Theoretical and Structural Study of Axial Symmetry Ce3+ Centers in the BaWO4 Single Crystal Doped with Cerium and Codoped with Sodium Ions

The spin-Hamiltonian parameters g-factors (g|| and g⟂) of the Ce³⁺ paramagnetic centers in BaWO₄: Ce and BaWO₄: Ce, Na single crystals with axial symmetry are investigated using the superposition model (SPM) via complete diagonalization procedure of energy matrix (CDM method). The calculated g-factors are in reasonable agreement with the experimental values. The fitted intrinsic parameters are comparable with data from other publications for rare-earth paramagnetic centers in a similar environment. The angular distortions of the cerium dodecahedron [CeO₈] are also studied. Structural analysis of paramagnetic centers with axial symmetry through the postulated cerium barium tetrahedron [CeBa₄] connected via oxygens bridges was carried out. The mechanism of the charge compensation and the role of the second dopant (Na⁺) is also discussed.

An Exchange Mechanism for the Magnetic Behavior of Er3+ Complexes

We study the magnetic properties of the erbium based compounds, Na9[Er(W5O18)2] and [(Pc)Er{Pc{N(C4H9)2}8}]·/-, in the framework of an effective spin exchange model involving delocalized electrons occupying molecular orbitals. The calculations successfully reproduce the experimental data available in the literature for the magnetic spectrum, magnetization and molar susceptibility in dc and ac fields. Owing to their similar molecular geometry, the compounds' magnetic behaviors are interpreted in terms of the same set of active orbitals and thus the same effective spin coupling scheme. For all three complexes, the model predicts a prompt change in the ground state from a Kramer's doublet at zero fields to a fully polarized quartet one brought about by the action of an external magnetic field without Zeeman splitting. This alteration is attributed to the enhancement of the effect of orbital interactions over the spin exchange as the magnitude of the external magnetic field increases.

The Fascinating World of Low-Dimensional Quantum Spin Systems: Ab Initio Modeling

In recent times, ab initio density functional theory has emerged as a powerful tool for making the connection between models and materials. Insulating transition metal oxides with a small spin forms a fascinating class of strongly correlated systems that exhibit spin-gap states, spin–charge separation, quantum criticality, superconductivity, etc. The coupling between spin, charge, and orbital degrees of freedom makes the chemical insights equally important to the strong correlation effects. In this review, we establish the usefulness of ab initio tools within the framework of the N-th order muffin orbital (NMTO)-downfolding technique in the identification of a spin model of insulating oxides with small spins. The applicability of the method has been demonstrated by drawing on examples from a large number of cases from the cuprate, vanadate, and nickelate families. The method was found to be efficient in terms of the characterization of underlying spin models that account for the measured magnetic data and provide predictions for future experiments.

Spin Hamiltonians in Magnets: Theories and Computations

The effective spin Hamiltonian method has drawn considerable attention for its power to explain and predict magnetic properties in various intriguing materials. In this review, we summarize different types of interactions between spins (hereafter, spin interactions, for short) that may be used in effective spin Hamiltonians as well as the various methods of computing the interaction parameters. A detailed discussion about the merits and possible pitfalls of each technique of computing interaction parameters is provided.

Three-dimensional mapping of single-atom magnetic anisotropy

Magnetic anisotropy plays a key role in the magnetic stability and spin-related quantum phenomena of surface adatoms. It manifests as angular variations of the atom's magnetic properties. We measure the spin excitations of individual Fe atoms on a copper nitride surface with inelastic electron tunneling spectroscopy. Using a three-axis vector magnet we rotate the magnetic field and map out the resulting variations of the spin excitations. We quantitatively determine the three-dimensional distribution of the magnetic anisotropy of single Fe atoms by fitting the spin excitation spectra with a spin Hamiltonian. This experiment demonstrates the feasibility of fully mapping the vector magnetic properties of individual spins and characterizing complex three-dimensional magnetic systems.

Software package SIMPRE--revisited

This article elucidates the pitfalls identified in the software package SIMPRE recently developed by Baldoví 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.

Two-dimensional molecular magnets with weak topological invariant magnetic moments: mathematical prediction of targets for chemical synthesis

An open problem in applied mathematics is to predict interesting molecules that are realistic targets for chemical synthesis. In this paper, we use a spin Hamiltonian-type model to predict molecular magnets (MMs) with magnetic moments that are intrinsically robust under random shape deformations to the molecule. Using the concept of convergence in probability, we show that for MMs in which all spin centres lie in-plane and all spin centre interactions are ferromagnetic, the total spin of the molecule is a 'weak topological invariant' when the number of spin centres is sufficiently large. By weak topological invariant, we mean that the total spin of the molecule depends only upon the arrangement of spin centres in the molecule, and is unlikely to change under shape deformations to the molecule. Our calculations show that only between 20 and 50 spin centres are necessary for the total spin of these MMs to be a weak topological invariant. The robustness effect is particularly enhanced for two-dimensional ferromagnetic MMs that possess a small number of spin rings in the structure.

Energy Levels, Wave Functions, Dipole and Quadrupole Transitions of Trivalent Gadolinium Ions in Sapphire

A computation is made of energy levels, wave functions and transition matrix elements of the Gd3+ ion in Al2O3. The crystal field parameters are taken from Geschwind and Remeika's paramagnetic resonance experiments. The transition probabilities are given for dipole radiation in three polarization directions. For ultrasonic work we give the real and imaginary parts of the five matrix elements of the quadrupole transition. From these one can easily deduce the transition probabilities in any given direction. The magnetic field directions are described by the angles θ and ϕ, the polar and azimuthal angles with respect to the crystalline c axis. The values of θ go from 0 to π/2 in six steps and two values of π are chosen, 0 and 2 π/3 for which the variation is largest. The magnetic field strengths are from 0 to 0.6 tesla (6000 gauss); beyond this value the spin can be considered as "free." Some consideration is given to the analytical behavior of the energy versus field diagram for the direction θ = ϕ = 0.