C A Bates

An analysis of the T ⊗ (e + t2) Jahn-Teller system with strong coupling

The T(X)(e+t2) Jahn-Teller system is studied in the strong-coupling approximation on a cluster model by transformation methods. An energy-minimisation procedure is used to show that the system will be localised in potential energy minima having either tetragonal, trigonal or orthorhombic symmetry depending upon the strengths of the e and t2 coupling constants. Detailed results are given for the orthorhombic case to underline the physical processes involved in the Jahn-Teller effect and provide a detailed mathematical framework for the calculation of other properties of the system (e.g. first- and second-order reduction factors, random-strain effects).

The properties of exchange-coupled triads of Cr3+ ions in ruby

The eigenstates and eigenvalues for a triad consisting of three exchange-coupled Cr3+ ions in ruby are derived from a phenomenological spin Hamiltonian. The terms included in the Hamiltonian are the isotropic, anisotropic and antisymmetric exchange interactions together with the single ion zero field term and dipole-dipole interaction term. The importance of each term is discussed in relation to various possible triads in ruby.

Lattice-ion interactions of Ti3+ in corundum I. The Jahn-Teller effect and the theory of the effects of electric field and strain

The magnetic properties of a Ti3+ ion in an Al2O3 lattice are discussed using a dynamic Jahn-Teller model in which an orbital triplet interacts with the vibrational E modes of the ligands. Calculations of the effect of applied electric field and strain on the electron paramagnetic resonance spectra are made. It is found that second-order vibronic effects are very important in both cases. The linear electric field effect gives rise to large g shifts of the order 10-4 for an applied electric field of 1 kv cm-1 while the strain tensors are of order 102 per unit strain. Comparison is made with experimental results.

The Jahn-Teller theory and calculations of the relaxation time and resonance lineshape for Fe2+ ions in Al2O3

Existing experimental data for the ground states of Fe2+:Al2O3 are accounted for by a multimode dynamic Jahn-Teller model in which an Fe2+ ion substitutes for an Al3+ ion. The first- and second-order Jahn-Teller reduction factors are found to be gamma =0.19, Fa= 0.0015 (cm-1)-1 and Fb=0.0024 (cm-1)-1 and satisfactorily account for the quenching of the trigonal field. The relaxation time T1, of the Fe2+ ion is then calculated to be approximately 2 mu s at 1.2K confirming that the Fe2+ ion is strongly coupled to the Al2O3 lattice. The main contribution to T1 is from the Etheta , Eepsilon components of the lattice momentum acting through the spin-orbit coupling and trigonal-field perturbations. The contributions to T1 from displacements due to other lattice modes are found to be smaller. An analysis of the APR or EF-EPR lineshape on the Jahn-Teller model is in agreement with all the experimental data.

Jahn-Teller effects in orbital triplets. I. Second-order contributions for D(T2) ions in cubic crystals coupled to E-type lattice distortions

Transformation methods are used to calculate the second-order contributions to the effective hamiltonian of a D(T2) ion coupled to E-type displacements in a cubic crystal. It is found that it is only possible to relate the first- and second-order Jahn-Teller reduction factors when a cluster model is used. For other lattice models, the parameters are unrelated. Finally, the orbital contribution to the magnetic susceptibility of a crystal containing delta (T2) ions is calculated.

The Jahn-Teller interaction and 3d9 ions at tetrahedral sites

Experimental data on 3d9 ions (Cu3+ and Ni+) at tetrahedral sites is reviewed and compared to the predictions of crystal field theory including the effects of covalency, 4p configurational mixing and the Jahn-Teller effect. Of the copper centres considered, only for the case of ZnO is this theory found acceptable and to make the optical and epr results consistent it is necessary to include second order Jahn-Teller effects. The first order reduction factor for angular momentum is found to be about 0.1. The hyperfine effect is explained using a reduction in the magnitude of the contact term caused by 4p mixing, as has previously been found in tetragonally distorted complexes.

Jahn-Teller effects in alkali halides containing S− and Se− ions

Abstract The EPR data from S− and Se− ions in alkali halide crystals were recently explained in terms of a strong T ⊗ t Jahn-Teller interaction together with spin-orbit coupling. An alternative model is proposed in which the Jahn-Teller interaction is dynamic and of T ⊗ e type with a trigonal crystal field also present.

Jahn-Teller theory of Cr2+ in corundum

The dynamic Jahn-Teller effect is used in a theoretical study of the properties of the Cr2+ ion in corundum. The ion is produced in ruby crystals by X-irradiation. The trigonal distortion in the crystal is taken into account in setting up the Jahn-Teller interaction, in choosing zeroth-order orbital states for the ion and in the magnetic interactions. Using the cluster approximation, the effective Hamiltonian is thus derived. The effects of trigonal distortion are found to be small and thus the problem closely resembles that of Cr2+: MgO discussed previously in which there is a very strong orbit-lattice interaction. Theoretical values for the parameters needed to describe the low-lying energy levels of Cr2+: Al2O3 are deduced. They are in agreement with values calculated from preliminary acoustic resonance results when the applied magnetic field is along the trigonal axis. It is hoped that the theory given will serve as a satisfactory basis for the discussion of more detailed acoustic resonance results and measurements of the magneto-thermal resistance in irradiated rubies.

Electric-field-induced thermally detected EPR of non-Kramers ions in Al2O3

The first EPR detection of the non-Kramers ions Cr2+ and Fe2+ in Al2O3 is reported. A technique employing thermal detection is used and shown to be advantageous for strongly coupled ions. It is proposed that the ionic displacements caused by radiofrequency electric fields induce transitions, giving APR-like absorption lineshapes. The mechanism applies to all magnetic ions in noncentrosymmetric sites.

The properties of Co2+ in zinc tungstate. I. The EPR spectrum and its interpretation

Measurements of electron paramagnetic resonance were made at 9.3 GHz and at liquid helium temperatures. The EPR spectrum was well represented by a spin hamiltonian of the form H=gx beta HxSx+gy beta HySy+gz beta HzSz+AxSxIx+AySyIy+AzSzIz+B(SxIz+SzIx) with gx=2.390+or-0.007, gy=3.41+or-0.02, gz=6.77+or-0.01, Ax=70+or-10 MHz, Ay=210+or-8 MHz, Az=900+or-5 MHz, mod B mod =30+or-5 MHz. The y axis coincides with the twofold b axis of the crystal and the x and z axes are the principal axes of the g tensor. These parameters reproduce the observed spectrum at all angles at which observations were made, within the experimental error of 5G. The value of B corresponds to a difference of approximately 1/4 degrees between the directions of the x axes of the g and A tensors. A theoretical analysis of the data is given and it is found that any Jahn-Teller effects are unimportant.