The optical-absorption and EPR spectra of octahedral Fe3+ center in yttrium aluminum garnet have been studied by diagonalizing the complete energy matrices for a d5 configuration ion in a trigonal ligand field. It is shown that the local lattice structure around an octahedrally coordinated Fe3+ center has an expansion distortion. The expansion distortion may be attributed to the fact that the radius of Fe3+ ion is larger than that of Al3+ion, and the Fe3+ ion will push the oxygen ligands outwards. Simultaneously, the local lattice structure distortion parametersR=0.0907

A quantum-admixture model for the d6 configuration ferrous complex molecules with the high-spin T lowspintransition has been established by using the unified crystal-field-coupling (UCFC) scheme. A generalstudy has been made on the spin transition of octahedrally coordinated d6 complexes, and a special applicationhas been given to an Fe(II) compound FeII(TRIM)2(PhCO2)(ClO4). The results show the following: (i) Thequantum picture of the spin transition of a d6 system, such as Fe(II), is much more complex than a simpletransition between the pure 5T2g and 1A1g states as usually understood. In practice, owing to spin-orbit coupling,spin is no longer a good quantum number and there is no longer a pure 5T2g or 1A1g state. Each of them splitsinto substates and each substate is a linear combination of various multiplets. The high-spin f low-spintransition of an octahedrally coordinated d6 ion is practically the crossover of the two lowest substates of 5T2gat the critical point. (ii) At the spin-transition critical point the magnetic moment íeff 5.22íB, which isobviously different from the simple average of the íeff values of high-spin and low-spin states but near thesaturation value. (iii) The calculation of the effective molecular magnetic momenteff for an octahedrallycoordinated Fe(II) ion shows that the íeff-T curve is in good agreement with Lemercier et al.’s experimentand both the low-spin value íeff ) 0.51íB and the high-spin value íeff ) 5.4íB are comparable with theexperimental values 0.76íB and 5.4íB, respectively. (iv) The T dependence of the crystal field parameter Dqin the spin-transition region is approximately linear.

A quantum admixture model for the d5 configuration of the high-spin T low-spin (HS T LS) transition (6A1T 2T2) Fe(III) complex molecules has been established by using the UCFC scheme. The analysis shows thatthere exists an indirect spin-orbital coupling interaction between the high-spin and low-spin states via theintermediate-spin states. This interaction may be described approximately by two small matrices (the orderis 25 and 14, respectively) of the Hamiltonian, which involves the electron-electron repulsion, the ligandfield,the spin-orbit coupling, and the Zeeman interactions. By diagonalizing these matrices, the electronicand magnetic structures of the Fe(III) molecules in the spin-transition region can be derived. The resultsshow a sensitive dependence on the ratio

Using the method of dynamical algebras, the solution of a homotriparticle linear spin cluster seach particlewith S=1/2d in a rotating magnetic field is obtained. We derive degeneracy energy levels and each level's Berry phase of this system. The Berry phase as a function of v and u has been determined by using the relationbetween the Berry phase and the angular velocityv of the rotating magnetic field as well as the angle ubetween the magnetic field and Zaxis. We obtain the changing diagram of the Berry phase of the basis state.

The EPR zero-field splitting of Fe3+in a trigonal-symmetry crystal field has been calculated on the basis of the complete matrices for ligand-field spin-orbit coupling of the d~configuration with C3 symmetry. The absorption spectrum, the EPR zero-field-splitting axial parameters D and F, and the cubic parameter a for the Fc3+ ion in sapphire have been interpreted uniformly.