Theoretical investigations of the spin Hamiltonian parameters and local tetragonal distortions for Cu²⁺in crystalline and amorphous TeO₂and GeO₂

Abstract

The spin Hamiltonian parameters (i.e., anisotropic g factors and hyperfine structure constants) and local tetragonal distortions for Cu 2 + in crystalline and amorphous TeO 2 and GeO 2 are theoretically investigated using the high-order perturbation formulas of these parameters for a tetragonally elongated octahedral 3d 9 cluster. The impurity Cu 2 + occupying the octahedral sites are found to experience the relative tetragonal elongation ratios of about 11.4% and 9.5% for crystalline TeO 2 and GeO 2 and 10.8% and 6.6% for amorphous TeO 2 and GeO 2 , respectively, along the C 4 axis due to the Jahn-Teller effect. This reveals the larger tetragonal elongation distortions for the Cu 2 + centres in crystalline than amorphous systems (especially TeO 2 ). The theoretical spin Hamiltonian parameters show good agreement with the experimental data. The results are discussed. IntroductionTeO 2 and GeO 2 containing copper show interesting thermal and conductive [1,2], mechanical [3], acousto-optic [4] and hyperspectral imaging [5], electronic [6], optical absorption [7-9] and photoluminescence properties [10]. Meanwhile, Cu 2 + impurities doped into crystals may be regarded as model systems due to the relatively simpler energy levels (only one ground state and one single excited state under ideal octahedral crystal-fields [11]) and have been an important topic of electron paramagnetic resonance (EPR) spectroscopic measurements [12,13]. EPR experiments were carried out for low concentration (0.1% mol) Cu 2 + doped crystalline and amorphous TeO 2 and GeO 2 , and the spin Hamiltonian parameters (i.e., anisotropic g factors g and g ⊥ and hyperfine structure constants A and A ⊥ ) were also measured at 77 K [14,15].As for the theoretical interpretation for the above experimental results, the previous analysis was generally unsatisfactory [14,15]. First, the simple second-order g formulas were adopted with various adjusted molecular orbital coefficients [14,15]. Moreover, local structures were not involved in the calculations. As a result, the calculated spin Hamiltonian parameters were not in good agreement with the observed values. In fact, the Jahn-Teller ion Cu 2 + may suffer the Jahn-Teller effect (i.e., the phenomenon of removal of degeneracy of energy levels via vibration interactions, resulting in lower symmetries and energies [11,16]) and thus bring forward modification in the local environments around the impurity as compared with the host cation sites.