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Magnetic Ions in Crystals

Magnetic Ions in Crystals

Copyright Date: 1997
Pages: 264
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  • Book Info
    Magnetic Ions in Crystals
    Book Description:

    There have been many demonstrations, particularly for magnetic impurity ions in crystals, that spin-Hamiltonians are able to account for a wide range of experimental results in terms of much smaller numbers of parameters. Yet they were originally derived from crystal field theory, which contains a logical flaw; electrons on the magnetic ions are distinguished from those on the ligands. Thus there is a challenge: to replace crystal field theory with one of equal or greater predictive power that is based on a surer footing. The theory developed in this book begins with a generic Hamiltonian, one that is common to most molecular and solid state problems and that does not violate the symmetry requirements imposed on electrons and nuclei. Using a version of degenerate perturbation theory due to Bloch and the introduction of Wannier functions, projection operators, and unitary transformations, Stevens shows that it is possible to replace crystal field theory as a basis for the spin-Hamiltonians of single magnetic ions and pairs and lattices of magnetic ions, even when the nuclei have vibrational motion.

    The power of the method is further demonstrated by showing that it can be extended to include lattice vibration and conduction by electron hopping such as probably occurs in high-Tc superconductors. Thus Stevens shows how an apparently successful ad hoc method of the past can be replaced by a much more soundly based one that not only incorporates all the previous successes but appears to open the way to extensions far outside the scope of the previously available methods. So far only some of these have been explored. The book should therefore be of great interest to all physicists and chemists concerned with understanding the special properties of molecules and solids that are imposed by the presence of magnetic ions.

    Originally published in 1997.

    ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

    eISBN: 978-1-4008-6446-1
    Subjects: Physics

Table of Contents

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  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-vi)
  3. Preface
    (pp. vii-2)
  4. 1 Introduction
    (pp. 3-36)

    From a microscopic point of view magnetic properties arise from two sources, the translational motion of charged particles, particularly electrons, and the magnetic moments associated with the spins of electrons and nuclei. The steps that eventually led to this picture began in the early 1900s, when Zeeman studied the changes that occur in the optical spectra of free ions in the presence of external magnetic fields. It was still a long road though, through classical physics, Bohr theory, quantum theory, and the introduction of a wide range of experimental techniques, before the present understanding of the properties of magnetic ions...

  5. 2 Group Theory
    (pp. 37-66)

    Group theory is a branch of pure mathematics dealing with concepts that often seem too abstract for a typical physicist. A common reaction is to feel that it is difficult to comprehend because it is unclear where it is going, an impression which is not helped by the extensive literature on the subject, most of which is not used in theoretical physics. Nevertheless, some of its ideas are extremely useful. This account, which does not aim to be a detailed account of group theory, should therefore be regarded as an attempt to introduce a selection of concepts in a way...

  6. 3 Perturbation Theory
    (pp. 67-82)

    Most problems in quantum mechanics cannot be solved exactly, so recourse has to be made to approximation methods. There is no single method that is universally satisfactory, and over the years a variety of different procedures have been introduced and lumped together under the title of perturbation theory. In this chapter an outline will be given of some of the methods which are particularly relevant to magnetic problems and which will be used subsequently. First, though, there are several general remarks that can be made. Two types of Hamiltonian are in use. The first does not contain time explicitly, while...

  7. 4 Crystal Field Theory
    (pp. 83-104)

    Crystal field theory is widely used in explaining the magnetism of crystals, particularly in its spin-Hamiltonian form. It was introduced by Van Vleck in the early 1930s (see Van Vleck, 1944) because the ionic crystals of the iron group elements had been found to show magnetic susceptibilities which varied inversely as the temperature with magnitudes that could not be explained unless their orbital magnetism was neglected. There was, therefore, a need to demonstrate that on placing an ion in a crystal lattice the electronic motion would be so changed by the internal electric field set up by the neighboring ions,...

  8. 5 Beyond Crystal Field Theory
    (pp. 105-128)

    The previous chapter has shown that the spin-Hamiltonian forms can be derived using crystal field theory and some general assumptions about orders of magnitude, such as that the term separations are small compared with the separations between the configurations but large compared with the crystal field splittings; the spin-orbit splittings are small compared with the term separations; in the iron group ions the crystal field splittings are large compared with the spin-orbit splittings; in the rare earth ions the spin-orbit splittings are large compared with the crystal field splittings. Such assumptions are not by any means enough to give the...

  9. 6 Second Quantization
    (pp. 129-150)

    It will be assumed that no eigenfunctions of any many-electron Hamiltonian are known exactly, which indicates that the task of finding even one is difficult. When this is compounded with the physical requirement that the only ones of physical interest have to be antisymmetric with respect to interchanges of electrons the task looks even more daunting, for how are these to be picked out ab initio? There is therefore interest in any technique that concentrates attention on functions that already incorporate the antisymmetric requirements, which is why Slater determinants were introduced. It must be admitted, though, that they are clumsy...

  10. 7 From Generic to Spin-Hamiltonian
    (pp. 151-170)

    With second quantization and Wannier functions, the study of a magnetic ion introduced as a substitutional impurity into an otherwise nonmagnetic host crystal can be reexamined. The procedure will be kept as similar as possible to that of crystal field theory, bearing in mind that the two cannot be identical because crystal field theory distinguishes between electrons.

    For a substitutional magnetic impurity in a nonmagnetic crystal, the generic Hamiltonian which corresponds to that used in crystal field theory is that of a system of electrons moving in the fields of the nuclei and repelling one another by their Coulomb interactions....

  11. 8 The Interactions between Ions
    (pp. 171-184)

    It has long been known that there are interactions between magnetic ions, and a natural extension of the spin-Hamiltonian concept is to assume that given two magnetic ions in a crystal each would have its own spin-Hamiltonian and there would be interactions between them, expressible in terms of their effective spins. Some authors went further and suggested that the Hamiltonian for the pair could be split into two single-ion crystal-field-like Hamiltonians, one for each ion, with a perturbation which represented the interaction between them, the implication being that a simple extension of crystal field theory would give the expected spin-Hamiltonian...

  12. 9 Cooperative Systems
    (pp. 185-206)

    The theory of pair interactions described in the previous chapter can be extended to fully concentrated magnetic crystals, when it produces an effective Hamiltonian in which each ion is described by a spin-Hamiltonian and all the ions are coupled to one another by exchangelike spin-spin interactions. This form is then usually simplified by assuming that the interactions between closely spaced ions dominate. It is difficult to claim that such a picture is supported by experimental observations, for unfortunately there are no techniques which give anything like the amount of detailed information about the energy levels of large clusters of magnetic...

  13. 10 Conductors
    (pp. 207-232)

    Although a good deal of attention has been paid to antiferromagnetism it is not easy to think of practical applications of it. This is in marked contrast with the closely related ferrimagnetism, which is widely used. The difference arises because although both share the property of being electrical insulators the ferrimagnets have the additional property of possessing macroscopic magnetic moments. From the theoretical point of view the two are not very different, for all that would seem to be needed is to have magnetic moments on theAsites that differ from those on theBsites. In fact, the...

  14. 11 Nuclear Symmetry
    (pp. 233-250)

    The generic Hamiltonian used in the previous chapters has been symmetric in nuclear as well as electronic variables, and yet in the subsequent discussion more emphasis has been placed on the antisymmetric requirement for electrons than on any symmetry requirements on nuclei. This is typical of most of solid state theory in that the requirement that the wave functions that describe nuclear motion should not distinguish between identical nuclei is either completely ignored or, in the relatively few examples where the problem is even considered, dismissed by a statement that since the wave functions of nuclei do not overlap the...

  15. Index
    (pp. 251-254)
  16. Back Matter
    (pp. 255-255)