Superposition Model Analysis Research Articles

Theoretical analysis of crystal field parameters and zero field splitting parameters for Mn2+ ions in tetramethylammonium tetrachlorozincate (TMATC-Zn)

Superposition model (SPM) analysis is employed for modeling the crystal field parameters (CFPs) as well as the zero field splitting (ZFS) parameters (ZFSPs) for Mn2+ ions doped into tetramethylammonium tetrachlorozincate, [N(CH3)4]2ZnCl4 crystal (denoted TMATC-Zn). SPM analysis utilizes structural data to predict CFPs and ZFSPs determined for the dopant ions by optical and EMR spectroscopy, respectively. We report model calculations aimed at investigating the two structural options for dopant Mn2+ ions in TMATC-Zn: substitutional and interstitial sites. SPM is employed to predict CFPs, which serve as input for the perturbation theory expressions to calculate the 2nd-rank orthorhombic ZFSPs and to re-analyze optical spectra. Independently SPM is employed to predict the 2nd- and 4th-rank ZFSPs. Correlation of optical and EMR spectroscopy data increases modeling reliability. Comparison of the predicted 2nd-rank ZFSPs with the available experimental ones and consideration of the magnitudes of distortions required to achieve good matching enables discriminating between the substitutional and interstitial sites as location of doped Mn2+ ions. Our study indicates that interstitial sites are more plausible than substitutional sites for Mn2+ ions in TMATC-Zn, in agreement with the experimental prediction. The results reveal the importance of combining two separate methods to determine more reliably the most likely site for substitution of paramagnetic ions. This study also tests the range of applicability of CF theory and SPM analysis for Mn2+ ions in TMATC-Zn crystals and prepares grounds for consideration of the properties of molecular nanomagnets containing Mn2+ ions.

(INVITED)Zeeman interactions in lanthanide doped nanocrystals

We report a crystal-field analysis of Nd3+-doped KY3F10 nanocrystals. As well as electronic energy levels obtained from absorption and fluorescence, we fit to magnetic-field splittings for fields of up to 4T. The resulting parameters accurately account for the Zeeman interaction, including non-linear effects. The fitted parameters are similar to those for bulk crystals. The parameters are compared with ab-initio calculations and superposition-model analyses.

Microscopic insight into electronic and structural properties of Cr3+ and Fe3+ impurities in Cs2NaAlF6 via DFT and SPM analyses

Allowing high transition metal (TM) ions doping concentrations makes the fluoroelpasolite crystals Cs2NaMF6 (M = Al, Ga) quite interesting in various laser applications. In this study, we explored the influence of the dopant ions on the electronic and structural properties of Cs2NaAlF6. Particular attention is paid to the influence of trivalent TM ions (Cr3+ and Fe3+) on the local structure around the possible substitutional cation sites by investigating the optimized geometry around impurity sites due to Cr3+ and Fe3+ using density functional theory (DFT). The obtained structural data are utilized for the calculations of zero-field splitting (ZFS) parameters (ZFSPs) and crystal field parameters (CFPs) of both dopant ions independently in the frame of semi empirical superposition model (SPM). It is shown that remarkable change on the ZFSPs comes not from the distortion on metal-ligand distance but from that on the angular positions of the ligands around the impurity centers. It is clearly shown that the substitution of both Cr3+ and Fe3+ ions take place with significant influence on electronic structure and geometry for the trivalent Al3+ sites. The presented results here have significant potential to better understand the low-symmetry effects in especially optical applications of Cs2NaAlF6:Cr3+ and Cs2NaYF6:Fe3+ systems. Particularly, the calculated CFPs for Cs2NaYF6:Fe3+ system may serve as the only record in literature.

Determination of the g-factors measured by EPR based on theoretical crystal field and superposition model analyses for lanthanide-based magnetically concentrated crystals – case study: double tungstates and molybdates

ABSTRACTThe methods developed for theoretical determination of g-factors measured by electron paramagnetic resonance (EPR) for single transition ions are extended to lanthanide-based magnetically concentrated crystals. The crystal field (CF) and superposition model (SPM) analyses are employed for optoelectronic materials: double tungstates and molybdates. Using the crystallographic data for Nd3+ ions in RbNd(WO4)2 and Yb3+ ions in KYb(MoO4)2 as input for SPM modelling, the CF parameters (CFPs) are predicted for the respective ions. The matrix for g tensor is calculated by the complete diagonalisation method. By matching three principal g values (gxx, gyy, gzz) to those measured by EPR, three adjustable SPM intrinsic parameters:, and are obtained. The reliability of the related CFPs is verified by comparative analysis of available data. The results demonstrate that the methods suitable for single lanthanide ions in crystal can be successfully applied to magnetically concentrated systems. The predicted g tensor anisotropy enables consideration of EPR linewidths arising from dipolar broadening in ALn(MO4)2 (A = alkali ions, Ln = lanthanide ions, M = W or Mo) systems based on the moment method, which requires accurate g-factors. The model parameters determined here may be utilised for SPM/CFP calculations for Nd3+ and Yb3+ ions in single-molecule magnets and single-ion magnets.

Modeling the zero-field splitting parameters and local structure of Co2+ ions doped into PbMoO4 crystal based on crystal field approach and superposition model analysis

Superposition model (SPM) analysis is employed for determination of the crystal field parameters (CFPs) for Co2+ ions doped into PbMoO4 crystal. SPM calculations utilize structural data to model parameters spectroscopically measured for the dopant ions. The CFPs predicted by SPM assuming axial site symmetry serve as input for the CFA/MSH package, which incorporates the CF analysis (CFA) and the microscopic spin Hamiltonian (MSH) modules. This approach enables modeling of the optical energy levels as well as the axial SH parameters: zero-field splitting parameter (ZFSP) D and gi factors: g|| and g⊥. The theoretical SH parameters are matched with the ones deduced from experimental electron magnetic resonance (EMR; EPR) data for Co2+(3 d7) ion using projection of gi for the effective spin S˜=32 onto gi' for the fictitious spin S'=12. Various structural models are considered to predict the CFPs and thus ZFSPs. The local distortion polar angles Δθ in the vicinity Co2+ ions in PbMoO4 are obtained for tetrahedral (Mo6+) and dodecahedral (Pb2+) sites for two possible structural configurations, thus confirming the structural distortions induced by Co2+ doping. This enables discerning between Co2+ ions located at the Pb2+ sites and those at the Mo6+ sites. The experimental data available for one type of the two observed Co2+ complexes in PbMoO4 are reanalyzed.

Temperature and pressure dependence of local structural changes around Gd3+ centers in RAl3(BO3)4 crystals: Modeling zero-field splitting parameters

The semi-empirical superposition model (SPM) analysis is applied to predict the zero-field splitting parameters (ZFSPs) of Gd3+ ions doped into RM3(BO3)4 (RAB) as well as the structural changes around these paramagnetic centers located at possible cation sites in these crystals. Theoretical investigations are aimed at explanation of the temperature dependence of the local structural parameters of Gd3+:RAB (R = Y, Eu, Tm). The results of spin Hamiltonian (SH) analysis of electron magnetic resonance (EMR; EPR – electron paramagnetic resonance) spectra serve for fine-tuning the theoretically predicted zero-field splitting (ZFS) parameters (ZFSPs) obtained using SPM. This approach enables determination of the local structure changes around Gd3+ centers in RAB crystals and explains the observed temperature dependence of the ZFSPs. For Gd3+:EuAB, due to availability of the data, also the observed pressure dependence of the ZFSPs is considered. For this purpose, the distortions parameters, i.e.m the changes in the ligand’s distances ΔRi and the angular distortions Δθi, have been treated as variable parameters in SPM analysis. This procedure yields good matching of the calculated ZFSPs and the experimental ones, and enables determination of the corresponding local distortions. The present results may be useful in future studies aimed at technological applications of the Huntite-type borates with the formula RM3(BO3)4. The model parameters determined here may be utilized for ZFSP calculations for Gd3+ ions at octahedral sites in single-molecule magnets and single-chain magnets.

Superposition model analysis of nickel(II) ions in trigonal bipyramidal complexes exhibiting huge zero field splitting (aka ‘giant magnetic anisotropy’)

Potential single-ion magnet Ni2+ systems: [Ni(Me6tren)Cl](ClO4) and [Ni(Me6tren)Br](Br) reveal unusually high zero field splitting (ZFS). The ZFS parameter (ZFSP) Dexpt=−120 to −180cm−1 was determined indirectly by high-magnetic field, high-frequency electron magnetic resonance (HMF-EMR). Modeling ZFSPs using the density functional theory (DFT) codes predicts D values: −100 to −200cm−1. Such ZFSP values may seem controversial in view of the D values usually not exceeding several tens of cm−1 for Ni2+ ions. To corroborate or otherwise these results and elucidate the origin of the huge ZFS (named inappropriately as ‘giant uniaxial magnetic anisotropy’) and respective wavefunctions, we have undertaken semiempirical modeling based on the crystal field (CF) and spin Hamiltonians (SH) theory. In this paper, a feasibility study is carried out to ascertain if superposition model (SPM) calculations may yield such huge D values for these Ni2+ systems. Using crystal structure data for [Ni(Me6tren)Cl](ClO4) and [Ni(Me6tren)Br](Br) as well as taking into account the Jahn-Teller distortions of five-fold coordinated Ni-complexes revealed by DFT geometry optimization, the ZFSPs are predicted for several structural models and wide ranges of model parameters. The results indicate that in the presence of the Jahn-Teller distortions, the SPM-predicted ZFSP D may achieve the observed magnitudes, whereas the positive as well as negative D-signs are obtainable. Further studies based on SPM calculations of CF parameters and diagonalization of the Hamiltonian (Hfree ion+HCF) will allow considering the wavefunctions compositions and thus actual origin of the splitting between the ground and first excited state.

Theoretical investigations of the optical and EPR spectra for trivalent cerium and ytterbium ions in orthorhombic YF3 crystal

The optical spectra and electron paramagnetic resonance (EPR) parameters (g factors and hyperfine structure constants A) for trivalent cerium and ytterbium ions in YF3 crystal with orthorhombic structure are investigated together by the complete diagonalization (of energy matrix) method (CDM). The obtained results are in reasonable agreement with the experimental ones. More importantly, two magnetically nonequivalent centers in YF3 crystal observed in EPR experiments are confirmed and ascribed to their specific positions in a unit cell by our calculations based on superposition model (SPM) analysis. Such identification of local sites with different magnetic properties would help us to understand not only the EPR spectra and magnetic susceptibility of other lanthanide ions doped in crystals with the same structure as YF3 but also the energy transfer scheme between two lanthanide ions occupying such two sites. All results are discussed carefully.

Effects of MnO doping on the electronic properties of zinc oxide: 406 GHz electron paramagnetic resonance spectroscopy and Newman superposition model analysis

MnO-doped ZnO ceramics have been synthesized through the conventional ceramic processing route. Mn2+ ions have been incorporated into the ZnO lattice within the limits of solid solubility. By using X-band-frequency and high-field electron paramagnetic resonance (EPR), we have resolved some of the main electronic transitions for the S = 5/2, I = 5/2 high-spin system and have determined accurately the EPR spin-Hamiltonian parameters. By combining data from crystallographic X-ray diffraction and EPR with the semi-empirical Newman superposition model, we have found the local configurational position of Mn2+ and have confirmed the symmetry of the lattice. The results presented in this contribution indicate that Mn ions substitute at Zn sites in ZnO. The effect of Mn2+ ions on the intrinsic defects becomes remarkable, thus the vacancy related intrinsic defect signals cannot be visible in the EPR spectrum. MnO doping affects the band gap energy of ZnO system which was confirmed via UV-Vis spectroscopy.

Modelling spectroscopic properties of NiSnCl6·6H2O as a probe for pressure calibration in high-magnetic field and high-frequency EMR measurements

Experimental and theoretical investigations were carried out to determine the pressure dependence of the axial zero field splitting (ZFS) parameter (ZFSP) D of Ni2+ ions in NiSnCl6·6H2O. The aim was to establish the applicability of this system as a probe for pressure calibration in high-magnetic field and high-frequency EMR (HMF–EMR) measurements. The superposition model (SPM) analysis of the ZFS parameters was employed to establish the magnetostructural correlations between the ZFS parameters and structural data for a wide range of values of the structural parameters as well as temperature and pressure. Due to lack of pertinent data for NiSnCl6·6H2O, data for NiCl2·6H2O and Sr3PbNiO6 compounds, which exhibit the closest ligand environment to that in NiSnCl6·6H2O, were utilized. The results indicate feasibility of pressure calibration up to 6GPa by measuring the EMR transitions originating from Ni2+ ions in NiSnCl6·6H2O.

Magnetostructural relationships for Ni(II) ions at octahedral sites in [NixZn1−x(C2O4)(dmiz)2]: Computational study of zero-field splitting and using superposition model

Superposition model (SPM) analysis of the zero-field splitting parameters (ZFSPs), for short SPM/ZFSP, is utilized to investigate magnetostructural relationships in Ni(II)-based magnetic systems: the pure Ni(C2O4)(dmiz)2 and mixed NixZn1−x(C2O4)(dmiz)2 derivatives, where dmiz is 1,2-dimethylimidazole. The pure system is considered as an example of the S=1 Heisenberg antiferromagnetic one-dimensional chain. The Haldane gap exhibited by such systems is the major motivation for their studies. SPM/ZFSP is based on knowledge of the model parameters, i.e. the intrinsic parameters – b¯k(R0), power law exponents – tk, and the reference distance – R0. As a first approximation we use the model parameter sets determined earlier for Ni(II) ions in the sixfold coordinated NiO6 with axial symmetry. Matching of the SPM predicted ZFSPs with the experimental ones is carried out for several model parameter sets and various models of distortions around Ni(II) ions. The axial (D) and rhombic (E) ZFSPs obtained by high magnetic field/high-frequency EMR (HMF–EMR) for the derivatives NixZn1−x(C2O4)(dmiz)2 for x=0.09 and 0.07 are employed. Three approaches accounting for the local structural distortions with respect to the undistorted host are considered, namely, the angular distortions, the distortions of the ligand–metal bond lengths, and simultaneous distortions of the two types. This enables a thorough study of the magnetostructural relationships for the doped Ni(II) ions in NixZn1−x(C2O4)(dmiz)2 and related crystals. Major finding is that SPM/ZFSP method is capable of yielding satisfactory matching of both the size and the signs of the predicted and experimental ZFSPs. Controversies concerning the very large D-values obtained by ab initio methods as compared with those usually observed in Ni(II) systems are discussed. Several inconsistencies concerning interpretation of experimental and theoretical data for Haldane gap systems are also clarified.

Crystal field interactions between Ce3+ ion and fluoride ligands: a theoretical investigation

Superposition model (SM) analyses combined with ab initio calculations are presented to investigate crystal field interactions between Ce3+ ions and their fluoride ligands. On the basis of energies and wave functions derived from complete active space self-consistent field (CASSCF) embedded cluster calculations, 4f and 5d crystal field parameters (CFPs) for Ce3+ in three typical fluoride compounds (Cs2NaYF6, CaF2 and KMgF3) are extracted, showing a good agreement with available experimental data. Moreover, the SM intrinsic parameters, which are usually used to depict physical interactions between the dopant and its ligands, are determined from the ab initio calculated CFPs. The aim of this work is to obtain the quantitative dependence of intrinsic parameters on geometric structures around Ce3+ in fluoride compounds. Thus, the spectral parameters and further the spectroscopic properties of Ce-doped fluoride compounds would be conveniently predicted according to the calculations and analyses in the present work.

EMR study and superposition model analysis of Cr3+ and Fe3+ impurity ions in mullite powders used in aerospace industry

Abstract In this work, the electron magnetic resonance (EMR) spectra of the mullites powders were measured for different grain sizes (0.07 and 0.12 mm). We have used EMR spectroscopy at X-band, combined with superposition model (SPM) calculations to reveal electronic structure and establish correlations between structure, and surroundings of these complexes.

Correlation of EMR and optical spectroscopy data for Cr3+ and Mn2+ ions doped into yttrium aluminum borate YAl3(BO3)4 crystal – Extracting low symmetry aspects

In this study, the crystal field analysis for Cr3+ and Mn2+ ions doped into yttrium aluminum borate YAl3(BO3)4, for short YAB, crystal has been carried out to complement earlier study of the zero-field splitting (ZFS) parameters (ZFSPs). This analysis utilizes data on the distortion models obtained from analysis of the ZFSPs obtained experimentally by EMR for Cr3+ and Mn2+ ions at the Y3+ and Al3+ sites in YAB. This approach enables to verify and enhance reliability of the ZFSP modeling based on superposition model (SPM) analysis and the distortion models predicted previously. Subsequently, modeling of the crystal field parameters (CFPs) based on SPM analysis is carried out for Cr3+ and Mn2+ ions located at possible cation sites in YAB. The SPM predicted CFP values serve as input for the Crystal Field Analysis (CFA) package to calculate the CF energy levels. The predicted physical ZFS of the ground spin state, i.e. the 4A2 state for Cr3+ ion and the 6S state Mn2+ ions, enable calculation of the theoretical ZFSP values, D and D & (a–F), respectively, using the microscopic spin Hamiltonian (MSH) module in the CFA package. In this way, data on the distortions around the Cr3+ centers in YAB (and to a certain extent also for Mn2+ centers) obtained using the ZFSP data from EMR measurements may be correlated with data on the CF energy levels measured by optical spectroscopy. This modeling approach uncovers certain incompatibilities in the existing data for Cr3+:YAB, which call for reanalysis of the previous assignments of the energy levels observed in optical spectra and more accurate experimental data.

EMR studies of the internal motion of Mn4+ ions in the Sr overdoped (La1−xSrx)(Ga1−yMny)O3 (x/y up to 8) supplemented by magnetic and optical spectroscopy measurements

The effect of the Sr doping on electronic structure in single crystals of (La1−xSrx)(Ga1−yMny)O3 solid solutions (LSGM) is investigated by means of electron magnetic resonance (EMR). The EMR results are supplemented by magnetic susceptibility and optical spectroscopy measurements. The compositions with small concentration of Mn doping (y<1%) and overdoped content of Sr (the ratio x(Sr)/y(Mn) up to 8) are used to maximally enhance the role of divalent doping. The experimental results provide evidence of the holes delocalization in the overdoped compound (x(Sr)/y(Mn)>1). This delocalization is accompanied by appearance of the new charge transfer transitions in the optical spectrum and dynamical valence change of manganese atoms. Additionally we observe the thermally activated narrowing of resonance EMR lines due to the internal motion, which is characterized by the energy barrier depending strongly on the ratio x(Sr)/y(Mn). The energy barrier is found to be associated with the charge carrier (hole) self-trapped energy. Fitting the EMR spectra in three orthogonal planes to an orthorhombic spin Hamiltonian enables extracting the zero-field splitting (ZFS) parameters and the Zeeman g-factors for Mn4+ (S=3/2) ions in LSGM. The experimental ZFS parameters are modeled using superposition model analysis based on an orthorhombic symmetry approximation.

Determination of superposition model parameters required for analysis of the zero-field splitting parameters for Ni2+ ions in NiO6 complexes

Superposition model (SPM) analysis of the zero-field splitting parameters (ZFSPs), in short SPM/ZFSP, enables correlation of crystallographic, spectroscopic, and magnetic data for transition ions with an orbitally non-degenerate ground state in crystals. SPM analysis of ZFSPs requires knowledge of the model parameters, i.e. the intrinsic parameters – b ¯ k ( R 0 ) , power law exponents – t k , and the reference distance – R 0 . An extensive survey of literature has revealed that the model parameters for Ni 2+ ( S =1) ions are not available as yet. Hence, in this study we set for determination of the model parameters sets applicable for SPM/ZFSP analysis of Ni 2+ ions in the six-fold coordinated NiO 6 with axial symmetry. Our method utilizes the relationships between the intrinsic parameters b ¯ k ( R 0 ) and the experimental data for the uniaxial-stress parameters obtained for Ni 2+ ions in several crystals. The present results enable modeling of the ZFSP b 2 0 = D for Ni 2+ ( S =1) ions, which hitherto has been hindered by the lack of suitable model parameters sets. Applications of SPM/ZFSP analysis are carried out for Ni 2+ ions doped into α-Al 2 O 3 (corundum), α-LiIO 3 , and LiNbO 3 , as well as the series of fluosilicate crystals with general formula: ABF 6 ·6R 2 O (A=Zn, Mg, Co, Ni, Fe; B=Si, Ti, Sn, BF 4 ; R=H, D). These results will be utilized in studies of Ni 2+ -based systems suitable for pressure sensors in high-pressure electron magnetic resonance (EMR) measurements and spectroscopic properties of Ni 2+ ions in Haldane gap systems. • The superposition model (SPM) parameters for Ni 2+ –O 2− combinations determined. • The applicability of the SPM parameters in the series of fluosilicate crystals analyzed. • Applications of SPM/ZFSP analysis for Ni 2+ in α-Al 2 O 3 , α-LiIO 3 , and LiNbO 3 carried out.

Theoretical investigations of EPR g factors for Ce3+ ion at monoclinic Cs site in YAlO3 crystal

Three EPR principal g values (gx, gy and gz) for monoclinic (Cs) Ce3+ center in YAlO3 crystal are calculated by the complete diagonalization (of energy matrix) method (CDM) based on the superposition model (SPM) analysis. The calculated g factors are more reasonably closer to experimental results reported by Asatryan et al. (2002) than their same work in 1997. The reliability of fitted crystal-field parameters of YAP:Ce3+ crystal is also analyzed. In SPM calculations, the seeming abnormal negative power-law exponent t6 is found to be actually reasonable and its underlying cause may be explained by future ab initio studies.

A theoretical analysis of zero-field splitting of Mn2+ doped Cs2NaLaCl6

Substitutions options for Mn2+ doped single crystals of Cs2NaLaCl6 at room temperature have been analyzed in detail using a semi-empirical superposition model (SPM) analysis. The presence of two structurally different Mn2+ centers have been shown theoretically and structural mechanisms around these centers have been investigated through various modeling cases. Comparison of the theoretical and experimental ZFSPs values obtained from EPR measurements enables analysis of the structural distortions at the Na+ and La3+ sites. It is found that (MnCl5O)5− cluster model for Na+ ion site and off-center displacement of Mn2+ ion model for La3+ ion site are suitable at the first center and the second center, respectively. It is shown that the structural situations after Mn2+ doping into Cs2NaLaCl6 can be reasonably explained within the framework of SPM calculations.

Electron paramagnetic resonance of Fe3+in gallium borate: Superposition model analysis

A series of high quality FexGa1−xBO3 single crystals with 0 ≤ x ≤ 1 was prepared and studied by electron magnetic resonance in the temperature range from 4 to 290 K. At low x, only the electron paramagnetic resonance (EPR) of diluted Fe3+ ions is present. The EPR spectra for different orientations of the magnetizing field have been computer simulated. With a conventional spin Hamiltonian including the Zeeman and fine-structure terms, two different sets of best-fit parameters have been found. This ambiguity has been resolved on the basis of the general spin Hamiltonian with parameters determined from the crystallographic data using the Newman superposition model. A detailed fitting to the experimental EPR spectra assuming statistical distributions of Fe3+ ligand coordinates has revealed the existence of a certain degree of local disorder in FexGa1−xBO3 single crystals.

Analysis of low symmetry aspects revealed by the zero-field splitting parameters and the crystal field parameters for Cr3+ ions doped into yttrium aluminum borate YAl3(BO3)4 crystal

Structural modeling has been carried out for Cr3+ centers in YAl3(BO3), YAB, single crystal, which is a potential laser host material. Superposition model (SPM) analysis is applied to predict the zero-field splitting parameters (ZFSPs) the as well as the crystal field parameters (CFPs) for Cr3+ ions located at possible cation sites in YAB. Our analysis of the crystal structure data and the available EPR spectra has revealed considerable low symmetry features. These findings indicate an approximated nature of the previous interpretation of EPR spectra and necessitate their reconsideration taking into account low symmetry aspects. The theoretically predicted ZFSPs and CFPs corroborate the significance of low symmetry aspects. Comparison of the theoretical and experimental ZFSP values obtained from EPR measurements enables analysis of the structural distortions at the Y3+ and Al3+ sites. It is shown that the ZFSPs of the six-coordinated Cr3+ centers are well described by a structural model for the Y3+ and Al3+ sites based on the angular distortions of the surrounding oxygens. The results obtained from our SPM analysis support the earlier finding that Cr3+ ions substitute for Al3+ ions in YAl3(BO3). The predicted ZFSPs and CFPs may be useful in future studies aimed at technological applications of the Huntite-type borates with the formula RM3(BO3)4.