Paweł Gnutek’s research while affiliated with West Pomeranian University of Technology and other places

We investigate Dy-based coordination polymer C11H18DyN3O9 (Dy-CP) exhibiting single-ion magnet (SIM) properties, e.g., quantum tunnelling of magnetization (QTM), magnetic anisotropy, magnetic relaxation, and effective energy barrier (Ueff). To elucidate the underlying mechanisms, crystal field parameters (CFPs) for Dy3+ ions were modelled using radial effective charge model (RECM) and superposition model (SPM), and computational packages SIMPRE and SPECTRE. The modelled CFPs enable predicting energy levels and associated wave functions, which successfully explain the field-induced Dy-CP SIM properties. So-calculated magnetic susceptibility and isothermal magnetization match experimental data reasonably well. The smaller energy separations of the first (01 31 cm1) and the second (02 = 74 cm1) excited Kramers doublets suggest small Ueff = 65 cm1 for Dy-CP. The magnetic moments of Dy3+ ions exhibit an easy-axis type magnetic anisotropy in the ground state, but change orientation in the excited states due to mixing of states from different Kramers doublet. Low-symmetry CF components play crucial role in connecting different |MJ> states within the ground multiplet, resulting in QTM and magnetic relaxation to the ground state occurring via the excited states. The RECM and SPM calculated CFP sets are standardized employing the 3DD package to enable meaningful comparison and assessing their mutual equivalence. The results demonstrate the correlation between structural and electronic features of the molecule and site symmetry and distortion of the local coordination polyhedra with SIM properties, offering insights for rational design of new SIMs. The importance of considering low-symmetry aspects in CFP modelling for accurate predictions of magnetic properties is highlighted. This study provides deeper understanding of field-induced behaviour in rare-earth-based SIMs and approaches for rationalization of experimentally measured SIMs’ properties.

We present crystal-field (CF) calculations of energy levels (Ei) of Eu3+ ions doped in various hosts aimed at exploring low-symmetry properties of CF parameters (CFPs) and reliability of CFP modelling with decreasing site symmetry. The hosts studied are: Li6Y(BO3)3, Li6Gd(BO3)3, YBO3, and ZnO with Eu3+ at triclinic sites; YAl3(BO3)4 with Eu3+ ions at trigonal D3 symmetry. Two independent CFP modelling approaches utilizing the hosts’ structural data, are employed: exchange charge model (ECM) and superposition model (SPM). We adopt the Eu3+ actual site symmetry and not approximated one. The Ei calculated using CFPs modelled by ECM and SPM mutually agree with the observed ones. For triclinic symmetry, the ECM/CFPs and SPM/CFPs were numerically distinct, yet turned out to be physically equivalent yielding identical rotational invariants, Sk (k = 2, 4, 6), and Ei. For trigonal symmetry, both CFP sets agree numerically, thus Sk and Ei are identical. This disparity poses a dilemma, since the modified crystallographic axis system was used in both approaches. The standardization of the triclinic CFPs using the 3DD package was performed to solve this dilemma. It has enabled discussing standardization aspects in experimental and computed CFP sets, and elucidating intricate low-symmetry aspects inherent in CFP sets. Understanding of low-symmetry aspects in CF studies may bring about better interpretation of the spectroscopic and magnetic properties of the rare-earth ions doped host crystals. Thus, our study could provide more deep insights into the importance of clear definitions of axis systems and adequate treatment of actual site symmetry in modelling of CFPs for low-symmetry cases which is essential for technological applications and engineering of the rare-earth activated phosphor materials.

Herein, we presented a comparative analysis of crystal-field (CF) effects on the energy levels of Mn4+ ions doped in the various host lattices exhibiting site symmetry from: triclinic: Y2MgTiO6, La2MgTiO6, Ca2YTaO6, Ca2YSbO6; trigonal: Ba2LaSbO6, LaTiSbO6; tetragonal: Ba2GdTaO6; to octahedral: Li2MgTiO4, Ba2GdSbO6, Ba2YSbO6. For modelling CF parameters (CFPs), we employed exchange charge model (ECM) using one model parameter (G), and superposition model (SPM) using four model parameters. A modified crystallographic axis system (CAS*) was adopted in ECM and SPM calculations for low symmetry hosts. The modelled CFPs served as input for crystal-field analysis/microscopic spin-Hamiltonian program to calculate the Mn4+ energy levels and match them with photoluminescence spectra of Mn4+-doped crystals. The 2nd-rank ECM/CFPs vary with G depending on distortions of the metal (M)-ligand (L) MLn polyhedron. The 4th-rank ECM/CFPs depend predominantly on the exchange charge effects. The ECM yields seemingly a better agreement between the observed and calculated energies than the SPM one. The disparity between the CFP sets calculated using SPM and ECM approaches in CAS*, while yielding same CFP strength, poses dilemmas. To solve these dilemmas, we employed the triclinic standardization of CFP sets, thus uncovering intricate low symmetry aspects inherent in ECM/CFPs, hitherto not realized. This method proved very useful for meaningful analysis and interpretation of CFP sets. Our CFP modelling illustrates importance of well-defined axis systems and adequate treatment of the actual triclinic (and monoclinic) site symmetry of dopant ions, instead of octahedral symmetry (usually adopted by experimentalists), in modeling of CFPs for triclinic symmetry cases. The relations between the Racah parameters, B and C, and 2Eg - 4A2g peak emission energy of Mn4+ ions are extended and suitably modified for triclinic symmetry. These modifications may be significant in engineering the local CF environment by suitably choosing the host crystals and dopant ions to improve the luminescence properties of phosphors for practical applications. The influence of dopant metal ions on the local structure and thus spectroscopic properties of doped crystals was also explored.

Superposition model (SPM) is applied to zero field splitting (ZFS) parameters (ZFSPs) and independently to crystal field parameters (CFPs). Correlation of optical and EMR spectroscopy data increases modeling reliability. The previous modeling SPM/CFP (valid but based on early structural data) and ZFSP (physically invalid) for Cr³⁺ ions in LiKSO4are 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/ZFSP modeling for Cr³⁺:LiKSO4 utilizing more recent structural data. The predicted ZFSPs match well experimental EMR ones. Consideration of various distortion models indicates that Cr³⁺ions enter LiKSO4 lattice at K⁺ sites. Orthorhombic standardization of ZFSPs and maximum rhombicity ratio are discussed. Independent SPM/CFPs modeling enables calculations, using CF analysis package, of optical energy band positions for Cr³⁺ in LiKSO4 yielding good agreement with experimental values.

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 S̃ = 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 S̃ 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⁺(S̃ = 3/2) complexes exhibiting very large or moderate zero-field splitting as molecular nanomagnets.