Theoretical Study On The Spin Hamiltonian Parameters And Knihght Shifts For 3d~9 Ions

The physical and chemical properties of Functional Materials(FM) can be improved by doped Transition Metal(TM) ions and the level of improvement largely depends on the electronic and local structures of the dopants. The mentioned microstructures of TM ions are usually characterized by related spectrums, particularly the Electron Paramagnetic Resonance(EPR: the anisotropic g factors, the hyperfine constants and the superhyperfine constants et al.) and Nuclear Magnetic Resonance(NMR: Knight Shifts). There are lots of EPR and NMR experiments for the 3d9 ions which are of specific representation and significance in the TM family due to their primitive energy structures. Unfortunately, most of the theoretical explanations related to the above experimental results are unsatisfactory because of the following shortcomings:(i) the contribution arising from the ligand orbitals and spin-orbital coupling are not included in the traditional crystal model.(ii) various adjustable parameters(eg. the crystal field parameters and so on) introduced in the description of the low-symmetry and the insufficient analysis of the Jahn-Teller(JT) effect are due to the fact that the defect local structures are not quantitativly connect with the discussion for the Spin Hamiltonian Parameters(SHP). Hence the local information of the impurity centers are difficult to obtain.(iii) The theoretical quantitative relationship between the g factors and Knight shifts are not derived in the previous theoretical study so that abundant adjustable parameters are brought in the simple fitting analysis.For the sake of overcoming the above disadvantages, the high order perturbation formulas deduced from the improved cluster model are utilized in the systematic theoretical treatments for the SHP of d9(Cu2+ and Pd+) and similar d7(Ni3+ and Pd3+) ions and the Knight Shifts of 3d9(Cu2+) ions. The complete spectral solution of the EPR and NMR spectra is successfully built, the local information of the defects are acquired and the following EPR and NMR phenomenon are reasonably interpreted:(1) The systematical illustrations for SHP of Cu2+ are achieved by adopting the high order perturbation formulas of g factors and hyperfine constants for a 3d9 ion in tetragonally and orthorhombically elongated octahedra and the defects local information are analyzed. i) The implicit normalized concentration at temperature T including the spin pseudogap(ΔAF) and the structural distortion attributed to the JT effect are taken into account during in theoretical performance for the temperature dependence of anisotropic g factors for the tetragonal and orthogonal Cu2+ centers in the underdoped High Temperature Superconductor(HTSC) YBa2Cu3O7-x(Tc=86.5K). Then, combining the cubic and tetragonal filed parameters, the orbital reduction parameter and other corresponding adjustable parameters, the experimental data can be satisfactorily explained. ii) The theoretical investigation for the Cu2+ sites lie in the alkali lead tetraborate glasses(90R2B4O7·9Pb O·Cu O, R=Li, Na and K) displays that the tetragonally elongated octahedra is formed in the way that the [Cu O6]10- complex stretches, respectively, along the C4 axis 18%, 23, and 30% for R=Li, Na and K attributed to the JT effect and the size and charge mismatch coming from the substitution of R+ by Cu2+. iii) Doping Cu2+ into Li Nb O3 posses trigonal structure will result in the orthogonal distortion which can be described as the relative planar bond length variations 0.16 ? along the a and b axes in the [Cu O5]8- cluster and the impurity Cu2+ will suffer a displacement 0.16 ? away from the effectively positive oxygen vacancy VO. Besides, the calculated anisotropic g(gx, gy and gz) factors and the hyperfine constants( Ax, Ay and Az) agree well with the spectrum experiments. iv) Based on the cluster model and JT effect, the spectrum data for the orthorhombically elongated octahedra Cu2+(1) center in the Pr Ba2Cu3O6+x powder are illustrated in a reasonable way. Theoretical computation reveals that the Cu?O bonds in the octahedra suffer a elongation 0.04 ? along c axis and a relative planar variations 0.09 ? along the a and b axes.(2) It is found that a fraction of the diamagnetic Cu3+ ions in La Cu O3-δ will transform into the paramagnetic Cu2+ ions due the oxygen defficiency for δ>0, the coordination number will decrease from 6 to 4 and form the tetrahedron [Cu O4]6- cluster. Moreover, the JT effect will lead to the distortion of Cu2+-O2? bonds along the C4 axis and thus form the tetraderally distorted tetrahedron. The anisotropic gx and gy obtained by the theoretical calculation in which the contrition from the ligand and the spin-orbital coupling are included are consistent with the experimental results and the distortion for Cu2+-O2? bond angle is found to be about 3.56? along the C4 axis.(3) The ground state and energy level configuration of d7 ions with low spin(S=1/2) in elongated(or depressed) octahedra are analogous to those for the 3d9 ions in depressed(or elongated) octahedra. Furthermore, the ligand and spin-orbital coupling contributions should be taken into account in the theoretical investigation due to the apparent covalent for low spin(S=1/2) d7 ions. i) One can find that the host Ni2+ in La2Ni0.5Li0.5O4 will become Ni3+(3d7) by the introduce of dopant Li+ and there will be a relative elongation 0.14 ? for the Ni3+-O2- bonds along the C4 axis which results in the produce of the tetragonally elongated octahedra, due to the JT effect. ii) The tetragonally elongated Pd+(4d9) and tetragonally depressed Pd3+(3d7) centers in NH4 Cl arising from doped Pd2+ on the interstitial site capturing one electron and hole, respectivly, during γ-irradiation at room temperature(RT). Theoretical study reveals that the above two impurity centers have the same anisotropy, i.e., ge(?2.0023)≤g?≤g//, which can be attributed to the tetragonally elongated 4d9 and the tetragonally depressed 4d7 ions have the same groud state 2B1 g. Besides, adjustable parameters are reduced by adopting the uniform theoretical formulas based on the modified cluster model and the ligand unpaired spin densities for Pd+ and Pd3+ are, respectively, fs(?0.62% and 0.69%) and fσ(?2.61% and 12.49%).(4) The investigated EPR(g factors and hyperfine constants) and NMR(Knight shifts) for Cu2+ centers in Cu Ge O3 and copper-based high temperature superconductors(YBa2Cu3O7,YBa2Cu3O7–σ,YBa2Cu4O8,Bi1.6Pb0.4Sr2Ca2Cu3O10,Tl Sr2 Ca Cu2O7–y,Tl2Ba2–Cu Oy and Hg Ba2Ca2Cu3O8+δ) are in accordance with the observed experimental values by utilizing the improved uniform high order perturbation formulas for a 3d9 ion in elongated octahedra. Based on the improved cluster model, the quantitative relationship between the anisotropic g factors and Knight shifts are established, the similar anisotropies of the g factors and Knigth shifts for tetragonally(or rombically and orthorhombically) elongated Cu2+ sites can be ascribed to the linear relationship(Kz–Ki)/(gz–gi)?6%(i=x,y).