Microscopic Explanations Of The Spin-Hamiltonian Parameters-"Equivalent Spin" Wave Function Method

The encouragement of this attempt comes from the extensive applications of theelectron paramagnetic resonance technique to various aspects of physics , chemistry, biology , and etc.Spin-Hamiltonian （SH） is the most e?ective theory to describe the electronparamagnetic resonance. It is well known that there exist two types of parameters,namely, the zero-field splitting parameters and the g factors. It is shown theo-retically and experimentally that the spin-Hamiltonian parameters are extensivelyrelated to the crystal structure and the electronic structure of the metal centralions. Microscopic study of the parameters of transition-metal 3dn ions in varioussymmetry crystals has become subject of a large amount of recent work.Until now, there are two approaches to calculate the spin-Hamiltonian parame-ters, namely, the complete diagonalization procedure and the perturbation method.However, the theories published early are not very much satisfactory because of thefollowing aspects:1. Some approximation are used and the limited applications and unsatisfactoryconvergencies.2. The theoretical approach of g factors in the complete diagonalization proce-dure recently large used in the literature is not right.This paper, we will develop an e?ective method to calculate the all spin-Hamiltonian uniformly. The main results are listed in the following:1. We proved that the method of calculating g factors in the complete diagonal-ization procedure is incorrect.2. We developed an e?ective method to calculate both the zero-field splittingparameters and the g factors–a fictitious-spin wave function method. Calcu-lations show that the spin-Hamiltonian parameters of the transition metal ion（3d₁～9） can be explained. 3. By means of the fictitious-spin wave function method, the spin-Hamiltonianparameters of the ions: Ni⁽2+（d₃）、Co³⁺（d₇）、V³⁺（d2）、Mn⁽2+（d5）、Fe³⁺（d5）、V⁽2+（d₃）、Cr³⁺（d₃）、Cr⁽2+（d4）、Fe⁽2+（d6） are investigated systematically.