Theoretical Studies On The Spin Hamiltonian Parameters For D~5 And D~7 Ions In Crystals

Functional materials doped with transition-metal impurities normally exhibit unique optical and magnetic properties, which strongly rely on the local structures and electronic states of the transition-metal dopants in the hosts. The local structural properties can be conveniently analyzed by means of electron paramagnetic resonance（EPR） technique due to the paramagnetism arising from the unpaired electrons. The microscopic mechanisms of the EPR spectra and the information of local structures can be obtained by analyzing the spin Hamiltonian parameters（SHPs）（i.e., g factors,zero-field splitting, hyperfine structure constants and superhyperfine parameters） of these systems.Among the transition-metal groups, d⁵ and d⁷ ions are very important and complicated systems which are not only the active centers of many functional materials such as laser crystals, luminescence materials and biological proteins but also contain abundant sources including strong, intermediate and weak fields as well as low and high spins. Sufficient EPR experimental data have been accumulated for d⁵ and d⁷ impurities in crystals, but the corresponding theoretical explanations are relatively scarce. There are some imperfections in the previous theoretical studies on these systems. 1) The previous analyses failed to quantitatively connect the SHPs with the defect structures of the impurity centers, simply by introducing various adjustable parameters to describe the low-symmetrical distortions. So it was hard to obtain the local structural information of the impurity centers. 2) The ligand orbital and spin-orbit coupling contributions were usually ignored on the basis of the conventional crystal-field（CF） model. Especially, the influences of the charge transfer（CT） mechanism were not taken into account for some strongly covalent systems. 3) The quantitative relationships have not been established for the unpaired spin densities based on the covalency of the systems, which were determined by fitting the two experimental superhyperfine parameters.In order to overcome the above imperfections, in this work, the perturbation formulas of the SHPs for d⁵ and d⁷ ions under distinct（cubic, trigonal, tetragonal and rhombic or orthorhombic） symmetries are adopted to systematically analyze some typical systems. They are Cr⁺ and Fe³⁺（3d⁵） under weak CFs with high spin and Ru3+（4d⁵） under strong CFs with low spin) as well as Co₂₊（3d⁷） under intermediate CFs withhigh spin and Rh2+（4d⁷） under strong CFs with low spin. Based on the studies, not only the EPR experimental results are satisfactorily explained, but also the information of the local structures are acquired for these systems.（1） The EPR data are systematically analyzed for 3d⁵ ions in strongly covalent cubic and trigonal distorted tetrahedra, including the contributions to g factors,hyperfine structure constants and zero-field splitting arising from the CT mechanism.And the quantitative relationships are theoretically established between the related model parameters and covalence of the systems and local structures around the impurities in the perturbation formulas of the SHPs. The above formulas are applied to study the cubic Cr⁺ centers in Zn X（X=S,Se,Te） and the trigonal or cubic Fe³⁺ centers in Cd X（X=S,Se,Te）. 1) The contributions from the CT mechanism are found to be important and should not be ignored. For the cubic cases, the CT contribution to g-shiftΔg CT is opposite（positive） in sign related to the CF one（Δg CF）, and its importance（characterized by the ratio |Δg CT/Δg CF|） is 11%, 66% and 104%（71%） for Zn S, Zn Se and Zn Te（Cd Te）, respectively. ACT from the CT contribution to hyperfine structure constant is the same（positive） in sign and about 50-53% in magnitude as compared with ACF from the CF one. As for the trigonal cases, the CT mechanism brings forward significant contribution to zero-field splitting, characterized by the ratios DCT/DCF（≈133 % and 1600 % for Cd S and Cd Se, respectively）. As regards the CT contributions to g factors, the g-shifts Δgi_CT（i = // and （?）） are positive in sign and much larger in magnitude than Δgi CF, increasing rapidly with increasing ligand atomic number（i.e., S <Se < Te）. Moreover, due to size and charge mismatch between impurity Fe³⁺ and host Cd²⁺ in Cd S and Cd Se, the impurity Fe³⁺ is found not to occupy exactly the host Cd²⁺sites but to undergo the small outward displacements 0.014 ? and 0.006 ?, respectively,away from the ligand triangles along the C3 axis.（2） The perturbation formulas of the anisotropic g factors and hyperfine structure constants for a 4d⁵ ion in rhombically distorted octahedra are established for the first time. The quantitative relationships are obtained between the related parameters（e.g.,the molecular orbital coefficients, the unpaired spin densities and the CF parameters）and covalence of the systems and the local structures of the impurity centers. These formulas are utilized to the various rhombic Ru³⁺ centers in Ag X（X=Cl, Br）. It is found that Ru³⁺ in center A or A’ undergoes the off-center displacement 0.022 or 0.017 ? along[110] axis, while the ligands closest to the silver vacancy（VAg） may move away fromthe vacancy by 0.030 or 0.005 ? in Ag Br or Ag Cl, respectively. The two axial ligands in center B or B’ experience the displacement 0.036 or 0.015 ? along Z（or [001]） axis and the four ligands closest to the VAg shift away from the vacancies by about 0.006 or0.001 ?, respectively. Ru3+ in center X or X’ may undergo the off-center displacement0.019 or 0.015 ? along [110] axis, whereas the halide ligands closest to the VAg can displace away from the VAg by 0.022 or 0.006 ?.（3） The perturbation formulas of SHPs are established from diagonalizing the 6 ′6 energy matrix of ground 4T1 state for a trigonally distorted octahedral 3d⁷ cluster. The contributions from the admixtures of various J（=1/2, 3/2, 5/2） states, the configuration interactions and the ligand orbital and ligand spin-orbit coupling interactions are taken into account in a uniform way. The above formulas are applied to the trigonal Co₂₊center in Mg Cl. It is found that the impurity-ligand bond angle shows an increase of3.44° related to that of the host Mg²⁺ site due to size mismatch, resulting in a more significantly compressed ligand octahedron. The contributions from the admixtures of various J states are important and cannot be ignored. The present studies on the local structure and the SHPs for Mg Cl2:Co₂₊ are tentatively extended to a more general case by comparing the relevant impurity behaviours for Co₂₊ in various trigonal（D3d）environments.（4） Based on the perturbation formulas of the SHPs for a 4d⁷ ion in rhombically（or orthorhombically） distorted octahedra, g factor, hyperfine structure constants and superhyperfine parameters are quantitatively connected with the local structures of the impurity centers. 1) The above formulas are adopted to the rhombic（or orthorhombic）Rh2+ centers R4 and R5 in Ag Cl. The impurities Rh²⁺ are found to suffer the small off-center displacements 0.006 and 0.008 ? along the [110 ] and [100 ] axes away from the substitute（s） H2 O in centers R4 and R5, respectively. Additionally, the intervening ligand Cl- in Rh²⁺ and VAg undergoes a small inward displacement 0.010 ? towards the center of octahedron in center R5. The local elongation distortions arise mainly from the nearest neighbor H₂ O substitute（s） in centers R4 and R5, quite different from the simpler conventional center R6 arising from the Jahn-Teller effect. The impurity and intervening ligand displacements ΔRC and ΔRP may enhance the rhombic distortions of these centers and provide more complication and significance of the present studies. 2)The SHPs and local structures are theoretically investigated for Rh²⁺ in NH₄ Cl based on the perturbation calculations. The tetragonally compressed Rh²⁺ center in the form of[Rh Cl₄（H₂O）₂]^2- group originates from interstitial Rh2+ associated with two adjacent axial NH⁴⁺ cations substituted by two H₂ O molecules due to charge compensation.（5） The energy levels and the ground states for 3d⁹（or 4d⁹） ions in elongated（or compressed） octahedra are similar to those for 4d⁷ ions in compressed（or elongated）octahedra. 1) The SHPs and local distortions for Cu²⁺ in crystalline and amorphous MO₂（M=Te and Ge） and(Tl_0.5Pb_0.5)Sr₂Ca Cu₂O₇ superconductors are investigated from the high order perturbation formulas for a tetragonally elongated octahedral 3d⁹ cluster. The impurity Cu²⁺ in MO₂ are found to suffer the tetragonal elongations of about 11.4% and⁹.5% for crystalline Te O₂ and Ge O₂ and 10.8% and 6.6% for amorphous Te O₂ and Ge O₂, respectively, due to the Jahn-Teller effect. The observed anisotropies（（?） > （?）and （?） > （?）） in(Tl_0.5Pb_0.5)Sr₂Ca Cu₂O₇ are ascribed to the 2B1 g ground state for Cu²⁺under tetragonal elongation distortion. 2) The SHPs are theoretically investigated for Rh⁰（4d⁹） in NH₄ Cl by use of the perturbation calculations. The orthorhombically compressed Rh⁰ center in the form of [Rh Cl₄（H₂O）₂]^4- group arises from the interstitial Rh⁰ with two adjacent axial NH⁴⁺ replaced by two H2 O molecules as charge compensators and the planar Rh0-Cl- bond length variation of about 0.042 ? along [011]and [ 110 ] axes due to the Jahn-Teller effect.