A theory is given of the nuclear hyperfine structure of the paramagnetic resonance in hydrated crystals. Starting from the states of a free ion, neglecting spin-dependent terms in the energy, successive steps of perturbation calculation introduce the effect of the crystalline electric field, the spin-orbit and spin-spin interactions, the coupling with an external magnetic field, and the coupling between the nucleus of the ion and the electrons. The self-consistent field approximation, in which the state of the free ion is described by a single electronic configuration, is found to be inadequate, and it is found necessary to consider admixtures, through configurational coupling, of configurations in which there are unpaired 8-electrons, as these contribute significantly to the hyperfine splitting. A review of the application of the theory to the ions of the iron transition group is given. The phenomenon of paramagnetic resonance, discovered by Zavoisky (1945, 1946), is by now well known. In crystals it normally takes the form of a number of lines, whose breadth is partly determined by the random distribution of the magnetic fields exerted on one ion by its neighbours, and partly by the rapid interchange of magnetic energy and the thermal energy of the lattice, and there may be considerable overlapping of the lines. In particular, the nuclear hyperfine structure, i.e. the splitting of the lines by the action of the nucleus of the ion, though present when the spin of the nucleus differs from zero, is not normally resolved. The line breadth can be substantially reduced by working at low temperatures using magnetically dilute crystals in which most of the magnetic ions are replaced by chemically similar non-magnetic ions forming an isomorphous crystal; and under these conditions the hyperfine structure can be resolved (Penrose I949). The purpose of this paper is to discuss the theory of the nuclear hyperfine structure of the paramagnetic resonance in salts of the iron transition group. The main reasons for confining the discussion to this group are that most of the experimental work has been done on it; and that although the general theory is common to all paramagnetic substances, the application to particular cases involves approximations which are different for the different groups of paramagnetics. In particular, for the iron group the dominating effect on the energy levels of an ion is the crystalline electric field; next in order of importance comes the spin-orbit coupling; then, under usual experimental conditions, the coupling of the ion with the external magnetic field; and last, the interaction with the nucleus. For the rare earths, on the other hand, the spin-orbit coupling may be the dominant effect, and the nuclear interaction may come second. Since up to the present little experimental work has been done on the hyperfine struc

Theory of the nuclear hyperfine structure of paramagnetic resonance spectra in crystals

The Magnetic Properties of Transition Metal Complexes

The typical colours of paramagnetic salts containing [M(H$\_{2}$O)$\_{6}$], M = 3d$^{n}$, complexes, are generally assumed to arise from optical transitions between the orbital energy levels of the 3d ion which are split by the crystalline electric field due to the surrounding water dipoles. The available optical absorption data are analyzed using this ionic model and the associated crystal field theory, and it is shown that while experiment and theory agree fairly well, there are systematic discrepancies. In addition, the orbital level separations given by the optical spectrum are found to be smaller than those predicted from magnetic data. It is shown how these discrepancies can be accounted for by introducing weak covalent bonds into the [M(H$\_{2}$O)$\_{6}$] complex, so that there is charge transfer between the paramagnetic ion and the attached water molecules.

The colours and magnetic properties of hydrated iron group salts, and evidence for covalent bonding

On the mechanism of paramagnetic relaxation

The paramagnetic resonance spectra of five nickel Tutton salts have been analyzed at 290?K. The positions and intensities of the absorption lines are adequately explained by a crystalline electric field of rhombic symmetry. The triplet ground state is resolved into three singlets with an overall splitting of the order of 3 cm-', and the spectroscopic splitting factor g is found to be 2-25 + 0 05. A comparison is made between the directly measured values of the magnetic anisotropy, and the values calculated using the resonance results. The main part of this paper describes the paramagnetic resonance spectra found in some nickel Tutton salts at 290? K for wave-lengths between 0-85 and 1'79 cm. Further measurements have been made on some salts at 90?K using a single wave-length of about 1-2 cm. The resonance method allows a detailed investigation of the behaviour of the lowest energy levels of the nickel ions in an applied magnetic field. This behaviour depends strongly on the nature of the crystalline electric field due to the octahedron of water molecules surrounding the nickel ion. In nickel fluosilicate the resonance method showed (Penrose & Stevens I950) that the non-cubic part of the field is of trigonal symmetry leaving a singlet and a doubly degenerate level in the lowest spin triplet (S -1). The behaviour of the hydrated sulphates of nickel presents a more difficult problem as pointed out by Ollom & Van Vleck (I95I). In these salts the crystal field is not usually of axial symmetry, which implies that all three levels of the lowest spin triplet are separated in zero magnetic field, and these separations are often larger than the energy of the microwave-lengths used ( - 1 cm-'). With a non-uniaxial electric field of this sort, the energy levels of the Ni2+ ion vary in a complicated way when an external magnetic field is applied, and if, as is usually the case, there are several inequivalent Ni2+ ions present whose spectra show up separately, then the resulting absorption lines become rather difficult to interpret. The present paper shows that in the nickel Tutton salts, where there are two inequivalent ions in unit cell, the resonance results can be interpreted by assuming that the non-cubic part of the crystalline field has rhombic symmetry. The directions of the rhombic axes, and the Stark splittings between adjacent levels of the lowest spin triplet, have been determined for five nickel Tutton salts at 290?K. Measurements at lower tem- peratures show that these directions and splittings do not change rapidly with temperature. This behaviour is also different from that of nickel fluosilicate where the splitting changes very rapidly with temperature. A preliminary account of the

Paramagnetic Resonance in the Nickel Tutton Salts

Über das Magnetische Verhalten vom Vanadium-ammonium Alaun

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Über das Magnetische Verhalten vom Vanadium-ammonium Alaun