Study On The Magnetic Interactions And MSH Theory For Transition Metal Active Ions In New Materials

The aim of this thesis is to investigate the magnetic interactions and themicroscopic spin Hamiltonian theory for the transition metal (TM) active ions in newmaterials. The main content of the dissertation are as following:Firstly, the theoretical background underlying the magnetic interactions and themicroscopic spin Hamiltonian theory is reviewed. This includes the spin-orbit (SO), thespin-spin (SS), spin-other-orbit (SOO) and orbit-orbit (OO) magnetic interactions aswell as the two approaches (including PTM and CDM) in the theoretical determinationof SH parameters.Secondly, in the intermediate crystal field (CF) coupling scheme, the completeenergy matrices for 3d^N (N = 2-8) ions at axial symmetry crystal field including thetrigonal and tetragonal symmetry have been constructed using two different irreduciblerepresentations basis functions, i.e. free ion irreducible representations basis for spheralsymmetry group (SO(3)) and irreducible representations basis for axial symmetry pointgroup (including trigonal basis and tetragonal basis). In addition to the SO magneticinteraction usually taken account, for the first time the SS, SOO, and OO magneticinteractions have also been included in the complete energy matrices. The fullconfiguration microscopic spin Hamiltonian (MSH) theory for 3d^N (N = 2-8) ions ataxial symmetry crystal field have been developed using the complete diagonalizationmethod (CDM). The CFA/MSH computer package and the CDM/MSH serial programhave been developed using Visual Basic. The CFA/MSH computer package in free ionirreducible representations basis for spheral symmetry group is based on the CFA(crystal field analysis) package developed by Yeung and Rudowicz. The CDM/MSHserial program in irreducible representations basis of the axial symmetry point group isbased on Fortran version developed by us for 3d^3/7 ions. The CFA/MSH computerpackage and the CDM/MSH serial program have obtained the same results if the allmicroscopic states for 3d^N ions are considered in axial symmetry including trigonalsymmetry and tetragonal symmetry. The CFA/MSH computer package and theCDM/MSH serial program enable us to study not only the energy levels and the fullconfiguration mixed wavefunctions but also the SH parameters. The CFA/MSHcomputer package can also be used to study the low symmetry effects (LSE) induced bythe distortion angle. The spin-Hamiltonian (SH) parameters are known to reflect verysensitively even small variations in the coordination of the TM impurity ions in crystal materials.Thus the theoretical studies of the SH and CF parameters can provide a great deal ofmicroscopic insight concerning the crystal structure, structural disorder, phase transitions andpressure behavior.Thirdly, the microscopic origins of the SH parameters for 3A2(3d2/8) and 4A2(3d3)state ions at trigonal (C3v, D3, D3d) symmetry as well as 4B1(3d3) state ions at tetragonal(C4v, D2d, D4, D4h) symmetry, for the first time taking into account the SS and SOOmagnetic interactions omitted in previous publications besides the SO magneticinteraction, have been investigated on the basis of CDM. We find that the SHparameters arise from four microscopic mechanisms, i.e. (1) SO coupling mechanism;(2) SS coupling mechanism;(3) SOO coupling mechanism;(4) SO～SS～SOO combinedcoupling mechanism. The SO coupling mechanism in the four coupling mechanisms isthe most important one, but the contributions to zero-field splitting parameter D fromother three coupling mechanisms cannot be omitted. The contributions to g-factors: ?g//and ?g⊥from other three coupling mechanisms is quite small. In addition, the studiesfind that the effect of the OO (orbit-orbit) coupling mechanism on the energy levels isappreciable whereas that on the SH parameters is negligible. For 3d3 ions, themicroscopic origins of the splitting for the lowest existed state 2Eg are studied. Thedifferent mechanisms of the splitting 2Eg state for C4v and C3v crystal field are explainedusing group theory method and physics method.Fourthly, the accuracy of the existing PTM formulae including Petrosyan's PTMfor 3A2(3d8) at trigonal symmetry, Macfarlane's PTM formulae for 4A2(3d3) at trignoalsymmetry and for 4B1(3d3) at tetragonal symmetry as well as Zdansky's PTM formulaefor 4A2(3d3) at trignoal symmetry, have been studied using CDM. It is found that that (i)Petrosyan's PTM formulae work well for g// and g⊥in the most of the crystal fieldparameter (CFP) ranges, whereas they fail for ZFS parameter D in most of the CFPranges;(ii) the results obtained by us using Macfarlane's PTM formulae for 4A2(3d3) attrignoal symmetry are close to those evaluated by our CDM. However, the PTMformulae developed by Zdansky for 4A2(3d3) at trignoal symmetry is not convergent inthe most of the CFP ranges. (ii) the approximate expression of ZFS parameter (D)developed by Macfarlane for0b24B1(3d3) at tetragonal symmetry is not convergent in themost of the CF ranges.Fifthly, The SH parameters and the crystal field (CF) energy levels for Ni2+ ions inLiNbO3 crystals have been investigated using the present CDM. The low-symmetryeffects (LSE) arising from the additional terms (ImB43≠0) induced at the C3 symmetrysites by the distortion angle ?, which have been omitted in earlier works, have also beendealt with. This study shows that for LiNbO3: Ni2+ the contributions arising from SSand SOO interactions to the zero-field splitting (ZFS) parameter D are appreciable,whereas those to g// and g⊥are quite small. Since the angle ? (? 0.68°) for LiNbO3: Ni2+is rather small, the contributions to the SH parameters arising from LSE are also small.A good overall agreement between the theoretical and experimental results for the SHparameters and the CF energy levels has been obtained.Sixthly, we consider three non-equivalent Cr3+ ions defect centers, namely, Cr3+(A)and Cr3+(B) at high temperature (HT) (T > 300 K) as well as Cr3+(LT) at lowtemperature (LT) (T < 300 K), occurring in Cr3+: α-LiIO3 single crystal. Suitable modelsfor these centers are proposed taking into account the combined contributions to the SHparameters from the single Li+ vacancy located on the [111]-axis above (for Cr3+(A)) orbelow (for Cr3+(B)) Cr3+ ions and double Li+ vacancy located on the [111]-axis aboveand below Cr3+ ions for Cr3+(LT) center as well as the lattice distortion. The quantitativerelationships between the SH parameters (D, g//, g⊥) and the local structure parametersof Cr3+ ion in α-LiIO3 crystals are established. The CDM/MSH program and thestructural models are applied to compute the SH parameters of the two HT Cr3+ defectcenters and the LT Cr3+ defect centers in α-LiIO3 crystals. The calculated results are ingood agreement with the experimental ones. A new type of the structural distortions forthe two HT Cr3+ centers and the LT Cr3+ defect centers in α-LiIO3 crystals istheoretically predicted. The CFA/MSH package has enabled to study for the first timethe additional contributions to the SH parameters arising from the low-symmetry (C3)"imaginary"CF parameters ImB4±3(C3) and the difference between the real CFparameters (ReB4±3(C3)-B4±3(C3v)) induced by the distortion angle φin C3 symmetry.Such contributions have been neglected in the C3v symmetry approximation used so farin the literature. The new findings are that g⊥depends strongly on the distortion angle ?,whereas g// and D are rather insensitive to ?.Finally, The local structure and the spin Hamiltonian parameters includingzero-field splitting parameter D, a+2F/3 and Zeeman g-factors g// and g⊥, aretheoretically investigated for Fe K3+-O I2 ?defect centre in KTaO3 crystals. It is found thatthe off-center displacement of the Fe3+ ion combined with an inward relaxation of theoxygen ligands and the interstitial oxygens are shown to give rise to a strongtetragonal crystal field which in turn results in the large-zero-field splitting.2?OI...