Crystal-field energy level analysis for Nd(3+) ions at the low symmetry C(1) site in [Nd(hfa)(4)(H(2)O)](N(C(2)H(5))(4)) single crystals

Comparative analysis of crystal-field parameters for rare-earth ions at monoclinic sites in AB(WO4)2 crystals: II. Pr3+ and Nd3+ ions in KRE(WO4)2 (RE = Y or Gd), Pr3+ ions in M+ Bi(XO4)2 (M+ = Li or Na and X = W or Mo), and Nd3+ ions in NaBi(WO4)2 and AgNd(WO4)2

In part I, the crystal-field (CF) parameter (CFP) sets for important potential solid state laser systems Tm(3+), Ho(3+), and Er(3+) ions in KGd(WO4)2 and Tm(3+) ions in KLu(WO4)2 were thoroughly revisited using a general framework for the analysis of CF levels and CFP modeling. In this part the non-standard CFP sets for Pr(3+) and Nd(3+) ions in KR(WO4)2 (R = Y or Gd) and the standard CFP sets for Pr(3+) ions in M(+)Bi(XO4)2 (M(+) = Li or Na and X = W or Mo) and Nd(3+) ions in the related systems NaBi(WO4)2 and AgNd(WO4)2 are analyzed. Due to structural similarity of the hosts, the CFP values for a given trivalent rare-earth (RE(3+)) ion should be quite close in these systems. However, the fitted (and model) CFP sets appear disparate for the systems in question. The standardization criteria are utilized to ensure direct comparability of the apparently disparate CFP sets reported in the literature. The CFP sets standardized by us are compared with the originally standard CFP sets for Pr(3+) and Nd(3+) ions in related AB(XO4)2 systems. Following part I, we argue that meaningful analysis of the mixed CFP sets, i.e. standard and non-standard ones, must take into account the intrinsic features of CF Hamiltonians for orthorhombic and lower symmetry cases, which have not been fully recognized in the literature as yet. The model or fitted CFP sets that belong to disparate regions in the CFP space are intrinsically incompatible, i.e. such sets should not be directly compared. The correlated alternative CFP sets are calculated using monoclinic standardization transformations. The closeness of the standardized CFP sets is assessed in a quantitative way using the closeness factors and the norms ratios. Comparative analysis of the monoclinic CFP sets reported for the titled ion-host systems is carried out and several inconsistencies in the previous studies are clarified. The CFP sets determined by standardization are utilized as starting sets for applications of the multiple correlated fitting technique to independently obtain and additionally verify the fitted CFPs based on published energy levels data. Multiple correlated fittings offer an advantage over the single-fitting tactics by enabling an improved fine-tuning of the final fitted CFPs as well as their interpretation and comparability with the sets obtained by others. The present consistent methodology may enable better understanding of the intricate aspects inherent in the spectroscopic studies for other ion-host systems exhibiting orthorhombic, monoclinic, and triclinic site symmetry.

Anisotropic paramagnetism of monoclinic Nd2Ti2O7 single crystals

The anisotropic paramagnetism and specific heat in Nd(2)Ti(2)O(7) single crystals are investigated. The angular dependence of the magnetization and Weiss temperatures show the dominant role of the crystal field effect in the magnetization. By incorporating the results from the diluted samples, contributions to the Weiss temperature from exchange interactions and crystal field interactions are isolated. The exchange interactions are found to be ferromagnetic, while the crystal field contributes a large negative part to the Weiss temperature, along all three crystallographic directions. The specific heat under a magnetic field reveals a two-level Schottky ground state scheme, due to the Zeeman splitting of the ground state doublet, and the g-factors are thus determined. These observations provide solid foundations for further investigations of Nd(2)Ti(2)O(7).

Interpretation of multiple solutions and selection of the final crystal field parameter sets for orthorhombic and lower symmetry--case study: Er3+ ions at orthorhombic sites in ErNiAl4

Existence of multiple solutions for the crystal field (CF) parameter (CFP) sets obtainable from fitting or matching procedures for orthorhombic (as well as monoclinic and triclinic) site symmetry has recently been gaining wider recognition. However, the peculiarities encountered in interpretation of multiple solutions and subsequent selection of the final CFP sets appears not to be properly understood in many cases. In this paper pertinent explanations for the peculiarities in question are provided. As a case study, we carry out analysis of the CFP sets for Er(3+) ions at orthorhombic sites in ErNiAl(4) obtained using theoretical calculations as well as Mössbauer spectroscopy and inelastic neutron scattering data. It turns out that the original and revised CFP sets reported for Er(3+) in ErNiAl(4) require reconsideration in view of these explanations. Clarifications concerning the matching procedure used as well as interpretation of the CFP sets and the assigned axis systems are provided. It appears that the specific constraints involved in matching have generated some incorrect CFP solutions. The crux of the problem is in the intrinsic features of CFP sets for orthorhombic symmetry, which previously were not fully utilized. Consideration of these features enables proper interpretation of multiple solutions as well as discrimination between the physically valid alternative CFP sets, which must be internally correlated, and the additional incorrect solutions generated by inappropriate matching or fitting procedures. Five alternative and correlated CFP sets are calculated for each set obtained for Er(3+) in ErNiAl(4). These considerations provide guidance for reinterpretation of CFP sets reported in literature and may facilitate subsequent fittings. This would enable experimental identification of the alternative CFP sets.

Comparative analysis of crystal-field parameters for rare-earth ions at monoclinic sites in AB(WO4)2 crystals: I. Tm3+ in KGd(WO4)2 and KLu(WO4)2, and Ho3+ and Er3+ ions in KGd(WO4)2

The crystal-field (CF) parameters determined by various authors for rare-earth ions at monoclinic sites in AB(WO(4))(2) crystals are reanalyzed using a methodology incorporating several approaches, namely standardization, multiple-correlated fitting technique and closeness of CFP sets. In Part I recent spectroscopic data for Tm(3+) ions in KGd(WO(4))(2) (KGdW) and KLu(WO(4))(2) (KLuW), and Ho(3+) and Er(3+) ions in KGdW, which were interpreted using the free-ion (FI) and CF parameter (CFP) sets, are thoroughly revisited. Our reanalysis enables clarification of several doubtful aspects involved in the previous studies. The initial CFPs for fitting, calculated using the simple overlap model (SOM), differ markedly from the fitted CFPs for Tm(3+) ions in KGdW and KLuW. An inspection of the pertinent CFP sets reveals deeper intrinsic differences between the model and fitted CFPs. The model CFPs and the fitted CFPs for RE(3+) ions in both KGdW and KLuW crystals turn out to be non-standard. Importantly, the model and fitted CFP sets for Tm-KLuW belong to disparate regions of the CFP space and thus are intrinsically incompatible, i.e. such sets should not be directly compared. Thus the CFP sets reported in the literature require reconsideration in view of the intrinsic properties of monoclinic CF Hamiltonians previously not taken into account. Standardization of the originally non-standard CFP sets is carried out to ensure direct comparability of the CFP sets in question with other literature data. The correlated alternative CFP sets are calculated for each original set to facilitate future applications of the multiple correlated fitting technique, which enables improving overall reliability of the fitted CFPs. The closeness of the standardized CFP sets is assessed in a quantitative way. Our considerations indicate also the importance of proper definitions of the axis system used in the CFP model calculations and provide arguments for the nominal meaning of the axis systems assigned to the fitted CFPs. The consistent methodology proposed here may be considered as a general framework for analysis of CF levels and CFP modelling for rare-earth and transition-metal ions at monoclinic symmetry sites in crystals. CFP sets for other rare-earth ions in AB(WO(4))(2) crystals will be reanalyzed in Part II.