferrimagnets, have resonance frequencies in the far infrared, say between 10 and 100 cm−1. The first experimental studies of these were by absorption spectroscopy but in the last 15 years attention has shifted to a more ‘optical’ point of view in the study of reflection and transmission. Experimental techniques that are now available should lead to a rapid expansion of such studies. This expansion is likely to include the application of far-infrared spectroscopy to characterisation, that is, the determination of the basic magnetic parameters of samples. Particular interest will attach to thin films and superlattices. We review the theoretical framework necessary for the interpretation of such experiments. The first part of the review is devoted to existing studies, particularly resonance, reflectivity and transmissivity studies of antiferromagnets and ferrimagnets. We include a brief section on growth of thin films and superlattices. The underlying quantity is the dynamic permeability tensor μ(ω). In the second part we discuss derivations of μ(ω) for various magnetic materials and then give an account of derivations of reflectivity from μ(ω). Experimental data often exhibit the property of non-reciprocity, that is, the reflectivity, for example, changes when the static magnetic field is reversed. In some cases non-reciprocity occurs only when the sample is dissipative while in others it is intrinsic. We pay attention to non-reciprocity throughout the review and in a final section we review the results of discussions based on thermodynamics.

Calculation of Nonlinear Susceptibility Tensor Components in Ferroelectrics

We present the formalism within which all second and third order nonlinear susceptibility coefficients can be calculated from the Landau expansion for an isotropic paraelectric phase by means of the Landau-Khalatnikov dynamical equations. Both first-order and second-order phase transitions are considered. Detailed results are given for all the second-order coefficients in the ferroelectric phase and for third harmonic generation, intensity-dependent refractive index and d.c. Kerr effect in both paraelectric and ferroelectric phases.