Publisher Summary There have been many reviews and books on electron spin resonance (ESR) and several on transition metal ions. Many of these publications have been written by physicists or theoreticians and are very comprehensive. This review is aimed at inorganic chemists, who have had no experience relating to electron spin resonance and who are becoming more and more likely either to use the technique or to need to appreciate the significance of the information available from the technique. The first part of the review gives an elementary account of the relevant theory. There are many good books for further reading for the inorganic chemist, who wishes to go deeper into the subject. The second part of the review is a comprehensive survey of the results of ESR studies on compounds of transition elements. Inevitably, there has had to be some selection of material, and the criteria for inclusion or rejection has been based upon the likely interest of an inorganic chemist might have in the species. This is particularly in the areas, where there is a lot of related work, e.g., the Mn2+ host-lattice data. In the case of copper dg complexes, there has been much duplication of work and papers devoted to the spectra of complexes where a minor substitutive change has been made to a bulky organic ligand.

Electron Spin Resonance of Transition Metal Complexes

The derivation, implementation, and validation of a method to calculate spin–orbit coupling (SOC) contributions to the hyperfine coupling (HFC) is reported. Due to this development it is now possible to calculate the complete ligand and metal nuclei HFCs at a consistent level of theory, i.e., spin unrestricted Hartree–Fock (HF) or density functional theory (DFT). The SOC contributions to the HFC are calculated as a second-order property and are treated by a coupled-perturbed HF or Kohn–Sham treatment. The method is applied to a representative collection of first row transition metal complexes. The calculated metal HFCs are in reasonable to good agreement with the experimental data, with the main error being probably due to the Fermi contact term that is not well represented by present day DFT functionals. Similarities and differences to the closely related field of electronic g-tensor calculations are discussed.

Metal and ligand hyperfine couplings in transition metal complexes: The effect of spin-orbit coupling as studied by coupled perturbed Kohn-Sham theory

Results of a self-consistent tight-binding calculation of the band structure of body-centered-cubic iron are reported. The basis set consisted of atomic wave functions for the $1s$, $2s$, $3s$, $4s$, $2p$, $3p$, and $4p$ states, expressed as linear combinations of Gaussian-type orbitals (GTO), and five individual GTO for each $3d$ state. The Coulomb part of the crystal potential in the first iteration was constructed from a superposition of overlapping neutral-atom charge densities; the atoms being in the $3{d}^{7}4{s}^{1}$ configuration. Exchange potentials for both spins were calculated utilizing the $X\ensuremath{\alpha}$ method. Self-consistent band structures were obtained for different values of the exchange parameter $\ensuremath{\alpha}$. Best results appear to be obtained for $\ensuremath{\alpha}=0.64$. In this case, 140 points in $\frac{1}{48}$ of the Brillouin zone (BZ) were used to determine the charge density. The resulting self-consistent potentials were then utilized to compute energy levels at 819 regularly spaced points in $\frac{1}{48}$ of the BZ. The results thus obtained are discussed and compared with other reported band-structure results for the same metal. The Fermi surface is analyzed in detail. The density of states has been computed. Magnetic and x-ray form factors are presented. The results are found to be in reasonably good agreement with experiment.

Energy Bands in Ferromagnetic Iron

Alloys of iron with cobalt, nickel, vanadium, chromium, manganese, aluminium and silicon have been studied using the Mossbauer effect. In ferromagnetic alloys the variation of hyperfine field at 57Fe nuclei with electron concentration is qualitatively similar to that of the saturation magnetic moment of the alloys. Owing to the lack of information concerning the relation between the spin density at the nucleus and the spin density in the environment, a more quantitative relationship with the individual magnetic moments of the iron and solute atoms cannot be derived at present. In atomically disordered alloys the line broadening, which measures the extent of the fluctuations in hyperfine field, depended upon the difference between the iron and solute atomic moments; in ordered alloys (e.g. Fe3Al) the lines were not broadened. Several of the non-ferromagnetic alloys showed magnetic ordering (presumably antiferromagnetic) at low temperatures.

https://iopscience.iop.org/article/10.1088/0370-1328/81/6/313/pdf

The Mössbauer Effect in Iron Alloys

Covalency and hyperfine structure constant A of iron group impurities in crystals

The origin of the effective magnetic fields at the nuclei of magnetic materials which have been determined by M\"ossbauer, nuclear magnetic resonance, electron paramagnetic resonance, specific heat, and nuclear polarization methods is investigated theoretically by means of the exchange polarization mechanism. Exchange-polarized iron series Hartree-Fock calculations were carried out for (a) free ions and neutral atoms, (b) ions in a (crude) crystalline field (as in a salt), and (c) spin densities and configurations which conform with energy band and neutron magnetic scattering observations for the ferromagnetic metals. The effective field data for metals, ferrites, rare-earth garnets, and salts are then discussed and it is shown that the dominant contribution to the effective field (in almost every case) arises from the (exchange) polarization of the core electrons by the spin density of the unpaired outer electrons. For the transition metals, the role of the conduction electrons is analyzed including some new contributions not previously considered. The data for ions like ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Mn}}^{++}$ may be understood mainly on the basis of the core polarization term but such factors as covalent bonding, charge transfer, crystal field effects (such as distortions from cubic symmetry) must also be included. For ions like ${\mathrm{Fe}}^{++}$ and ${\mathrm{Co}}^{++}$ the (large) field due to unquenched orbital angular momentum must also be considered and several cases in which the orbital field dominates are discussed. The exchange polarization method and the accuracy of the analytic spin-polarized Hartree-Fock functions are discussed with regard to the sensitivity of the internal field to orbital descriptions, the effect of crystalline environments, and to expansion and contraction of the spin density. Each factor is investigated in detail by means of accurate exchange-polarized calculations. In conjunction with these studies a restricted Hartree-Fock calculation for ${\mathrm{Mn}}^{++}$ was carried out (and is reported as an Appendix) which is more accurate than existing calculations and indicates the accuracy of earlier analytic Hartree-Fock calculations.

A. J. Freeman

Papers

Origin of effective fields in magnetic materials