J R Fletcher

Time delay in tunnelling through a potential barrier

A simple method is proposed for calculation of the time taken for a particle to tunnel through a potential barrier. The method is applicable to long or short wave packets. For short wave packets the time is reduced below the results given by the stationary phase method.

The Jahn-Teller effect of octahedrally co-ordinated 3d4 ions

The chromous ion in magnesium oxide is studied and an interpretation is given of the acoustic paramagnetic resonance results of Marshall and Rampton. Because of the very strong orbit-lattice interaction it is important to take full account of the Jahn-Teller effect. The cluster approximation justified previously is used, and then are added the spin-orbit coupling, anharmonic forces, external magnetic field and random lattice strains. The resultant secular equations are usually solved numerically in terms of parameters to describe the strains and anharmonic couplings. It is postulated that the observed line shapes reflect random strain distributions and that peaks in the lines are correlated with turning points in the strain-resonance field curves. Parameters are chosen to fit the observations for a definite field orientation and it is shown that a good interpretation can then be given for the results for a variety of orientations. The energy-level diagram of the chromous ion is shown to be quite complicated, and it is pointed out that many more transitions than have yet been observed can be expected.

A variational groundstate for the dynamic Jahn-Teller effect

A set of variation states is constructed for a defect with degenerate states of E symmetry interacting with the modes of vibration of a cubic crystal. A projection operator is used to ensure that the states have the symmetry corresponding to the hamiltonian of the system. The energies of the ground and some excited states are derived together with the reduction factors for perturbations. Comparison shows that the cluster model cannot consistently give the values of these quantities except in the limit of strong interactions.

An EPR study of 3d4 ions in Al2O3 by thermal detection

A study by thermally detected EPR of the 3d4 ions Cr2+ and Mn3+ as trace impurities in the Al2O3 lattice has been undertaken. A complete and accurate description of the EPR spectra obtained from the first excited triplet of the ground manifold is given for magnetic fields in the range 0-1.6 T. The overall behaviour of the EPR lineshape for these strongly-coupled Jahn-Teller ions is shown to be consistent with the present theoretical understanding of the 3d+ ground state of these ions.

Temperature dependent electron-phonon coupling in FeCl2 observed by Raman scattering

Strong coupling between an electronic transition in the 5T2g(5D) manifold of Fe2+ ions in FeCl2 and the Eg optical phonons in this material has been observed by light scattering. The Raman spectrum is temperature dependent and shows a marked change at the antiferromagnetic ordering temperature. Above TN, the spectrum contains a symmetric band which becomes asymmetric on the high energy shoulder when the temperature is lowered. Just below TN the band comprises two sharp features accompanied by a third broad band. Well below TN the sharp features have coalesced. A simple model is presented which successfully accounts for the observed temperature dependence of the band position, width and structure.

The Jahn-Teller and Barnett effects

The Barnett effect (magnetisation by rotation) is shown to involve a coupling of the lattice momentum to localised electronic states in solids. If the electronic states are degenerate, the resulting Jahn-Teller effect is shown to be modified by this coupling, and numerical values of reduction factors are calculated. The effect can be particularly important for spin resonance in molecular crystals.

The role of the Jahn-Teller effect in chromium-doped GaAs

A dynamical Jahn-Teller model for Cr2+ and Cr3+ in GaAs is proposed in order to account for existing and new experimental data. In contrast to previous models, based on a static Jahn-Teller displacement, the tetragonal nature of the EPR spectrum is shown to arise from sites having particular values for the random strain. It is also shown that the data indicate the existence of at least two classes of chromium. In one class, chromium replaces gallium substitutionally and has Td symmetry, while in the second class chromium is at a site having trigonal symmetry.

Reduction factors for a Jahn-Teller cluster model with momentum coupling

It is shown that the Ham relationship 2q=1+p for the ground state reduction factors of the E*e Jahn-Teller cluster model breaks down when the interaction of the electronic states with the momentum of the cluster is included. In some symmetries this coupling is observed in the Barnett effect. Thus the breakdown of the Ham relation does not necessarily imply interaction with more than one E mode.

The angular dependence of strain broadened resonance lines

The angular dependence of resonances broadened by random internal strains or electric fields in trigonal crystals is derived for magnetic fields applied in directions close to the c axis. Two cases arise, in the first the line shows the expected 2 pi /3 periodicity, in the second the line divides into two components, each having 4 pi /3 periodicity.

Orbital states in Td symmetry

A brief discussion is given of some problems associated with the modelling of F-state ions in Td symmetry.