Investigations of the Defect Structure for Cu²⁺ in SrLaAlO₄

Abstract

The defect structure for Cu 2+ in SrLaAlO 4 is theoretically investigated by the perturbation formulas of the spin Hamiltonian parameters (g factors g , g ⊥ and the hyperfine structure constants A and A ⊥ ) for a 3d 9 ion in tetragonally elongated octahedra. Based on these studies, the tetragonal center may be attributed to Cu 2+ occupying the host Al 3+ site, associated with one hole delocalized at the four oxygen ligands in planar coordination. Furthermore, the four Cu,O bonds (perpendicular to the four-fold axis) are found to suffer an outward stretch of about 0.06Å due to (i) the local tenseness in this plane, arising from the size mismatching substitution of the smaller Al 3+ by the larger Cu 2+ and (ii) the weaker electrostatic attraction of the less charged Cu 2+ acting upon the four oxygen ions containing the delocalized hole. The calculated spin Hamiltonian parameters agree well with the experimental data. The defect structure of this center is discussed.

Theoretical Studies of the Spin Hamiltonian Parameters and Local Structures for the Two Tetragonal Cu2+Centers in Ca(OH)2

“…Meanwhile, the higher cubic orbital triplet 2 T 2g may split into an orbital singlet 2 B 2g (|xy ) and a doublet 2 E g (|xy , |yz ) [15]. Since the covalency of the studied Ca(OH) 2 :Cu 2+ is not strong and the ligand spin-orbit coupling interaction is very weak, the high order perturbation formulae of the SH parameters based on the conventional crystal-field model [18] containing merely the central ion orbital and spin-orbit coupling contributions can be reasonably adopted here. Thus, we have [18]:…”

“…Here g s (≈ 2.0023) is the spin-only value, k is the orbital reduction factor, ζ d and P are, respectively, the spin-orbit coupling coefficient and the dipolar hyperfine structure parameter for the 3d 9 ion in crystals, κ is the core polarization constant, N (≈ k) is the average covalency factor, characteristic of the covalency effect of the studied systems, E 1 and E 2 are the energy separations between the excited 2 B 2g and 2 E g and the ground 2 B 1g states [18], which can be determined from the energy matrices for a 3d…”

Theoretical studies of {63}^Cu Knight shifts of the normal state of YBa_2Cu_3O_7

“…Utilizing the perturbation method [11], the perturbation formulas for an orthorhombically elongated 3d 9 cluster can be derived as follows [10]:…”

Theoretical studies of the spin Hamiltonian parameters and the local structures for the tetragonal Cu2+ centers in the LKB glasses

“…Meanwhile, the higher cubic orbital triplet 2 T 2g may be split into an orbital singlet 2 B 2g (|xyN) and a doublet 2 E g (|xzN, |yzN) [5,10]. In order to study the EPR spectra and the local structures for the Cu 2+ centers in the LKB glasses, the high (fourth) order perturbation formulas [15] of the g factors and the hyperfine structure constants for a tetragonally elongated octahedral 3d 9 cluster can be adopted here. Since the studied Cu 2+ centers in the oxygen octahedra have insignificant covalency as well as weak ligand orbital and spinorbit coupling interactions, the formulas based on the conventional crystal-field model containing merely the central ion orbital and spinorbit coupling contributions are usually suitable treatments for such systems.…”

“…Since the studied Cu 2+ centers in the oxygen octahedra have insignificant covalency as well as weak ligand orbital and spinorbit coupling interactions, the formulas based on the conventional crystal-field model containing merely the central ion orbital and spinorbit coupling contributions are usually suitable treatments for such systems. Thus, we have [15]:…”