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The rare-earth or 3d transition metal dopants in perovskites have potential to induce interesting features, thus opening opportunities for investigations and applications.

Comparative modelling of the crystal-field parameters (CFPs), CF energy levels, and effective spin-Hamiltonian parameters of the ground state 4A2g of the Cr3+ dopant ions in Y2Ti2O7 and Y2Sn2O7 is carried out.

Current advances in molecular magnetism are aimed at the construction of molecular nanomagnets and spin qubits for their utilization as high-density data storage materials and quantum computers. Mononuclear coordination compounds with low spin values of

Current advances in molecular magnetism are aimed at the construction of molecular nanomagnets and spin qubits for their utilization as high-density data storage materials and quantum computers. Mononuclear coordination compounds with low spin values of S=½ are excellent candidates for this endeavour, but their construction via rational design is limited. This particularly applies to the single copper(II) spin center, having been only recently demonstrated to exhibit slow relaxation of magnetisation in the appropriate octahedral environment. We have thus prepared a novel, modular organic scaffold that would allow one to gain in-depth insight into how purposeful structural differences affect the slow magnetic relaxation in monometallic, transition metal complexes. As a proof-of-principle, we demonstrate how one can construct two, structurally very similar complexes with isolated Cu(II) ions in an octahedral ligand environment, the magnetic properties of which differ significantly. The differences in structural symmetry effects and in magnetic relaxation are corroborated with a series of experimental and theoretical techniques, showing how symmetry distortions and crystal packing affect the relaxation behaviour in these isolated Cu(II) systems. Our highly modular organic platform can be efficiently utilized for the construction of various transition-metal ion systems in the future, effectively providing a model system for investigation of magnetic relaxation via targeted structural distortions.

Due to their potential applications, single atoms on surfaces (adatoms) have been extensively studied using STM, IETS, INS, and EPR techniques or using DFT and ab initio methods. Especially interesting are Fe2+ (S = 2) adatoms on CuN/Cu(100) and Cu2N/Cu(100) surfaces due to their non-Kramers features described by the zero field splitting (ZFS) Hamiltonian. The 4th-rank ZFS parameters (ZFSPs), allowed for spin S = 2, are commonly disregarded. By extracting 4th-rank ZFSPs from DFT predicted spin energy levels for the Fe2+@CuN/Cu(100) system, we show that including only 2nd-rank ZFSPs yield incomplete description of magnetic and spectroscopic properties. The algebraic method developed by us is used to extract 2nd- and 4th-rank ZFSPs utilizing knowledge of energy levels without a magnetic field, which may be obtained experimentally or theoretically. Reasonable constraints on particular 4th-rank ZFSPs are considered based on comparison of data on ZFSPs and energies for Fe2+@CuN/Cu(100) and other Fe2+ (S = 2) systems. Influence on energies due to 2nd-rank ZFSPs alone versus that of both 2nd- and 4th-rank ZFSPs is analyzed. A series of simulations of ZFS energies for different ZFSP variants is carried out. The results prove the importance of 4th-rank ZFS parameters. Our method enables a more accurate description of 3d4 and 3d6 (S = 2) ions in various systems, including S = 2 adatoms.

Transition metal atoms adsorbed on surfaces (adatoms) behave like magnets in nanoscale and have potential applications in quantum computing. Scanning tunneling microscopy and inelastic tunneling spectroscopy studies yield the spin Hamiltonian parameters. Semi-empirical approach based on crystal-field and microscopic spin Hamiltonian theory is employed for modeling of the zero field splitting parameters b k q , and Zeeman g-factors for Fe2+(S = 2) adatoms on Cu2N/Cu(1 0 0) surface. These parameters are determined for wide ranges of the microscopic parameters: the spin-orbit (λ), spin-spin (ρ) coupling constants, and crystal-field energy levels (Di) within the 5D multiplet. Matching theoretical and experimental 2nd-rank parameters ( b 2 0 , b 2 2 ) yields suitable values of {λ, ρ, Di}. For the first time, also the 4th-rank parameters ( b 4 q ) as well as the g-factors and their ρ-contributions are estimated. Using EasySpin program we show that the transition energies and mixing coefficients obtained using only b 2 q differ significantly from those using both ( b 2 q , b 4 q ). This indicates that b 4 q significantly affect the spin energy levels. Hence interpretations of experimental data may be inaccurate if b 4 q are neglected. Our approach enables bridging the gap between semi-empirical and DFT/ab-initio methods and may be utilized for Fe2+(S = 2) adatoms on other surfaces and Fe2+-based molecular nanomagnets.

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 separa...

Studies of magnetic adatoms on surfaces utilize experimental techniques (scanning tunneling microscopy (STM), inelastic tunneling spectroscopy (ITS) and ab-initio modeling methods. Several fundamental issues involved in these studies, being of utmost importance in view of potential technological applications, are critically examined and elucidated. This includes applications of the correspondence principle and relationships between the notions: magnetic anisotropy (MA), magnetic anisotropy energy (MAE), single-ion anisotropy (SIA), zero-field splitting (ZFS) as well as spin-flip energy of tunneling electrons and energy barrier to magnetization reversal. Proper quantum–mechanical relations between the uniaxial SIA constant K and the axial ZFS parameter D valid for the cases D > 0 and D

Due to their potential applications, single atoms on surfaces (adatoms) have been extensively studied using STM, IETS, INS, and EPR techniques or using DFT and ab initio methods. Especially interesting are Fe2+ (S = 2) adatoms on CuN/Cu(100) and Cu2N/Cu(100) surfaces due to their non-Kramers features described by the zero field splitting (ZFS) Hamiltonian. The 4th-rank ZFS parameters (ZFSPs), allowed for spin S = 2, are commonly disregarded. By extracting 4th-rank ZFSPs from DFT predicted spin energy levels for the Fe2+@CuN/Cu(100) system, we show that including only 2nd-rank ZFSPs yield incomplete description of magnetic and spectroscopic properties. The algebraic method developed by us is used to extract 2nd- and 4th-rank ZFSPs utilizing knowledge of energy levels without a magnetic field, which may be obtained experimentally or theoretically. Reasonable constraints on particular 4th-rank ZFSPs are considered based on comparison of data on ZFSPs and energies for Fe2+@CuN/Cu(100) and other Fe2+ (S = 2) systems. Influence on energies due to 2nd-rank ZFSPs alone versus that of both 2nd- and 4th-rank ZFSPs is analyzed. A series of simulations of ZFS energies for different ZFSP variants is carried out. The results prove the importance of 4th-rank ZFS parameters. Our method enables a more accurate description of 3d4 and 3d6 (S = 2) ions in various systems, including S = 2 adatoms.

Transition metal atoms adsorbed on surfaces (adatoms) behaving like magnets are important for potential applications in quantum computing and memory storage. Better insight into their magnetic properties, described by spin Hamiltonian (SH) parameters, is essential. Comprehensive modeling of SH parameters for Fe2+ with spin S = 2 adatoms on various surfaces is carried out using two approaches: (1) semiempirical CF/MSH [based on crystal field (CF) and microscopic spin Hamiltonian (MSH) theory], and (2) density functional theory (DFT). Here preliminary results of modeling of zero-field splitting parameters (ZFSPs) for Fe2+ on Cu2N/Cu(100) surface [for short Fe2+@Cu2N/Cu(100)] are presented. We focus on the orthorhombic second-rank ZFSPs in the conventional notation (D, E) measured for Fe2+@Cu2N/Cu(100). The fourth-rank ZFSP in the Stevens notation ( $$B_{k}^{q}$$ , k = 2, 4) measured for Fe2+ on CuN/Cu(100) surface are considered elsewhere. Using the CF/MSH approach within 5D approximation, the ZFSPs (k = 2, 4) and Zeeman g-factors are calculated for wide range of the microscopic parameters: spin–orbit (λ), spin–spin (ρ) coupling constants, and the crystal field energy levels (∆i). The ρ-contributions and the fourth-rank ZFSPs are found important. Computations of the ZFSPs (D, E) are done using the SIESTA code by mapping of the physical energy levels to those of effective ZFS Hamiltonian. Comparison of the results enables bridging the gap between DFT methods and CF/MSH ones. The present results will also be utilized in ongoing studies of adatoms on other surfaces, single molecule magnets and single-ion magnets.

Experimental spectroscopic and magnetic data for Co2+(3d7) ions in various systems are reviewed and critically examined. The focus is on Co2+ ions with the electronic spin S = 3/2, properties of which may be interpreted using the spin Hamiltonian with the effective S = 3/2 or the fictitious ‘spin’ S (S′) = ½. Possible distinct ground states of Co2+(3d7) ions arising from crystal field energy levels are discussed. Distinctions between the concepts of the effective spin S and the fictitious ‘spin’ S′ are outlined to clarify the terminological confusion encountered in literature. Sample cases of the ground state assignments and options for the ‘spin’ S′ = ½ origin are considered for better understanding of the Co2+ ions local environment in various systems, including low symmetry cases. Present study is motivated by potential applications of Co2+(S = 3/2) complexes exhibiting very large or moderate zero-field splitting as molecular nanomagnets.

The methods developed for theoretical determination of g-factors measured by electron paramagnetic resonance (EPR) for single transition ions are extended to lanthanide-based magnetically concentra...

Mn2+ doped PbS (PbS:Mn2+) semiconductor nanocrystals have been synthesized by standard chemical method and characterized using various techniques for possible applications in quantum dots. This work describes new physical properties of these nanocrystals that have emerged from our investigations. The PbS:Mn2+ nanocrystals have cubic structure (space Group Fm3m) and the average crystallite size lies between 5 and 10 nm as characterized by X-ray diffraction (XRD) and Transmission Electron Microscopy (TEM) analysis. The structural properties of PbS:Mn2+ nanoparticles are also studied by UV/Vis absorption spectrum and High-Resolution Transmission Electron Microscopy (HRTEM). The quantitative chemical analysis of pure and Mn2+ doped PbS nanocrystals has been done by Energy Dispersive Spectroscopy (EDS) spectra. The energy band gaps have been determined by UV/Vis absorption study using Tauc Plot as (in eV):1.79, 1.90, 2.23, and 2.39 for Mn2+ concentration equal to 0, 0.05, 0.26, and 0.52%, respectively. The luminescence behavior of the nanocrystals has been studied by photoluminescence (PL) spectra. The magnetic and electronic properties of PbS:Mn2+ nanocrystals were studied using Electron Paramagnetic Resonance (EPR) spectroscopy. Analysis of EPR spectra enabled determination of the electronic g-factor, the second-rank axial zero-field splitting parameter D and the hyperfine parameter A.

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.

Synthesis and characterization of systems containing divalent lanthanide elements (Ln2+) is still largely an unexplored area. Until recently the absorption spectra were obtained nearly exclusively for Ln2+:CaF2 crystals, whereas most studied ions are Sm2+, Eu2+, Tm2+ and Yb2+. The scarcity of data on spectral properties of Ln2+ ions and usage of different methodologies for their analysis hinders uncovering systematic changes in Hamiltonian parameters and thus inherent trends across the Ln series. Here we report the first calculations of the crystal-field (CF) energy levels for the 4f35d1 configuration of Nd2+ ion. The novel absorption spectra for Nd2+ and Dy2+ ions in SrCl2 as well as new spectra for Sm2+, Eu2+, Tm2+, and Yb2+ ions in SrCl2 obtained independently by us are analyzed using uniform methodology proposed here. Our data are supplemented by comprehensive reanalysis of available spectral data for Sm2+, Eu2+, Tm2+, and Yb2+ ions in SrCl2. This approach yields refined and more consistent sets of Hamiltonian parameters. Systematic analysis of free-ion parameters and CF parameters for the six Ln2+ ions in SrCl2 studied by us provides sufficiently large amount of data that allows to reveal inherent trends across the Ln series. Our results enable for the first time to check if identified trends would be sufficiently systematic to allow for predicting the spectrum for any lanthanide ion based on the sets of parameters derived from the spectra obtained for another ion in the same matrix.

Utilizing the package MSH/VBA, based on the microscopic spin Hamiltonian (MSH) approach, spectroscopic and magnetic properties of Fe 2+ (3d 6 ; S = 2) ions at (nearly) orthorhombic sites in Fe(NH 4 ) 2 (SO 4 ) 2 ·6H 2 O (FASH) are modeled. The zero-field splitting (ZFS) parameters and the Zeeman electronic (Ze) factors are predicted for wide ranges of values of the microscopic parameters, i.e. the spin-orbit (λ), spin-spin (ρ) coupling constants, and the crystal-field (ligand-field) energy levels (Δ i ) within the 5 D multiplet. This enables to consider the dependence of the ZFS parameters b k q (in the Stevens notation), or the conventional ones (e.g., D and E ), and the Zeeman factors g i on λ, ρ, and Δ i . By matching the theoretical SH parameters and the experimental ones measured by electron magnetic resonance (EMR), the values of λ, ρ, and Δ i best describing Fe 2+ ions in FASH are determined. The novel aspect is prediction of the fourth-rank ZFS parameters and the ρ(spin-spin)-related contributions, not considered in previous studies. The higher-order contributions to the second- and fourth-rank ZFSPs are found significant. The MSH predictions provide guidance for high-magnetic field and high-frequency EMR (HMF-EMR) measurements and enable assessment of suitability of FASH for application as high-pressure probes for HMF-EMR studies. The method employed here and the present results may be also useful for other structurally related Fe 2+ ( S = 2) systems.

The virtual lack of information on electronic spectra of divalent lanthanide elements (Ln2+) other than Sm2+, Eu2+, Tm2+, and Yb2+ has prompted us to set for synthesis and characterization of novel Ln2+ systems. First successful attempt concerned SrCl2/Nd2+ single crystals. Here, we report stabilization of divalent dysprosium in a chloride host. Importantly this has been accomplished with Dy ions introduced in a divalent state during synthesis, unlike by γ-irradiation of Dy3+ systems employed previously. This synthesis method yields good quality SrCl2/Dy2+ single crystals. The electronic absorption spectra of Dy2+ doped in SrCl2 have been recorded with high resolution at liquid helium temperature (4.2 K). Identification of the absorption bands occurring in the spectral range of 5000-45000 cm-1 is achieved. On the basis of theoretical calculations using semiempirical Hamiltonian model, assignment of bands and determination of the Hamiltonian parameters for Dy2+(4f95d1) configuration is carried out. The experimental and theoretical studies reveal fine structure and zero-phonon transitions and thus enable high-resolution assignment of spectral lines. It is shown that spin-forbidden transitions gain relatively high intensity due to significant admixing of low-spin character to nominally high-spin states.

Lanthanides have relatively recently been recognized as ideal candidates for the construction of advanced magnetic materials that would allow for their future applications in spintronics and high-density data storage. Despite enormous progress that deals with the control of magnetic anisotropy and slow relaxation of magnetization in Single Molecule Magnets (SMMs), further improvements are still indispensable to go beyond the ultra-low temperature regime. We have thus prepared four lanthanide complexes ([ErL2(OTf)(MeOH)2](OTf)2 (1), [YbL2(OTf)2](OTf) (2), [ErL(NO3)3(H2O)](3) and [YbL(NO3)3(MeOH)]·MeCN (4)) with a tridentate Schiff-base ligand L, to unravel magneto-structural correlations in this new family of field-induced Single Ion Magnets (SIMs). Interestingly, as revealed by the single crystal X-ray diffraction, their structures are synthetically tuned by the choice of the applied counterion. The static and dynamic magnetic properties of 1–4 were investigated revealing that all compounds behave as field-induced Single Ion Magnets (SIMs). Their energy barriers Ueff decrease in the sequence: 4, 2, 3, 1, with an order of magnitude difference between the highest and the lowest value. To correlate the observed magnetic properties with spectroscopic data, low-temperature absorption spectroscopy was performed. This has allowed the determination of the energy levels of the Ln(III) ions and the exact composition of the state vectors for the Ln(III) ground multiplets via crystal-field analysis (CFA) and semiempirical superposition model (SPM) approach. Theoretical and magneto-structural correlation studies indicate that one can modulate the heterotopic coordination spheres around the prolate Er(III) and Yb(III) solely with the counterions. This leads to rarely observed high-coordinate SIM species with the LnNxOy first coordination sphere (where Ln – Er or Yb, x = 3 or 6, y = 2, 3 or 6). Their performance can be related to the intricate interactions between the electron density on the Ln ion and the crystal field created by the surroundings.

Recent wide-band (65–850 GHz) electron magnetic resonance (EMR) study determined the zero field splitting (ZFS) parameters (ZFSPs) for Fe2+ in natural and synthetic forsterite (Mg2SiO4) based on the fictitious spin S′ = 1 approach. So-obtained ZFSPs (D′, E′) are incompatible with those available in literature for 3d6 (Fe2+) and 3d4 (Fe4+, Mn3+, Cr2+) ions with the electronic spin S = 2, which predominantly pertain to the effective spin S ˜ = 2. Background for the effective spin S ˜ versus the fictitious ‘spin’ S′ (J′) approaches is provided with focus on application to Fe2+ ions. To enable comparison of the S′ = 1 ZFSPs with the S ˜ = 2 ones methodology for conversions has been worked out and appropriate conversion relations derived for various combinations of the possible energy level schemes for the spin S ˜ = 2 and S′ = 1. The second-rank S′ = 1 ZFSPs (D′, E′) measured by high-frequency EMR for Fe2+ in Mg2SiO4 are converted to the S ˜ = 2 ZFSPs (D, E) and compared with literature data. Suitability of Fe2+:Mg2SiO4 systems for application as high-pressure probes for high-magnetic field and high-frequency EMR (HMF-EMR) is then considered. The results of this study may be applied to other cases of 3d6 and 3d4 (S = 2) ions in various hosts.

Theoretical investigations are carried out to determine the temperature dependence of the local structural parameters of Cr3+ and Mn2+ ions doped into RAl3(BO3)4 (RAB, R = Y, Eu, Tm) crystals. The zero-field splitting (ZFS) parameters (ZFSPs) obtained from the spin Hamiltonian (SH) analysis of EMR (EPR) spectra serve for fine-tuning the theoretically predicted ZFSPs obtained using the semi-empirical superposition model (SPM). The SPM analysis enables to determine the local structure changes around Cr3+ and Mn2+ centers in RAB crystals and explain the observed temperature dependence of the ZFSPs. The local monoclinic C2 site symmetry of all Al sites in YAB necessitates consideration of one non-zero monoclinic ZFSP (in the Stevens notation, b 2 1 ) for Cr3+ ions. However, the experimental second-rank ZFSPs ( D = b 2 0 , E = 1 / 3 b 2 2 ) were expressed in a nominal principal axis system. To provide additional insight into low symmetry aspects, the distortions (ligand's distances ΔRi and angular distortions Δθi) have been varied while preserving monoclinic site symmetry, in such way as to obtain the calculated values (D, E) close to the experimental ones, while keeping b 2 1 close to zero. 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 Cr3+ and Mn2+ ions at octahedral sites in single-molecule magnets and single-chain magnets.

The spin Hamiltonian (SH) parameters experimentally determined by EMR (EPR) may be corroborated or otherwise using various theoretical modeling approaches. To this end semiempirical modeling is carried out for high-spin (S=2) manganese (III) 3d4 ions in complex of tetraphenylporphyrinato manganese (III) chloride (MnTPPCl). This modeling utilizes the microscopic spin Hamiltonians (MSH) approach developed for the 3d4 and 3d6 ions with spin S=2 at orthorhombic and tetragonal symmetry sites in crystals, which exhibit an orbital singlet ground state. Calculations of the zero-field splitting (ZFS) parameters and the Zeeman electronic (Ze) factors (g||=gz, g⊥=gx=gy) are carried out for wide ranges of values of the microscopic parameters using the MSH/VBA package. This enables to examine the dependence of the theoretically determined ZFS parameters bkq (in the Stevens notation) and the Zeeman factors gi on the spin-orbit (λ), spin-spin (ρ) coupling constant, and the ligand-field energy levels (Δi) within the 5D multiplet. The results are presented in suitable tables and graphs. The values of λ, ρ, and Δi best describing Mn(III) ions in MnTPPCl are determined by matching the theoretical second-rank ZFSP b20(D) parameter and the experimental one. The fourth-rank ZFS parameters (b40, b44) and the ρ (spin-spin)-related contributions, which have been omitted in previous studies, are considered for the first time here and are found important. Semiempirical modeling results are compared with those obtained recently by the density functional theory (DFT) and/or ab initio methods.

Given the virtual lack of information on electronic spectra of divalent neodymium we set for synthesis and characterization of Nd2+ systems. Herein, we report stabilization of neodymium in a chloride host, which importantly has been accomplished with Nd ions introduced in a divalent state during synthesis, unlike by gamma-irradiation of Nd3+ system employed previously. This synthesis method yields good quality SrCl2:Nd2+ single crystals. For the first time the novel electronic absorption spectra of Nd2+ doped in SrCl2 have been recorded with high resolution at liquid helium temperature (4.2 K). Identification of the absorption bands occurring in the spectral range of 5000 - 40000 cm1 (i.e. 2000 - 250 nm) has been achieved and their tentative assignment proposed. This uniquely detailed Nd2+ absorption spectrum provides basis for fingerprinting method enabling identification of the presence of Nd2+ ions in future spectra as well as in existing but as yet not fully resolved spectra.

Potential single-ion magnet Ni 2+ systems: [Ni(Me 6 tren)Cl](ClO 4 ) and [Ni(Me 6 tren)Br](Br) reveal unusually high zero field splitting (ZFS). The ZFS parameter (ZFSP) D expt = −120 to −180 cm −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 −200 cm −1 . Such ZFSP values may seem controversial in view of the D values usually not exceeding several tens of cm −1 for Ni 2+ 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 Ni 2+ systems. Using crystal structure data for [Ni(Me 6 tren)Cl](ClO 4 ) and [Ni(Me 6 tren)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 ( H free ion + H CF ) will allow considering the wavefunctions compositions and thus actual origin of the splitting between the ground and first excited state.

The zero-field splitting parameters (ZFSPs), aka magnetic anisotropy (MA) parameters, are crucial for description of transition ions. Compatibility of ZFSPs is indispensable for proper interpretation of experimental and theoretical data. To achieve compatibility of orthorhombic ZFSPs reported for single magnetic 3dN adatoms on surfaces, the distinct nature of ZFS quantities and MA ones, and their interrelationships, are elucidated. The terminological confusion prevalent in adatoms studies results in detrimental consequences, e.g. erroneous values of the true uniaxial MA constant K and/or the axial ZFSP D. It is shown that the intrinsic features of the true orthorhombic ZFSPs: D and E (rhombic) in the conventional notation or B 2 q ( b 2 q , q = 0, 2) in the Stevens notation, bear critically on compatibility of ZFSP sets. Since the standard ZFSP sets (0

Allowed transitions observed using electron magnetic resonance (EMR) in transition metal (3dN or 4fN) complexes may be predicted by the selection rules. Non-standard selection rules justified by mixing of wavefunctions emerge for nominally forbidden transitions. We present tutorial guide on selection rules in EMR, optical, and inelastic neutron scattering spectroscopy. This includes basic concepts in quantum mechanics and group theory underlying derivations of selection rules and useful rules for nonzero matrix elements. These rules provide crucial information for practitioners. Survey of usage of selection rules in EMR and related studies of novel systems in emerging areas is provided at an introductory level. Applications to modern case systems include: parallel field EMR excitations for integer spin vs half-integer spin ions, nitrogen vacancies in diamond, Haldane gap systems, exchange coupled systems and molecular nanomagnets, and magnetic adatoms on surfaces. Various misconceptions concerning crucial notions, which constitute terminological confusion, have been clarified.

Superposition model (SPM) is applied to zero field splitting (ZFS) parameters (ZFSPs) and independently to crystal field parameters (CFPs). The previous SPM/CF modeling (valid but based on early structural data) and subsequent ZFSP calculations (physically invalid) for Cr3+ ions in LiKSO4 are revisited and extended. Implications of invalid conversions of CFPs to ZFSPs, arising from mixing up the CF and ZFS quantities, are exposed. This invalid procedure based on the CF = ZFS confusion is avoided by independent SPM/ZFS modeling for Cr3+:LiKSO4 utilizing more recent structural data. Two substitutional sites, K+ and Li+, for Cr3+ ion entering LiKSO4 crystal and several distortion models are considered. The predicted ZFSPs match well experimental EMR ones. Orthorhombic standardization of ZFSPs and maximum rhombicity ratio are discussed. SPM-calculated CFPs are used as input for CF analysis package to obtain Hada optical energy bands for Cr3+ in LiKSO4. Microscopic spin Hamiltonian theory of ZFSPs in conjunction with SPM/ZFS and SPM/CF approaches enable to consider correlation of optical and EMR spectroscopy data. Overall results indicate that Cr3+ ions enter LiKSO4 lattice at K+ sites.

The standardization idea is nowadays tacitly accepted in EMR area, however, its usefulness in magnetism studies has not been fully recognized as yet. This idea arises due to intrinsic features of orthorhombic Hamiltonians of any physical nature, including the crystal (ligand) field (CF/LF) Hamiltonians or the zero-field splitting (ZFS) ones. Standardization limits the ratio of the orthorhombic parameter to the axial one to a fixed range between 0 and a specific value that depends on the notation used. For the ZFS parameters expressed in the conventional spin Hamiltonian (SH) notation the ratio λ=E/D can always be limited to the range (0, ±1/3) by appropriate choice of coordinate system. Implications of standardization of orthorhombic spin Hamiltonians for interpretation of experimental magnetic susceptibility data are considered. Using a numerical example, we show the existence of alternative solutions for ZFS parameters potentially obtainable from fitting experimental magnetic data and discuss their importance. For the first time algebraic applications of the standardization to the expressions for magnetic susceptibility tensor derived earlier for localized spin models with S=1, 3/2, 2, 5/2 and with rhombic anisotropy are explored. The numerical and algebraic results allow us to formulate an 'invariance principle'. These considerations facilitate interpretation of experimental magnetic data and provide an additional check of correctness of analytical magnetic susceptibility expressions.

Survey of spectroscopic studies of trivalent rare-earth (RE3+) ions at orthorhombic or monoclinic sites in various crystals, which are important in view of promising technological applications, has revealed a number of crystal field (CF) parameter (CFP) sets belonging to different ranges in the CF parameter space. This indicates that the major properties of orthorhombic and monoclinic CF Hamiltonians have not been fully realized in literature. This includes the existence of alternative, i.e. physically equivalent, CF parameter (CFP) sets and incorrectness of comparison of such alternative yet disparate CFP sets, which due to their intrinsic features cannot be directly compared. Proper methodology for dealing with such CFP sets has been outlined earlier. In this paper we consider implications of these properties for interpretation of (i) spectroscopic data for rare-earth ions obtained from several experimental techniques and (ii) the axis systems in which the fitted CFPs are supposedly expressed. Since these aspects are not realized by many researchers, incorrect conclusions concerning, e.g. the strength of CF and structural implications, have often been drawn. The standardization approach is employed for meaningful comparative analysis of the CFP sets for RE3+ ions at monoclinic sites in selected laser crystals. The following ion-host systems are studied: Nd3+: LuAlO3, Nd3+: BaY2F8, Eu3+: Gd2O3, Eu3+, Pr3+, Tb3+, Ho3+, Tm3+, Nd3+, Sm3+, Dy3+, Er3+: Y2O3, Er3+: Er2O3, Pr3+, Sm3+, Gd3+, Er3+: LaF3, Er3+: YAlO3. A representative sample of CFP sets is analyzed, standardized, and presented in a unified way. The alternative CFP sets provided here may be utilized in the multiple correlated fitting technique to improve reliability of final fitted CFPs. The present approach may facilitate future spectroscopic determination of CFPs as well as increase reliability of fitted and theoretical CFPs for fN (RE3+) ions at lower symmetry sites.

The microscopic spin Hamiltonian (MSH) theory developed up to the fourth-order perturbation theory for 3d4 and 3d6 ions with spin S=2 within the 5D approximation is employed to predict the zero field splitting (ZFS) parameters and the Zeeman electronic (Ze) ones. The SH parameters, measurable by electron magnetic resonance (EMR), are expressed in terms of the microscopic parameters, i.e. the spin–orbit (λ), spin–spin (ρ) coupling constants, and the crystal-field (ligands-field) energy levels (∆i) within the 5D multiplet. The energies, ∆i, are indirectly related with structural data, thus enabling investigation of magnetostructural correlations. As a case study Fe2+ (3d6; S=2) ions at orthorhombic sites in FeCl2·4H2O and FeF2·4H2O crystals are considered. Calculations of the ZFS and Ze parameters are carried out for wide ranges of values of the microscopic parameters using the package MSH/VBA. Dependence of the theoretically determined ZFS parameters b k q (in the Stevens notation) and the Zeeman factors gi on λ, ρ, and ∆i is examined and suitable graphs are presented. The absolute value of dominant ZFS parameter | b 2 0 | is predicted to be in the range from nearly 8.5 to 1.4 cm−1. Matching the theoretical SH parameters and the experimental ones enables determination of the suitable values of λ, ρ, and ∆i. The fourth-rank ZFS parameters and the ρ(spin–spin)-related contributions, considered for the first time here, are found important. The MSH predictions may be verified and fine-tuned by high-magnetic field and high-frequency EMR measurements. The method employed here and the present results may be also useful for other structurally related systems.

There exists a controversy in the hitherto reported studies concerning the actual space group that accounts for spectroscopic results observed for the trivalent lanthanide (Ln3+) ions doped into β-NaLnF4 hosts. The two competing assignments of the space group: P 6 ¯ or P63/m, bear on the associated point symmetry groups, which describe the local site symmetry of the dopant Ln ions. This paper aims at resolving this controversy. For this purpose two approaches are utilized. First, several new samples were synthesized and characterized by photoluminescence (PL) spectroscopy. Both the emission and excitation PL spectra have been measured. The analysis of the present experimental data indicates unequivocally that the dopant Ln3+ ions enter the crystal lattice β-NaGF4 and β-NaYF4 at two crystallographically distinct sites. Hence, the correct space group for these hosts is P 6 ¯ and not P63/m. The intricacies arising from the sample preparation methods, which bear on the interpretation of the results, are also clarified. Second, the theoretical modeling of the crystal-field parameters (CFPs) is carried out based on superposition model to correlate the available crystallographic and spectroscopic data. The crystal-field analysis enables to ascribe unambiguously the spectroscopically determined sites to the crystallographic sites 1a and 1f. In this way an interpretation of photoluminescence spectra is achieved that fully corroborates the available crystallographic data. The influence of structural disorder occurring in β-NaLnF4 family of compounds on the 5D0 → 7F1 photoluminescence spectra of dopant Eu3+ ion and its role in interpretation of experimental data is also discussed.

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 ( R 0 ) , 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.

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.

The interface between optical spectroscopy, electron magnetic resonance (EMR), and magnetism of transition ions forms the intricate web of interrelated notions. Major notions are the physical Hamiltonians, which include the crystal field (CF) (or equivalently ligand field (LF)) Hamiltonians, and the effective spin Hamiltonians (SH), which include the zero-field splitting (ZFS) Hamiltonians as well as to a certain extent also the notion of magnetic anisotropy (MA). Survey of recent literature has revealed that this interface, denoted CF (LF) ↔ SH (ZFS), has become dangerously entangled over the years. The same notion is referred to by three names that are not synonymous: CF (LF), SH (ZFS), and MA. In view of the strong need for systematization of nomenclature aimed at bringing order to the multitude of different Hamiltonians and the associated quantities, we have embarked on this systematization. In this article, we do an overview of our efforts aimed at providing a deeper understanding of the major intricacies occurring at the CF (LF) ↔ SH (ZFS) interface with the focus on the EMR-related problems for transition ions.

Spectroscopic and magnetic properties of uranium (5f3)- and lanthanide (4fN)-based single-ion magnets (SIMs) as well as single-molecule magnets (SMMs) are modelled using two interrelated crystal field (CF) approaches. The complete approach is based on the full Hamiltonian within the whole nfN configuration. This approach includes the free ion and CF terms, and thus it incorporates the intermediate coupling and the J-mixing. The restricted approach is based on the limited Hamiltonian within the ground multiplet and includes only the CF terms in the LS coupling approximation. The recently reported data on the representative SIMs, namely, U(III) complexes U(Ph2BPz2)3, U(H2BPz2)3, and UTp3 as well as the two pyrazolylborate Dy(III) and Nd(III) complexes are analyzed using both approaches. Modelling includes simulation of the energy levels and wave functions as well as the magnetic susceptibility. The results enable establishing the ranges of applicability of the restricted approach as compared with the complete one. This study reveals that, due to inherent limitations, the applicability of the former approach is severely reduced. Major findings are: (1) the restricted approach is grossly inadequate for modelling of the spectroscopic and/or magnetic properties of uranium-based SIMs, (2) this approach is barely suitable for modelling of the spectroscopic properties for lanthanide complexes, (3) it may serve for an approximated modelling of the magnetic properties but the values of the so-determined CF parameters should be treated with caution, (4) the complete approach provides significantly better and more reliable interpretation of the experimental spectroscopic data on the energy levels determined from optical absorption spectra as well as of the temperature dependence of magnetic susceptibility for the U(III)- and Ln(III)-based SIMs.

The effect of the Sr doping on electronic structure in single crystals of (La(1-x)Sr(x))(Ga(1-y)Mn(y))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 (y1%) 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 Mn(4+) (S=3/2) ions in LSGM. The experimental ZFS parameters are modeled using superposition model analysis based on an orthorhombic symmetry approximation.

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 – tk, and the reference distance – R0. An extensive survey of literature has revealed that the model parameters for Ni2+ (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 Ni2+ ions in the six-fold coordinated NiO6 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 Ni2+ ions in several crystals. The present results enable modeling of the ZFSP b 2 0 = D for Ni2+ (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 Ni2+ ions doped into α-Al2O3 (corundum), α-LiIO3, and LiNbO3, as well as the series of fluosilicate crystals with general formula: ABF6·6R2O (A=Zn, Mg, Co, Ni, Fe; B=Si, Ti, Sn, BF4; R=H, D). These results will be utilized in studies of Ni2+-based systems suitable for pressure sensors in high-pressure electron magnetic resonance (EMR) measurements and spectroscopic properties of Ni2+ ions in Haldane gap systems.

This review provides a summary of distinct Hamiltonians used to describe magnetic and spectroscopic properties of paramagnetic and magnetic coordination compounds. Based on the origins and the underlying physical principles, clear recommendations are formulated on when these Hamiltonians are appropriate and how they relate to each other. The interface, denoted CF (LF) ↔ SH (ZFS), encompasses the physical Hamiltonians, which include the crystal field (CF) [or equivalently ligand field (LF)] Hamiltonians, and the effective spin Hamiltonians (SH), which include the zero-field splitting (ZFS) Hamiltonians, as well as, to a certain extent, also the notion of magnetic anisotropy (MA). Survey of recent literature has revealed that the intricate web of interrelated notions has become dangerously entangled over the years. A given crucial notion is often referred to by one of the three names that are not synonymous: CF (LF), SH (ZFS), or MA, each having a well-defined and established meaning in optical spectroscopy, electron magnetic resonance (EMR), and magnetism, respectively. The terminological confusions occurring in literature call for in-depth clarifications, which are provided in this review. For this purpose, crucial notions are systematically defined and their logical interrelationships illustrated by concept maps. The operator types used to express the CF (LF) and SH (ZFS) Hamiltonians, i.e. the Stevens and Wybourne ones, are classified and their distinct properties discussed. Several key aspects are considered in the nutshell: basic forms of Hamiltonians and definitions of the associated parameters, distinct properties of the Stevens and Wybourne CF (LF) parameters and implications for conversion relations, distinctions and interrelationships between the CF (LF) and SH (ZFS) Hamiltonians or parameters, conversion relations between the Stevens ZFS parameters and conventional ones. The general focus is on the fundamental aspects underlying physics and chemistry of single transition (4fN and 3dN) ions in coordination compounds as well as the novel single-ion and polynuclear magnetic systems. This includes the single-ion magnets and the exchange coupled systems (ECS) based on transition ions, especially the single molecule magnets (SMM) or molecular nanomagnets (MNM). The general aim is to provide deeper understanding of the major intricacies involved in the CF (LF) ↔ SH (ZFS) interface. The level of presentation is geared toward experimentalists with background in chemistry or physics.

The virtual lack of information on electronic spectra of divalent lanthanide elements (Ln

Survey of recent literature has revealed a doubly-worrying tendency concerning the treatment of the two distinct types of Hamiltonians, namely, the physical crystal field (CF), or equivalently ligand field (LF), Hamiltonians and the zero-field splitting (ZFS) Hamiltonians, which appear in the effective spin Hamiltonians (SH). The nature and properties of the CF (LF) Hamiltonians have been mixed up in various ways with those of the ZFS Hamiltonians. Such cases have been identified in a rapidly growing number of studies of the transition-ion based systems using electron magnetic resonance (EMR), optical spectroscopy, and magnetic measurements. These findings have far ranging implications since these Hamiltonians are cornerstones for interpretation of magnetic and spectroscopic properties of the single transition ions in various crystals or molecules as well as the exchange coupled systems (ECS) of transition ions, e.g. single molecule magnets (SMM) or single ion magnets (SIM). The seriousness of the consequences of such conceptual problems and related terminological confusions has reached a level that goes far beyond simple semantic issues or misleading keyword classifications of papers in journals and scientific databases. The prevailing confusion, denoted as the CF=ZFS confusion, pertains to the cases of labeling the true ZFS quantities as purportedly the CF (LF) quantities. Here we consider the inverse confusion between the CF (LF) quantities and the SH (ZFS) ones, denoted the ZFS=CF confusion, which consists in referring to the parameters (or Hamiltonians), which are the true CF (LF) quantities, as purportedly the ZFS (or SH) quantities. Specific cases of the ZFS=CF confusion identified in recent textbooks, reviews and papers, especially SMM- and SIM-related ones, are surveyed and the pertinent misconceptions are clarified. The serious consequences of the terminological confusions include misinterpretation of data from a wide range of experimental techniques and, most recently, have lead to pitfalls and errors of substance bearing on understanding of physical properties. Clarification of the incorrect terminology is timely in order to bring about better understanding of the physical principles and prevent further proliferation of the confusion.

There is a lack of information on electronic spectra of divalent neodymium, and thus the synthesis and characterization of Nd

Recent developments in high-magnetic field/high-frequency electron magnetic resonance (HMF-EMR) techniques offer improved capabilities for determination of the spin Hamiltonian (SH) parameters, including the fourth-rank zero field splitting (ZFS) parameters (ZFSPs) for spin S = 2 systems. However, the density functional theory (DFT) and ab-initio methods provide predictions of the ZFS energies from which usually only the second-rank ZFSPs are obtained. Here we present an analytical method for determination of the fourth-rank ZFSPs from the ZFS energy levels for S = 2 ions at orthorhombic sites. This enables assessment of their significance and determination of the dominant parameters. Applications of this method for Fe2+ in [Fe(H2O)6](NH4)2(SO4)2, Fe2+ in forsterite (Fe2+:Mg2SiO4), and Cr2+ ions in (ND4)2Cr(D2O)6(SO4)2 and Rb2Cr(D2O)6(SO4)2 indicate an important role of the fourth-rank ZFSPs. The analytical formulas derived by us may be applied to other 3d6 and 3d4 (S = 2) ions at orthorhombic sites in various hosts for better modeling of spectroscopic and magnetic properties of these systems.

The single transition ions in various crystals or molecules as well as the exchange coupled systems (ECS) of transition ions, especially the single molecule magnets (SMM) or molecular nanomagnets (MNM), have been extensively studied in recent decades using electron magnetic resonance (EMR), optical spectroscopy, and magnetic measurements. Interpretation of magnetic and spectroscopic properties of transition ions is based on two physically distinct types of Hamiltonians: the physical crystal field (CF), or equivalently ligand field (LF), Hamiltonians and the effective spin Hamiltonians (SH), which include the zero-field splitting (ZFS) Hamiltonians. Survey of recent literature has revealed a number of terminological confusions and specific problems occurring at the interface between these Hamiltonians (denoted CF (LF)↔SH (ZFS)). Elucidation of sloppy or incorrect usage of crucial notions, especially those describing or parameterizing crystal fields and zero field splittings, is a very challenging task that requires several reviews. Here we focus on the prevailing confusion between the CF (LF) and SH (ZFS) quantities, denoted as the CF=ZFS confusion, which consists in referring to the parameters (or Hamiltonians), which are the true ZFS (or SH) quantities, as purportedly the CF (LF) quantities. The inverse ZFS=CF confusion, which pertains to the cases of labeling the true CF (LF) quantities as purportedly the ZFS quantities, is considered in a follow-up paper. The two reviews prepare grounds for a systematization of nomenclature aimed at bringing order to the zoo of different Hamiltonians. Specific cases of the CF=ZFS confusion identified in the recent textbooks, review articles, and SMM (MNM)- and EMR-related papers are surveyed and the pertinent misconceptions are outlined. The consequences of the terminological confusions go far beyond simple semantic issues or misleading keyword classifications of papers in journals and scientific databases. Serious consequences include misinterpretation of data from a wide range of experimental techniques and, most recently, have lead to pitfalls and errors of substance bearing on understanding of physical properties. Clarification of the incorrect terminology may prevent further proliferation of the problems and confusions, and thus bringing about better understanding of the physical principles involved.

This article elucidates the pitfalls identified in the software package SIMPRE recently developed by Baldovi et al. (J. Comput. Chem. 2013, 34, 1961) for modeling the spectroscopic and magnetic properties of single ion magnets as well as single-molecule magnets. Analysis of the methodology used therein reveals that the crystal field parameters (CFPs), expressed nominally in the Stevens formalism, exhibit features characteristic for the CFPs expressed in the Wybourne notation. The resemblance of the two types of CFPs introduces a serious confusion that may lead to wrong comparisons of the CFPs taken from various sources. To clarify this confusion, the properties of the CFPs Bkq ( Akq, Ckq) associated with the Stevens operators Okq(X = S, J, or L), which belong to the class of the tesseral-tensor operators, are contrasted with those of the CFPs Bkq associated with the Wybourne operators Cq(k), which belong to the class of the spherical-tensor operators. Importantly, the confused properties of Stevens and Wybourne operators may bear on reliability of SIMPRE calculations. To consider this question independent calculations are carried out using the complete approach and compared with those of the restricted approach utilized earlier. It appears that the numerical results of the package SIMPRE are formally acceptable, however, the meaning of the CFPs must be properly reformulated. Several other conceptual problems arising from misinterpretations of the crucial notions and the CFP notations identified therein are also discussed and clarified.