R. J. Elliott

Neutron Scattering from a Liquid on a Jump Diffusion Model

The incoherent inelastic scattering cross section of slow neutrons from liquids is calculated using a simple model in which the liquid is assumed to have appreciable short range order in a quasi-crystalline form. Diffusive motion takes place in large discrete jumps, between which the atoms oscillate as in a solid. The model predicts a definite, easily calculable cross section which is not dominated by diffusion effects as when continuous diffusion is assumed, but shows a characteristic variation with angle which could be looked for experimentally. The related pair correlation functions are dominated at small r and t by vibrational effects. Although simple and extreme the model explains several aspects of the observations of Brockhouse and Pope in 1959 and others. A brief discussion of the coherent scattering cross sections for the model is given although explicit formulae are not obtained.

Theory of the absorption edge in semiconductors in a high magnetic field

Abstract A theory based on the effective mass approximation is given for hole-electron pairs in a semiconductor in a magnetic field. The intensity of the absorption edge is determined by the wave function of relative motion of the pair, so that essentially it becomes necessary to solve the Schrodinger equation for a hydrogen atom in a magnetic field. This is done in an approximation valid in high fields which assumes that the Coulomb term affects only the motion along the field, and uses a potential form which allows the solutions to be written in terms of confluent hypergeometric functions. The results show that the main intensity in each magnetic sub-band transition is thrown into the lowest exciton line and that the absorption in the continuum is reduced to an insignificant shoulder. The peaks observed in the so-called magneto-optic effect will all be exciton peaks.

The Theory of Magnetic Resonance Experiments on Salts of the Rare Earths

A general account is given of the theory of paramagnetic resonance in rare-earth crystals, assuming that the crystalline electric field splitting is less than the spin-orbit splitting. The treatment is related, as far as possible, to numerical parameters, which are sufficiently comprehensive for it to be a straightforward process to pass from a given crystalline field to the spin-Hamiltonian.

Raman scattering and theoretical studies of Jahn—Teller induced phase transitions in some rare-earth compounds

The rare-earth crystals DyVO4, DyAsO4 and TbVO4 undergo structural phase transitions at 14, 12 and 34 K respectively induced by a cooperative Jahn-Teller effect. An experimental investigation of the phase changes has been made using Raman scattering methods. For purposes of comparison, the Raman spectra of DyPO4, YVO4 and GdVO4 (which do not undergo phase transitions) have also been measured. A detailed theory of the phase transitions has been developed which accounts for the electronic and vibrational Raman spectra. The lowest four electronic levels of Dy3+ and Tb3+ are treated in a pseudospin formalism, and the theory is discussed in terms of mixed phonon and pseudo-spin excitations. The singly degenerate κ ≈ 0 optic phonons are not measurably affected by the transitions, but splittings of up to 20 cm-1 developed in the doubly degenerate Eg phonon modes in the Raman spectra owing to anharmonic couplings with the electronic states. Splittings are also observed in the lowest electronic levels of the rate earth ions below the transition temperature; these electronic modes effectively constitute the soft mode which causes the transitions to occur. A molecular field model is first used in the theoretical analysis. The equations of motion of the coupled excitations are then found and the energies, line widths and dispersion of the mixed excitations are discussed. The connexion between the static strain and the acoustic phonon mode coupling is investigated, and a thermodynamic treatment of the elastic constants is given. From the Raman data, it appears that in TbVO4 the acoustic mode coupling is stronger than the optic mode coupling.

Theory of the Resistance of the Rare Earth Metals

The electrical resistance of the heavy rare earth metals shows strong anomalies at the temperatures where the magnetic order changes. These are most marked in measurements made along the hexagonal axis. A simple theory of the effect is given on the basis of two mechanisms. The spiral spin structures found in these materials cause an exchange field at the conduction electrons with a lower symmetry than that of the lattice. This introduces new boundaries in the Brillouin zone and distorts the Fermi surface. This distortion and the scattering of the conduction electrons by the spin disorder in these materials is calculated. The order of magnitude of the effect agrees with that calculated for a simple spherical Fermi surface. Agreement between experiment and theory is improved by assuming that the Fermi surface lies inside a boundary of the original zone and is cut by a new superlattice boundary near its extremity. Further improvement is made by including the variation of the spiral pitch with temperature.

The Magnetic Properties of Certain Rare-Earth Ethyl Sulphates

The theory of the magnetic properties of rare-earth ions in crystals, which has been developed in preceding papers, is here applied to the ethyl sulphates. The magnetic resonance and susceptibility results are discussed at length, and it is shown that the observations can be explained by using fields of C3۸ symmetry which vary in a systematic way as one rare-earth ion is replaced by another.

The Vibrations of an Atom of Different Mass in a Cubic Crystal

The modes of vibration of an atom of different mass substituted in a cubic crystal without change of force constant are studied by the Green function method of Lifshitz. In particular, explicit formulae involving only the density of states of the perfect lattice are obtained for the amplitude of oscillation of the defect atom itself as a function of frequency. For light masses localized modes appear with frequencies above the range of the unperturbed modes. For all defects the perturbed modes with frequencies in the continuum are changed near the defect. For heavy masses there are resonant frequencies near which these modes are considerably affected. The results are evaluated for a Debye spectrum of lattice modes. The mean-square amplitude and velocity of the defect atom, which are of interest in the Mössbauer effect are computed from these at various temperatures, and studied analytically in the classical limit.

Theory of fine structure on the absorption edge in semiconductors

Abstract General equations are derived for the details of the direct absorption edge in a semiconductor when the effects of excitons and of an applied external magnetic field are included. The effects produced by magnetic fields and excitons separately are readily derived as special cases and these are briefly reviewed with reference to work already published. The problem including both simultaneously could not be solved in general but expressions for the continuous absorption are obtained in an approximation valid in large magnetic fields. Simple spherical bands are assumed throughout and spin effects neglected.

Current-driven switching of magnetic layers

The switching of magnetic layers is studied under the action of a spin current in a ferromagnetic metal/non-magnetic metal/ferromagnetic metal spin valve. We find that the main contribution to the switching comes from the non-equilibrium exchange interaction between the ferromagnetic layers. This interaction defines the magnetic configuration of the layers with minimum energy and establishes the threshold for a critical switching current. Depending on the direction of the critical current, the interaction changes sign and a given magnetic configuration becomes unstable. To model the time dependence of the switching process, we derive a set of coupled Landau-Lifshitz equations for the ferromagnetic layers. Higher order terms in the non-equilibrium exchange coupling allow the system to evolve to its steady-state configuration.

Magnetic Phase Transitions

Phase transitions are an important class of physical phenomena with enormous practical applications which also raise fundamental theoretical problems. In magnetic systems both of these aspects are evident. It was the existence of magnetic order in materials like iron which first attracted attention to the subject of magnetism. With our enhanced understanding of the fundamental theory of magnetism these materials now form what is probably the most important testing ground of the theory of phase transitions since it is often possible to obtain a simple but realistic model Hamiltonian to describe the system. For example the most studied theoretical model which displays a phase transition is the Ising model and this forms a good description of some,magnetic systems.