Studies on the Local Structure and the Spin Hamiltonian Parameters for Co²⁺ in CaTiO₃

Abstract

The local structure and the spin Hamiltonian parameters g factors gi (i =x, y and z) and the hyperfine structure constants Ai for Co2+ in orthorhombic CaTiO3 are theoretically investigated from diagonalization of 6 × 6 energy matrix within the 4T1 ground state for a 3d7 ion in orthorhombic symmetry. In the calculations, the contributions from the admixtures of various J states (J=1/2, 3/2, 5/2), the ligand orbitals and spin-orbit coupling and the fourth-order orthorhombic field parameter, which were usually neglected in the previous works, are taken into account. The crystal-field parameters are determined from the superposition model in consideration of the suitable lattice distortion due to the charge and size mismatching substitution of Ti4+ by Co2+. Based on the studies, the bond lengths R1 and R2 in the xy plane are estimated to suffer the relative alternation R ≈ 5.4%, yielding more significant orthorhombic distortion in the impurity center as compared with that for the host Ti4+ site in pure crystal. The calculation results based on the above local lattice distortion show reasonable agreement with the observed values. The various contributions to the spin Hamiltonian parameters are discussed. Present studies may theoretically verify that the impurity Co2+ occupies the 6-fold coordinated Ti4+ site rather than the 12-fold coordinated Ca2+ site, associated with the enhanced orthorhombic distortion due to the mismatching substitution.

Theoretical Investigations on the Off-Center Displacement of Co2+in SrO by Analyzing Its AnisotropicgFactors

“…It is proved that taking into account these factors is significant, the relevant detailed discussion may reference our previous work. [22,23] In summary, the off-displacement value ∆𝑅 ≈ 0.023 nm for Co 2+ ions in SrO is obtained by fitting the calculated 𝑔 factors to the observed values, it is very close to the value ∆𝑅 ≈ 0.021 nm in previous works, the calculated 𝑔 factors based on the off-center displacement show good agreement with the experi-086103-3 mental data. It is necessary to consider the contributions from 𝐽-admixtures, the fourth-order term 𝐷 𝜂 of rhombic crystal-fields and ligand orbital and spinorbit coupling interactions which are usually neglected in the course of the calculation of 𝑔 factors.…”

Defect properties of cobalt-doped hexagonal barium titanate ceramics

“…Hence, the parameter ( ) B 0 4 3 determined from the fit of χ mol (T) is the more reliable one. To our knowledge, apart from the studies of Lu et al [43] on the Spin Hamiltonian parameters of Co 2+ in CaTiO 3 , there are no further reports on the ligand field parameters of Co 2+ incorporated at B site of a perovskite. Lu et al [43] reported a 10Dq value of about 14 000 cm −1 which corresponds only roughly with the 10Dq value of 20 000 cm −1 obtained from our susceptibility data (section 3.4.1).…”

“…To our knowledge, apart from the studies of Lu et al [43] on the Spin Hamiltonian parameters of Co 2+ in CaTiO 3 , there are no further reports on the ligand field parameters of Co 2+ incorporated at B site of a perovskite. Lu et al [43] reported a 10Dq value of about 14 000 cm −1 which corresponds only roughly with the 10Dq value of 20 000 cm −1 obtained from our susceptibility data (section 3.4.1). CONCORD also allows the simultaneous fit of the ΔE values for different directions of the magnetic field, which can be applied for Co 2+ (Q-band) was fitted.…”