Zero Field Splittings of t23 Cubic Terms

We have investigated the possibility of obtaining good approximate analytical expressions for the zero field splittings of cubic terms belonging to the t23 configuration. Spin—orbit, and trigonal and tetragonal field perturbations are considered, and a perturbation expansion based on a strong cubic field zeroth‐order Hamiltonian is used. Only in the case of 4A2 and a2E terms does the expansion converge sufficiently rapidly for a single order of perturbation theory to provide a useful approximation for octahedral Cr3+ or tetrahedral Co2+ complexes. In the case of trigonal symmetry, we investigate the range of validity of the perturbation expressions, by comparison with exact numerical solutions of the crystal‐field eigenvalue problem for the complete d3 configuration.

[1]  A. Schawlow,et al.  Fluorescence of MgO:Cr3+Ions in Noncubic Sites , 1965 .

[2]  M. Sturge.  Effect of Stress on the Level Splittings of Ruby: Origin of the Ground‐State Splitting , 1965 .

[3]  M. Nathan,et al.  Cr 3+ Fluorescence in Garnets and Other Crystals , 1965 .

[4]  P.-O. Loewdin,et al.  Studies in Perturbation Theory. IX. Connection Between Various Approaches in the Recent Development—Evaluation of Upper Bounds to Energy Eigenvalues in Schrödinger's Perturbation Theory , 1965 .

[5]  R. Macfarlane.  On the Ground‐State Splitting in Ruby , 1965 .

[6]  R. Macfarlane.  Analysis of the Spectrum of d3 Ions in Trigonal Crystal Fields , 1963 .

[7]  M. Sturge.  Strain-Induced Splitting of the 2E State of V2+ in MgO , 1963 .

[8]  H. Kamimura.  Anisotropic Spin-Orbit Coupling ofd3andd8Solutes in Corundum , 1962 .

[9]  H. Weakliem.  Optical Spectra of Ni2+, Co2+, and Cu2+ in Tetrahedral Sites in Crystals , 1962 .

[10]  J. Griffith,et al.  The Theory of Transition-Metal Ions , 1962 .

[11]  A. Schawlow,et al.  Strain-Induced Effects on the Degenerate Spectral Line of Chromium in MgO Crystals , 1961 .

[12]  Y. Tanabe,et al.  Absorption Spectra of Cr3+ in Al2O3 Part A. Theoretical Studies of the Absorption Bands and Lines , 1958 .

[13]  Y. Tanabe,et al.  On the Absorption Spectra of Complex Ions IV:The Effect of the Spin-orbit Interaction and the Field of Lower Symmetry on d electrons in Cubic Field , 1958 .

[14]  J. Wertz,et al.  Crystal Vacancy Evidence from Electron Spin Resonance , 1957 .