Modeling techniques for analysis and interpretation of electron magnetic resonance (EMR) data for transition ions at low symmetry sites in crystals—A primer for experimentalists

Electron magnetic resonance (EMR) studies of paramagnetic centers exhibiting monoclinic and triclinic local site symmetry have gained renewed importance, since such centers occur often in various technologically important materials and biological systems. The intricate low symmetry aspects, which arise for such centers, bear on meaningful interpretation of EMR data and their correlation with structural data. This review provides a primer for experimentalists who wish to utilize efficiently the modeling techniques for analysis and interpretation of EMR data for transition ions, especially ions located at low symmetry sites in crystals. This requires proper understanding of the low symmetry effects observable in EMR spectra as well as related theoretical questions concerning, e.g., (i) existence of physically equivalent zero-field splitting (ZFS) parameter sets, (ii) clear definitions of the axis systems, (iii) proper forms of spin Hamiltonians, and (iv) distinction between apparent and actual low symmetry cases. The question (i) involves consideration of the orthorhombic standardization, which provides basis for standardization of monoclinic and triclinic ZFS parameters. Thus, the aspects pertaining to orthorhombic site symmetry are also outlined. To solve other questions several modeling techniques have been utilized and related computer packages have recently been developed in our group: (1) the superposition model calculations of the zero-field splitting parameters (ZFSPs) in arbitrary symmetry, (2) the procedure for diagonalization of the 2nd-rank ZFSPs and transformation of respective 4th- and 6th-rank ZFSPs, (3) the pseudosymmetry axes method for approximation of the 4th- and 6th-rank ZFSPs to higher symmetry, and (4) the closeness factors and norm ratios for quantitative comparisons of various ZFSP sets. These modeling techniques enable deeper analysis and interpretation of the low symmetry aspects involved in the fitted and theoretical ZFSPs. The computer packages facilitate extracting useful structural information inherent in monoclinic and triclinic ZFSP sets. Illustrative examples taken from recent studies of low symmetry ion-host systems are discussed.     

Superposition model in electron magnetic resonance spectroscopy – a primer for experimentalists with illustrative applications and literature database

We review applications of the superposition model (SPM) in EMR area, which enables semi-empirical modeling of zero-field splitting (ZFS) parameters (ZFSPs) for transition ions in crystals by separation of geometrical and physical information. Nomenclature used for ZFS and crystal field (CF) Hamiltonians is presented to expose common framework underlying two independent implementations: SPM/ZFS and SPM/CF, which require distinct model parameters. SPM/ZFSP applications in EMR area for S-state 3d⁵ (4f⁷) ions and 3d^N ions with orbital singlet ground state are reviewed. SPM/ZFS methodology for ML_n complexes [central metal (M) ion surrounded by n ligands (L)] with specific symmetry is presented. SPM-related computer packages combined with other methods, role of axis systems in SPM analysis, and structural models for several ion-host systems, are discussed. Extensive survey of SPM/ZFS applications is provided to elucidate usefulness of SPM modeling for interpretation of ZFSPs. This review is geared for EMR practitioners interested in practical utilization of SPM/ZFS (or SPM/CFP) analysis. Database of SPM/ZFS references is compiled for studies of single molecule magnets and single ion magnets based on transition ions. Due to its comprehensiveness, suitable sets of model parameters required for practical utilization SPM/ZFS may be easily located using source references as pointers.     

Theoretical interpretation of the zero-field splitting parameters for Fe3+ ions in wide-band gap semiconductor TlGaSe2 single crystal

Superposition model (SPM) calculations are carried out to provide theoretical interpretation of the zero-field splitting (ZFS) parameters and investigate the local environment around the Fe³⁺ centers in a TlGaSe₂ single crystal. Experimental electron magnetic resonance (EMR) data are analyzed and compared with the ZFS parameter values predicted by SPM based on the orthorhombic approximation of structural data. The results provide an adequate interpretation of the ZFS parameters obtained by fitting EMR spectra and indicate that Fe³⁺ ions substitute for the Ga³⁺ ions in TlGaSe₂ crystal.     

Superposition model (SPM) analysis of zero-field splitting parameters of Mn doped ZnAl2S4 crystal

In this study, superposition model (SPM) is employed to investigate the local environment around the different Mn²⁺ centers in ZnAl₂S₄ spinel. Using SPM and crystallographic data, the zero-field splitting (ZFS) parameters b₂⁰, b₄⁰, and b₄³ are calculated for Mn²⁺ at the B-site (with local symmetry D_3d), whereas b₄⁰ and b₄⁴ for the A-site (T_d). The lattice relaxation due to Mn²⁺ impurities is analyzed in terms of the bonding lengths and the angles between the Mn-S bond and the crystallographic axis [1 1 1]. Our SPM analysis of ZFS parameters indicates that satisfactory agreement can be achieved between the theoretical and the experimental results. Additional structural information about Mn²⁺ impurity centers is also obtained.     

Blue and red long lasting phosphorescence (LLP) in β-Zn3(PO4)2:Mn,Zr

Multi-color long lasting phosphorescent (LLP) phenomenon in β-Zn₃(PO₄)₂:Mn²⁺,Zr⁴⁺ was systematically investigated. It is found that the red (λ_Em=616 nm) LLP performance of Mn²⁺ such as brightness and duration is largely improved, and that the blue (λ_Em=475 nm) LLP of Zr⁴⁺ with lower intensity appears when Zr⁴⁺ ions are co-doped into the matrix. The fluorescence, phosphorescence and thermoluminescence (TL) spectra show that Mn²⁺ ion is solely expected as a luminescent center, while Zr⁴⁺ ion not only acts as a luminescent center, but also induces an electron trap (Trap_Zr) associated with a TL peak at 344 K. The trap depth for Trap_Zr is 0.25 eV, while that for the intrinsic trap is 0.38 eV, associated with a dominant peak at 385 K for Zn₃(PO₄)₂:Mn²⁺. The Zr⁴⁺-induced trap with suitable depth is responsible for the improvement of the red LLP of Mn²⁺ ion and the appearance of the blue LLP of Zr⁴⁺ ion. The LLP mechanism is also investigated.     

Local structure distortion and spin Hamiltonian parameters of oxide-diluted magnetic semiconductor Mn-doped ZnO

The local structure distortion, the spin Hamiltonian (SH) parameters, and the electric fine structure of the ground state for Mn²⁺(3d⁵) ion in ZnO crystals are systematically investigated, where spin--spin (SS), spin--other--orbit (SOO) and orbit--orbit (OO) magnetic interactions, besides the well-known spin--orbit (SO) coupling, are taken into account for the first time, by using the complete diagonalization method. The theoretical results of the second-order zero-field splitting (ZFS) parameter D, the fourth-order ZFS parameter (a-F), the Zeeman g-factors: g_// and g_⊥, and the energy differences of the ground state: \delta₁ and \delta₂ for Mn²⁺ in Mn²⁺: ZnO are in good agreement with experimental measurements when the three O^2- ions below the Mn²⁺ ion rotate by 1.085^o away from the [111]-axis. Hence, the local structure distortion effect plays an important role in explaining the spectroscopic properties of Mn²⁺ ions in Mn²⁺: ZnO crystals. It is found for Mn²⁺ ions in Mn²⁺: ZnO crystals that although the SO mechanism is the most important one, the contributions to the SH parameters, made by other four mechanisms, i.e. SS, SOO, OO, and SO～SS～SOO～OO mechanisms, are significant and should not be omitted, especially for calculating ZFS parameter D.     

Temperature dependence of the luminescence of nanocrystalline CdS/Mn

The temperature dependence of the luminescence properties of nanocrystalline CdS/Mn²⁺ particles is investigated. In addition to an orange Mn²⁺ emission around 585 nm a red defect related emission around 700 nm is observed. The temperature quenching of both emissions is similar (T_q≈100 K). For the defect emission the reduction in the lifetime follows the temperature dependence of the intensity. For the Mn²⁺ emission however, the intensity decreases more rapidly than the lifetime with increasing temperature. To explain these observations a model is proposed in which the Mn²⁺ ions are excited via an intermediate state involving shallowly trapped (≈40 meV) charge carriers.     

Influence of chemical bond length changes on the crystal field strength and “ligand-metal” charge transfer transitions in Cs2GeF6 doped with Mn and Os ions

Detailed study of dependence of the crystal field strength 10Dq and lowest charge transfer (CT) energies for different interionic distances in Cs₂GeF₆:Mn⁴⁺ and Cs₂GeF₆:Os⁴⁺crystals is presented. The calculations were performed using the first-principles discrete-variational Dirac-Slater (DV-DS) method. As a result, the functional dependencies of 10Dq and lowest CT energy on the metal-ligand distance R were obtained without any fitting or semiempirical parameters. It was shown that 10Dq depends on R as 1/Rⁿ, with n=4.0612 and 4.3874 for Cs₂GeF₆:Mn⁴⁺ and Cs₂GeF₆:Os⁴⁺, respectively. Two approximations (linear and quadratic) are obtained for the dependence of the lowest CT energy on R; CT energy decreases when R increases with dE(CT)/dR=−638 and −1080 cm⁻¹/pm for Cs₂GeF₆:Mn⁴⁺ and Cs₂GeF₆:Os⁴⁺, respectively, if the linear approximation is used. These values can be used for estimations of the lowest CT energies for Mn⁴⁺ and Os⁴⁺ ions in other hosts with fluorine ligands. Estimations of the electron-vibrational interaction (EVI) constants, Huang-Rhys parameters, and Stokes shifts for all the above-mentioned crystals were performed using the obtained 10Dq and E(CT) functions.     

Electron spin resonance of diluted solid solutions of MnO2 in Y2O3

Electron spin resonance spectra of Mn²⁺ in diluted solid solutions of MnO₂ in Y₂O₃ have been studied at room temperature for Mn concentrations between 0.20 and 2.00 mol%. Isolated Mn²⁺ ions in sites with two different symmetries were observed, as well as Mn²⁺ ions coupled by the exchange interaction. The relative concentration of isolated to coupled Mn²⁺ ions decreases with increasing manganese concentration. The results are consistent with the assumption that the manganese ions occupy preferentially the C₂ symmetry sites. A theoretical calculation based on this model yields an effective range of the exchange interaction between Mn²⁺ ions of 0.53 nm, of the same order as that of Mn²⁺ ions in CaO.     

Electrical properties of copper-manganese spinel solutions and their cation valence and cation distribution

The cation valence and distribution in copper manganese spinels containing 1.0-1.6 mol copper per formula unit (Cu_xMn_3−xO₄) was resolved from their electrical conductivity and thermoelectric properties. The limit of thermal stability of the cubic spinel phase was also determined for each stoichiometry. A corrected phase diagram for the Cu-Mn-O system in air is proposed accordingly. The electronic defect structure could be described through a chemical approach, involving the competition between the redox of Cu⁺ and Mn⁴⁺ to Cu²⁺ and Mn³⁺ and the disproportionation of the Jahn-Teller ion Mn³⁺ into Mn²⁺ and Mn⁴⁺. Thermodynamic parameters for the redox reaction were determined from experimental data as well as calculated, confirming the validity of the modeled defect equilibria.     

EPR, luminescence and IR studies of Mn activated ZnGa2O4 phosphor

Electron paramagnetic resonance (EPR), luminescence and infrared spectra of Mn²⁺ ions doped in zinc gallate (ZnGa₂O₄) powder phosphor have been studied. The EPR spectra have been recorded for zinc gallate phosphor doped with different concentrations of Mn²⁺ ions. The EPR spectra exhibit characteristic spectrum of Mn²⁺ ions (S=I=5/2) with a sextet hyperfine pattern, centered at g_eff=2.00. At higher concentrations of Mn²⁺ ions, the intensity of the resonance signals decreases. The number of spins participating in the resonance has been measured as a function of temperature and the activation energy (E_a) is calculated. The EPR spectra of ZnGa₂O₄: Mn²⁺ have been recorded at various temperatures. From the EPR data, the paramagnetic susceptibility (χ) at various temperatures, the Curie constant (C) and the Curie temperature (θ) have been evaluated. The emission spectrum of ZnGa₂O₄: Mn²⁺ (0.08 mol%) exhibits two bands centered at 468 and 502 nm. The band observed at 502 nm is attributed to ⁴T₁→⁶A₁ transition of Mn²⁺ ions. The band observed at 468 nm is attributed to the trap-state transitions. The excitation spectrum exhibits two bands centered at 228 and 280 nm. The strong band at 228 nm is attributed to host-lattice absorption and the weak band at 280 nm is attributed to the charge-transfer absorption or d⁵→d⁴s transition band. The observed bands in the FT-IR spectrum are assigned to the stretching vibrations of M-O groups at octahedral and tetrahedral sites.     

EPR spectra of Fe centers in layered TlGaSe2 single crystal

A single-crystal TlGaSe₂ doped by paramagnetic Fe ions has been studied at room temperature by electron paramagnetic resonance (EPR) technique. The fine structure of EPR spectra of paramagnetic Fe³⁺ ions was observed. The spectra were interpreted to correspond to the transitions among spin multiplet (S=5/2, L=0) of Fe³⁺ ion, which are splitted by the local ligand crystal field (CF) of orthorhombic symmetry. Four equivalent Fe³⁺ centers have been observed in the EPR spectra and the local symmetry of crystal field at the Fe³⁺ site and CF parameters were determined. Experimental results indicate that the Fe ions substitute Ga at the center of GaSe₄ tetrahedrons, and the rhombic distortion of the CF is caused by the Tl ions located in the trigonal cavities between the tetrahedral complexes.     

Crystal field parameters for Yb ions at orthorhombic centers in garnets—Revisited

The major purpose of this paper is to clarify the deficiencies identified in the recent paper by Liu et al. (J. Lumin. 130 (2010) 103) as well as to reanalyze the available data and provide corrected results for the orthorhombic crystal field parameters (CFPs) for selected rare-earth ions in garnets. It appears that Liu et al., when utilizing the computer package for standardization of CFPs, have inadvertently confused the properties of CFPs expressed in the Wybourne notation with those in the extended Stevens operator notation. This confusion has led to misinterpretations concerning the orthorhombic standardization transformations and incorrect labeling of the CFP sets as supposedly ‘standardized’ for Yb³⁺, Pr³⁺, Nd³⁺, and Er³⁺ ions in various garnets. These deficiencies have prompted us to reconsider the CFP sets determined earlier by matching the experimental data, i.e. the orthorhombic spin Hamiltonian parameters (g factors, g_i, and hyperfine structure constants, A_i; i=x, y, z) and available optical spectral band positions, with the theoretical data calculated using the complete diagonalization method. To further verify the correctness of the present results the CFPs for orthorhombic Yb³⁺ centers in Yb₃Al₅O₁₂ and Yb₃Ga₅O₁₂ garnets are calculated using the superposition model (SPM), which requires adoption of a well-defined symmetry-adapted axis system (SAAS). Hence, the SPM calculations enable reanalysis of available CFP sets based on the correct standardization procedure and establishing the correspondence between the SAAS and the ‘nominal’ axis systems assigned to fitted CFP sets. Using the proper SAAS and general transformations of the axis systems, the relations between the calculated g_i and/or A_i values and the respective principal values determined by EPR experiments can be established. The consistent methodology utilized here may be helpful for proper reanalysis of spectroscopic data for rare-earth and transition-metal ions at orthorhombic symmetry sites in various crystals.     

Semi-ab initio calculations of superposition model and crystal field parameters for Co ions using the exchange charge model

This paper attempts for the first time to establish a reliable linkage between the two well-known and independent models of crystal field (CF), namely the exchange charge (ECM) and superposition models (SM). Our approach aims to show that the SM parameters can be reliably extracted from the distance dependence of the CF invariants for Co²⁺ as derived from the ECM through some semi-ab initio calculations which involved a single fitting parameter and a set of newly constructed procedures. Complete sets of the numerical values of SM parameters and t_k for Co²⁺ in its own host lattices of Li₂Co₃(SeO₃)₄, CoSO₄·H₂O, CoSeO₄·H₂O, and Co(OH)₂ are obtained and they are found to be around 13,000-16,000 cm⁻¹ for , 4100-5700 cm⁻¹ for , 4.1-5.0 for t₂ and 6.2-6.5 for t₄. The present results generally agree with but should be much better than those incomplete sets of results found by previous researchers using the conventional fitting approach. Plausible explanations for some noticeable discrepancies are also discussed together with the effects of different CF contributions on values of the SM parameters.     

Characterization of ZnGa2O4:Mn nanophosphor synthesized by the solvothermal method in 1,4-butanediol-water system

We characterized ZnGa₂O₄:Mn²⁺ (ZnGa₂O₄—zinc gallate) nanophosphor synthesized by the solvothermal method in 1,4-butanediol-containing water to increase the amount of Mn²⁺ ions incorporated in the ZnGa₂O₄ matrix without post-heat treatment. We investigated the influence of water content in the solvent on the photoluminescence (PL) intensity and the Mn amount, the latter being measured by X-ray fluorescence analysis and electron paramagnetic resonance spectroscopy. The PL intensity per Mn amount reached the maximum at the 50 wt% water content. The addition of water promotes repeated dissolution and precipitation, resulting in homogeneous Mn²⁺ distribution in the ZnGa₂O₄ matrix. This suggests that the solvothermal method in the 1,4-butanediol-water system is useful for increasing the amount of Mn²⁺ ions incorporated in the ZnGa₂O₄ matrix without post-heat treatment. At the water content >50 wt%, the decrease in PL intensity is attributed to the optical absorption of the by-product, MnOOH.     

EPR investigation of two types of Syrian's natural zeolites

Two different samples of natural zeolite have been investigated by X-band electron paramagnetic resonance (EPR) spectroscopy. The observed EPR spectra are typical to those observed for Fe³⁺ and Mn²⁺ ions. The lines, related to the iron, are observed, respectively at g≈4.3 and g≈2. The observed six lines, at g≈2, are the hyperfine structure due to the Mn²⁺ ions. The simulation of the experimental EPR spectra suggests that both of the manganese and the iron are present in more one site. The temperature dependence of the EPR spectra has been also investigated. The nature of the different sites involved in the EPR absorption is discussed.     

First-principles study of the effect of iron doping on the electronic and magnetic properties of TbMn2O5

We have studied the electronic and magnetic properties of TbFe_xMn_2−xO₅ (x=0, 0.125, 0.25) samples using first-principles density functional theory within the generalized gradient approximation (GGA) schemes. The crystal structure of TbMn₂O₅ is orthorhombic containing Mn⁴⁺O₆ octahedra and Mn³⁺O₅ pyramids. The structure changes to monoclinic symmetry for the Fe-doping at the Mn sites. Our spin-polarized calculations give an insulating ground state for TbMn₂O₅ and a metallic ground state for Fe-doped TbMn₂O₅. Based on the magnetic properties calculations, it is found that the magnetic moment enhances with increase in the Fe-content in TbMn₂O₅. Most interestingly, the enhanced magnetic moment is due to a substantial reduction of the magnetic moments at the Fe sites.     

Study of crystal-field excitations and Raman active phonons in o-DyMnO3

In DyMnO₃ orthorhombic single crystals, the weak Raman active phonon softening below T=100 K is correlated with the study of infrared active Dy³⁺ CF excitations as a function of temperature and under applied magnetic field. We detect five H_13/2 CF transitions that we predict with appropriate CF Hamiltonian and we confirm that the magnetic easy axis lies in the ab plane. While the CF energy level shifts below T=100 K reflect different displacements of the oxygen ions that contribute to the phonon softening, lifting of the ground state Kramers doublet degeneracy (∼30 cm⁻¹) is observed below T_N=39 K due to the anisotropic Mn³⁺−Dy³⁺ interaction, which could be responsible for the stability of the bc-cycloid ferroelectric phase.     

Fluorescence and Judd-Ofelt analysis of Nd ions in oxyfluoride glass ceramics containing CaF2 nanocrystals

Judd-Ofelt analyses of Nd³⁺ ions in the oxyfluoride glasses and glass ceramics containing CaF₂ nanocrystals are performed to evaluate the intensity parameters Ω_2,4,6, spontaneous emission probability, radiative lifetime, quantum efficiency, as well as stimulated emission cross-section. The influences of Nd³⁺-doping level and heating temperature on these parameters for the ⁴F_3/2→⁴I_J (J=9/2, 11/2, and 13/2) transitions are systematically discussed. The decrease of intensity parameter Ω₂ evidences the incorporation of Nd³⁺ ions into CaF₂ nanocrystals after crystallization. With increasing of Nd³⁺-doping level, the measured lifetime and quantum efficiency gradually decrease, while the stimulated emission cross-section keeps almost unchanged. For 1.0 mol% Nd³⁺-doped sample, both the emission intensity and the measured lifetime enhance with increasing of heating temperature up to 650 °C. The results indicate that the investigated glass ceramics are potentially applicable as the 1.06 um laser host.     

New spectroscopic results of trivalent chromium in magnesium gallate

Cr³⁺ centers in MgGa₂O₄ powder samples are investigated by excitation and emission spectroscopic measurements at 4.2, 77 and 300 K. The ²E(²G)→⁴A₂ (⁴F) and ⁴T₂(⁴F)→⁴A₂(⁴F) electronic transitions are observed in the red and infrared regions and associated with chromium trivalent ions in octahedral sites. The results show that the material presents both high and intermediate crystal fields for these ions. The crystal-field parameter, Dq, and Racah parameters, B and C, are determined from the measurements.