Theory Study Of The Electron Paramagnetic Resonance（EPR） Parameters Of Cu²⁺（3d⁹） Ions In PbTiO₃

3d9ions are an important class of the transition metal ions, which appear in many nonlinear optical crystals and laser crystals and so on. When3d9ions dope to the crystal, it will change the performance of the crystal significantly, which attracted the attention of scientists in production and theoretical studies. A lot of scientists have used a large number of theoretical calculations and experimental studies to study the electron paramagnetic resonance (EPR) parameters (g factors and hyperfine structure constants A value) of this type ions, the data obtained by the experiment which can effectively explain the local structure of doping crystal. However, most of the theoretical calculations of the EPR parameters are based on the perturbation theory. Use perturbation method to calculate the EPR parameters is popular. The perturbation calculation method can give the analytical expression, let the physical meaning is clear and easy to use by experimental workers, but the convergence of the perturbation term is difficult to determine and we can’t use the perturbation method theory to explain the accuracy of the formula. The sensitivity of the EPR parameters relative to the local structure of the doped crystal is high, so that the EPR parameters value calculate by the perturbation will make the error analysis of the local structure information of the doped crystal. To make the theoretical analysis of the EPR parameters to accurate response the local structure information of the doped crystal, in this article we use the complete diagonalization method and base on the crystal field theory to get the EPR parameters value which are satisfactory and consistent with the experimental value. The complete diagonalization method is a precise way, if we combine these two methods (perturbation and full diagonalization method) together, we can make the physical meaning clear of the calculation process, but also get accurate results.Use complete diagonalization method to calculate the EPR parameters of lead titanate PbTiO3(PTO):Cu2+have not done, In this article, we calculate the crystal field potential matrix elements and spin-orbit coupling matrix element in the D4h symmetry of3d9ion on the basis of Sugano four corners and the crystal field theory, establish a3d9ion complete diagonalization procedure, use the complete diagonalization method (CDM) and third-order perturbation method (PTM) to calculate the EPR parameters of PbTiO3(PTO):Cu2+. Compare this two calculated results, show that the CDM and PTM calculations close, and coincide with the experimental values. We can determine the local defect structure of the [CuO6]-10ion cluster is D4h symmetry, Rx=Ry=0.1952nm, Rz=0.2076nm by the calculated EPR parameters.