Theoretical Study On The Spin Hamiltonian Parameters For D^1,2 Ions Under Low Symmetries

Defect structures in functional materials play an important role in optical andmagnetical properties of these systems. Information about electronic states and localstructures of transition-metal dopants are usually vital to understand properties of thesematerials. The above information can be conveniently revealed by electronparamagnetic resonance （EPR） technique, whose experimental results are normallydescribed by the spin Hamiltonian parameters （e.g., zero-field splitting, anisotropic gfactors and hyperfine structure constants）. In this work, the systematic theoreticalstudies on the EPR spectra and spin Hamiltonian parameters were carried out for d^1,2impurities in crystals from the cluster approach based on the crystal-field and EPRtheories. d^1,2ions are representative and important systems in the transition-metalgroup and have attract extensive interest of researchers due to relatively simpler energylevels. So abundant EPR experimental results have been reported for crystals andcompounds with d^1,2dopants. However, the theoretical explanations to the aboveexperimental findings are largely unsatisfactory. There are following imperfections inthe previous theoretical studies.（i） The conventional crystal-field model was usuallyadopted in the previous works, and the contributions from the ligand orbital andspin-orbit coupling interactions were not taken into acount.（ii） The previous studiesdid not correlate the local structures of impurity centers with the spin Hamiltonianparameters. Instead, various adjustable parameters were introduced to describe lowsymmetrical distortions, and it was difficult to acquire information about defectstructures in the previous analysis.（iii） As for the treatments of the Jahn-Teller effect,the previous works failed to establish unified theoretical models and formulas, andadoption of the relevant model parameters was somewhat arbitrary. In addition, thetreatments of the configuration interactions and the low symmetrical distortions werealso oversimplified.In order to overcome the above shortcomings, the systematic theoreticalinvestigations of the spin Hamiltonian parameters of d^1,2ions are performed in thiswork, including the following aspects.（1） For d^1,2ions under tetrahedra, the contributions from the ligand orbitals and spin-orbit coupling interactions which wereusually ignored in the previous treatments are taken into account here. Further, thecontributions to the spin Hamiltonian parameters from the charge transfer mechanismare included for3d2ions in such covalent systems.as semiconductors.（2） For d^1,2ionsunder triangonally and tetragonally distorted octahedra, the improved perturbationformulas of the spin Hamiltonian parameters are established on the basis of theJahn-Teller effect and the cluster approach, by considering the contributions from theligand orbitals and spin-orbit coupling interactions and the configuration interactions.The quantitative relationships between the local structures of impurities and therelevant model parameters are constructed, and the number of adjusted parameters isconsiderably decreased as compared with the previous treatments. Then the abovetheoretical models and formulas are applied to the following systems:（1） For the tetragonal Ti³⁺-VOcenters in BaTiO3bulks and thin films, thecontributions from the ligand orbital and spin-orbit coupling interactions areconsidered on the basis of the cluster approach. As for the [TiO5]7–cluster in BaTiO3bulks, the impurity Ti³⁺is found to suffer the displacement of about0.15away fromthe nearest neighbour oxygen vacancy VO（arising from charge compesation） along theC4axis due to the electrostatic repulsion. As for the [TiO4]5–cluster in BaTiO3thinfilms, the local impurity-ligand bond angle is found to increase to55.88o due to theJahn-Teller effect. For the rhombic Nb4+centers in MO2（M=Sn, Ti and Ge）, the[NbO6]8clusters are found to experience the relative compressions （≈0.01-0.02）along C2axis and the planar （perpendicular to C2axis） angular increases （≈3°） due tothe Jahn-Teller effect and size mismatch. As a result, the ligand octahedra aretransformed from original elongation on host tetravalent cation sites to rhombicallycompressed octahedra in the impurity centers. The theoretical spin Hamiltonianparameters based on the above local structures show good agreement with theexpetimental data.（2） The unified perturbation formulas of the spin Hamiltonian parameters basedon the Jahn-Teller effect for octahedral3d2clusters are applied to α-Al₂O₃:V³⁺,Cr4+, bycorrelating the EPR analysis to the local structures of the systems. It is found that thelocal impurity-ligand bond angles exhibit variations of about1.5-1.9o related to thehost values due to the dynamical Jahn-Teller effect, yielding more regular octahedra around the impurities. So, the experimental zero-field splitting, anisotropic g factorsand spin-lattice coupling coefficients are satisfactorily interpreted for α-Al₂O₃:V³⁺,Cr4+here. As for the tetragonal3d2impurity centers in alkaline earth oxides, the ligandoctahedra are found to suffer the relative elongations of about1.5%,4.4%and4.6%for MgO:V³⁺, CaO:V³⁺and CaO:Ti2+, respectively, due to the dynamical Jahn-Tellereffect.（3） The spin Hamiltonian parameters and local structures are theoretically studiedfor3d2ions under tetrahedral envornments. For ZnO:V³⁺, the analysis based on thehigh order perturbational formulas of the spin Hamiltonian parameters for a trigonallydistorted tetrahedral3d2cluster indicates that the impurity V³⁺may not occupy theideal Zn2+site but suffer an outward displacement of about0.08away from theoxygen triangle along the C3axis. As for the studies on Si:Cr4+, Mn5+with highvalence state of impurities and strong covalence of the host, the contributions from thecharge transfer mechanism and the ligand orbitals are found to be important and shouldbe taken into account. The calculated g factors and hyperfine structure constantscontaining the contributions from both the crystal-field and charge transfermechamisms show good agreement with the observed values.（4） The studies on the tetragonal V4+and Cr4+centers in Bi4GeO12（BGO） revealthat the local impurity-ligand bond angles are found to be about4.91and5.64for V4+and Cr4+, respectively, smaller than the angle of the host Ge4+site. And the ligandtetrahedra transform from original compression at the host Ge4+site into elongation inthe impurity centers due to size mismatching substitution of the smaller Ge4+by thelarger impurities. Meanwhile, the Jahn-Teller effect can also bring forward someinflucence on the local structure of the V4+center.（5） The surface structures of silicon quantum dots （Si-QDs） and performance offiber gas senors made of Si-QDs are investigated in this work. The response and itsreversibility of the sensors to different analytes are measured. When exposed todifferent vapors, the Si-QDs show variations of luminescence intensity over timescalesof a few seconds to hours. However, quantification of the vapor concentration in theatmosphere is worthy of further study. The microscopic mechanism of luminescence ofSi-QDs under irradiation of blue or ultraviolet light can be illustrated as follows. First,surfacial Si-H bonds of the nanoparticles break, leaving behind non-radiative traps （possibly the neutral P_bcenters）, resulting in decreases of the strength and the lifetimeof luminescence. Then oxidation or hydration of the dangling bonds leads to a gradualincrease in luminescence intensity over a period of hours at room air.