Corners And Rhombic Octahedral 3d 7 Ion Spin Hamiltonian Parameters Theoretical Research

As an effective tool to investigate optical and magnetic properties of crystals doped with transition-metal and rare-earth ions,electron paramagnetic resonance(EPR) technique has been widely applied in many fields such as physics,chemistry,material science and life science.Experimental results of EPR are usually characterized by the spin Hamiltonian parameters,i.e.,zero-field splitting,g factors and hyperfine structure constants.Co²⁺(3d⁷) is a very important system among transition-metal ions and often plays a unique role in properties and applications of some functional materials.A large number of documents for EPR studies on Co²⁺ octahedral clusters have been reported, whereas the related theoretical explanations are not satisfactory yet due to some imperfectness in theoretical models and formulas.In order to overcome the above weakness,in this work,the energy matrix of ground state ⁴T₁(F) for 3d⁷ ions in tetragonal and orthorhombic(rhombic) symmetries are established from Abragam's fiction angular method.Then the calculation formulas for g factors and the hyperfine structure constants are obtained from diagonalization of the energy matrix.In the formulas,the contributions from the admixtures among various J states,the fourth-order term(D_ηor B₄²) of orthorhombic(or rhombic) crystal-fields and ligand orbital and spin-orbit coupling interactions,which were usually neglected in the previous works, are taken into account here from the cluster approach.Furthermore,investigations of the spin Hamiltonian parameters are related to the local structures of impurity ions in crystals.These formulas are applied to some tetragonal(e.g.,NH₄I:Co²⁺ and SrLaAlO₄: Co²⁺) and orthorhombic/rhombic octahedral Co²⁺ centers(e.g.,CaTiO₃:Co²⁺ and SrO:Co²⁺).Based on the calculations,the admixtures among J=1/2,J=3/2 and J=5/2 states have significant contributions to the spin Hamiltonian parameters are fond to be important.In addition,for the systems having large spin-orbit coupling coefficient or strong covalency(such as NH₄I:Co²⁺),the contributions from the ligand orbitals and spin-orbit coupling interactions cannot be neglected.Besides,the contributions from the fourth-order term of the orthorhombic/rhombic crystal-fields are also important and should be considered.By analyzing the EPR spectra of above systems,the information about local structures for Co²⁺ is also obtained.The tetragonal Co²⁺ center in NH₄I can be described as a compressed octahedron due to the stronger crystal-fields of axial H₂O molecules.For tetragonal Co²⁺ centers in SrLaAlO₄,Co²⁺ replacing the host Al³⁺ may induce an elongation of the perpendicular bond lengths byΔR≈0.05(?),since the sum of the radii for Co²⁺ and O^2- is much large than the bond length R_⊥for the host Al³⁺ site. For the orthorhombic Co²⁺ center in CaTiO₃,since the impurity Co²⁺ differs from the host Ti⁴⁺ in ionic radius and charge,the bond lengths along two directions may suffer a relative variation by about 5.4%,yielding the more significant orthorhombic distortions. For the rhombic Co²⁺ center in SrO,since the ionic radius of Co²⁺ is much smaller than Sr²⁺,the impurity may not occupy exactly the host Sr²⁺ site but suffer an off-center displacementΔR_Co≈0.23(?) along[110]axis,reducing the local symmetry from cubic in the pure crystal to rhombic in the impurity center.