Yu Wan-Lun

An investigation of the zero-field splitting of Fe3+ ions at the tetragonal FeF5O site in Fe3+:KMgF3 crystals

The extremely large zero-field splitting of Fe3+ ions at the tetragonal FeF5O site in Fe3+:KMgF3 crystals has been interpreted on the basis of a second- to sixth-order perturbation approach, in which the spin-orbit coupling is regarded as the perturbation to the crystal-field and electrostatic interactions. The replacement of O2- for F- and its induced lattice relaxation are shown to give rise to a strong tetragonal crystal field which in turn results in the large zero-field splitting. Of the various sources contributing to the zero-field splitting, the displacements of the O2- and F- ions are found to be important.

Crystal field analysis for 3d4 and 3d6 ions with an orbital singlet ground state at orthorhombic and tetragonal symmetry sites

Abstract The energy level structure of 3 d 4 and 3 d 6 ions in an orthorhombic crystal field in the 5 D approximation is studied. The first and the second kind of orthorhombic symmetry sites in crystals, which differ in the orientation of the crystal field axes, are considered. Possible energy level schemes with an orbital singlet ground state are established and analysed in detail. General conditions for the orthorhombic crystal field parameters necessary to obtain a given energy level scheme are derived. Results are presented in the form of suitable ground state “phase’ diagrams to facilitate the analysis of spectroscopic data. Using the superposition model the formulas relating the crystal field parameters with the crystal structure parameters are derived for 3 d 4 and 3 d 6 ions at octahedral sites with the first and second kinds of orthorhombic distortion, as well as for tetrahedral orthorhombically distorted sites. Due to the ascent in symmetry method the results are also applicable to those tetragonal symmetry cases involving real crystal field terms. A literature survey has revealed numerous cases of Fe 2+ (3 d 6 ) ions with high-spin S = 2 at the first and second kinds of orthorhombic symmetry sites as well as at tetragonal symmetry sites. Several pertinent cases for 3 d 4 (Cr 2+ , Mn 3+ , Fe 4+ ) and 3 d 6 (Co 3+ ) ions have also been identified. The present crystal field analysis provides grounds for subsequent microscopic spin-Hamiltonian and high frequency EPR studies of 3 d 4 and 3 d 6 ions.

Determination of the MnF2 and ZnF2 crystal structure from the EPR and optical measurements of Mn2

The authors calculate the crystalline parameters for MnF2 and ZnF2 from EPR and optical measurements on Mn2+ ions. The results support the structure data previously reported by Stout and Reed (1954) rather than that by Baur (1958). In addition, the fourth-order perturbation formulae for the EPR parameters D and E are derived.

High-order perturbation formulae for the zero-field splitting of a 6S ion in C3 symmetry and its application to Mn(I):Ca5(PO4)3F

The relationship between the zero-field splitting parameter D and the C3 crystalline potential components for 6S ions is established with the use of the high-order perturbation method. It is found that the effect of the spin-spin interaction within the d5 configuration is comparable with the mechanism suggested by Orbach et al. (1962). By using the d-orbital theory proposed by Zhao et al. (1982, 1983, 1984) the optical levels and the zero-field splitting of Mn(I):Ca5(PO4)3F are calculated. The results agree well with the values measured experimentally.

Determination of the temperature variation of the crystal structure of CdCl2 from the EPR data for Mn2

The d-orbit theory and high-order expressions for the zero-field splitting in trigonal symmetry are used to analyse the temperature variation of the crystal structure of CdCl2 using the experimental EPR data for Mn2+:CdCl2 at different temperatures. The dimension c of the hexagonal unit cell varies linearly with temperature at different rates below and above T0=375+or-10K at which the structure forms a regular octahedron. An accurate value u=0.2435(2) is obtained, which is consistent with the observed value u=0.25(1). Further accurate X-ray measurements are required for testing the results obtained.

Reduction tables for tensorial products of irreducible tensor operators O(k)(J) used in spectroscopy

Double and multiple irreducible products of irreducible tensor operators O(ki)(J) obeying special commutation relations arising from the properties of angular momentum operators are considered. It is shown that the double product can be expressed in terms of another set O(k) associated with a coupling coefficient epsilon k(k1,k2) defined by (O(k1)*O(k2))(k)= epsilon k(k1,k2)O(k). An analytical expression has been derived for the coupling coefficient epsilon k(k1,K2) and its values are tabulated for k1 and k2 up to 3. It is proved that (O(k1)*O(k2))(k)=(O(k2)*O(k1))(k). Multiple irreducible products are also discussed. The coupling coefficients for triple products are tabulated for Sigma iki up to 6. Some important special cases of quadruple products are dealt with explicitly. Applications of the present results to high-order effects in spectroscopy are investigated.

Spin-lattice coupling of Mn2+ ions in calcite

It is found theoretically that the spin-lattice coupling constant GA1 is proportional to the axial zero-field splitting parameter D for a 6S-state ion in D3d symmetry. A study of the ratio GA/sup //1D provides an effective way of deciding the relative importance of the various mechanisms which contribute to the zero-field splitting. For Mn2+ in calcite (CaCO3) the spin-orbit coupling mechanism accounts for the parameters D, GA1 and GA2 and the ratio GA1/D very well; either the point-charge model or the superposition model of a crystal field is adopted. In contrast, no other mechanism fits the ratio. This indicates that the spin-orbit coupling mechanism is the most important. In addition, the superposition model of the spin Hamiltonian is found to interpret the parameters D, GA1 and GA2 very well.

Determination of the crystalline structure of Mn2+:CaZnf4 by EPR and optical spectra of Mn2+

The fourth-order perturbation formula for the axial field splitting of 6S(d5) in D4h (or D2d) crystal field is derived. According to the formula obtained and the d-orbital theory proposed by Zhao (Zhao et al. 1982), the crystalline structure of Mn2+:CaZnF4 has been determined from EPR and optical spectra data of Mn2+. The results (R=1.93 AA, theta =57 degrees ) are in good agreement with the X-ray data (R=1.93 AA, theta =58.3 degrees ).

The effect of uniaxial stress on the zero-field splitting of Mn2+ ions in MgO, CaO, MnO and SrO crystals

Two distinctive perturbation schemes are employed to study the effect of uniaxial stress on the zero-field splitting of Mn2+ ions in MgO, MnO, CaO and SrO crystals. It is found that the effect can be explained well in terms of the spin-orbit coupling mechanism if the crystal-field parameters are used for fitting the optical spectra. The theory predicts G11>0 and G44<0 for a 6S-state ion in an Oh crystal.

Local distortion of the orthorhombic charge-compensation defect sites in Cr3+:MgO

Abstract Relationships are established between the zero-field splitting and the local distortion parameters for Cr 3+ at the orthorhombic sites in MgO. These are used to derive the ligand positions from the experimental EPR data. The results obtained are quite consistent with those calculated recently, by Groh et al . (1994), using the embedded-quantum-cluster ICECAP method.