“…. For the truth of the conclusions of physical science, observation is the supreme Court of Appeal….” (Sir Arthur Eddington, The Philosophy of Physical Science.) In this paper we shall review the theoretical and experimental results obtained on simple magnetic model systems. We shall consider the Heisenberg, XY and Ising type of interaction (ferro and antiferromagnetic), on magnetic lattices of dimensionality 1, 2 and 3. Particular attention will be paid to the approximation of these model systems in real crystals, viz. how they can be realized or be expected to exist in nature. A large number of magnetic compounds which, according to the available experimental information, meet the requirements set by one or the other of the various models are considered and their properties discussed. Many examples will be given that demonstrate to what extent experiments on simple magnetic systems support theoretical descriptions of magnetic ordering phenomena and contribute to their understanding. It will a...

Experiments on simple magnetic model systems

Critical phenomena and renormalization-group theory

Publisher Summary This chapter discusses quadrupole effects in nuclear magnetic resonance studies of solids. The first evidence that many nuclei possess magnetic moments came from the study of the hyperfine structure of atomic spectra in the visible region. The interaction of the nuclear magnetic moment with the magnetic field produced by the atomic electrons gives rise to a hyperfine spectrum that is relatively simple, being characterized by the well known “interval rule.” Marked departures from this interval rule do occur in a few cases, however, and some of the departures can definitely be attributed to the presence of a nuclear electric quadrupole interaction. The methods of radio-frequency spectroscopy are very well adapted for the investigation of the very small interaction energies to which nuclear moments give rise. They have led not only to much more precise determinations of nuclear magnetic moments, but also to a vastly increased knowledge of nuclear electric quadrupole effects. The first outstanding success along this line was the discovery, by the molecular beam resonance method, of the quadrupole moment of the deuteron. The field of electric quadrupole interactions in nuclear magnetic resonance can be divided roughly into two areas according to the relative magnitude of the nuclear quadrupole interactions.

Quadrupole Effects in Nuclear Magnetic Resonance Studies of Solids

The development and current status of microwave ferrite technology is reviewed in this paper. An introduction to the physics and fundamentals of key ferrite devices is provided, followed by a historical account of the development of ferrimagnetic spinel and garnet (YIG) materials. Key ferrite components, i.e., circulators and isolators, phase shifters, tunable filters, and nonlinear devices are also discussed separately.

Ferrite devices and materials

The present status of the temperature dependence of magnetocrystalline anisotropy, and the l(l+1)2 power law

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On the Origin of the Magnetic Anisotropy Energy of Ferrites

Effects of covalency on the nuclear magnetic resonance in ionic crystals are discussed on the basis of perturbation calculations. Formulas for the chemical shift, the I – I coupling and the quadrupolar relaxation time are derived. Using the degree of covalency deduced from the experimental values of the chemical shift, the coefficient of the I - I coupling and the quadrupolar relaxation time are estimated for some ionic crystals. It is shown that, when the degree of covalency is several percent, the quadrupolar relaxation time becomes much shorter than in pure ionic case. For instance, the relaxation time of Br in KBr, assuming the degree of covalency of 1 percent, is estimated to be 1 sec, which is only several times larger than the experimental value.

The Effects of Covalency on the Nuclear Magnetic Resonance in Ionic Crystals

The antiferromagnetism of a single crystal is considered, basing on the Van Vleck model, modified by introducing an anisotropy energy of one spin, arising mainly from the crystalline field of the surrounding anions. On this model are derived the anisotropy of the susceptibility above the Curie point, the temperature variation of the anisotropy constant below the Curie point and the field dependency of the susceptibility under a comparatively strong magnetic field.

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On the Antiferromagnetism of Single Crystals

dipole intera~tion arises from the anisotropic exchange interaction which has original,ly been proposed by Van Vleck. Therefore, we derive the anisotropic exchange interaction on the basis of the perturbation method and estimate the anisotropy constants KI and K2 due to this interaction by use of the ex­ perimental g-values which are relating to the energy differences between the ground state and the excited 'states of Cu2+ ions. Thus it is shown that the sum of theoretical anisotropy constants due to both origins gives the vatues of the same order with that of the experimental values. The anisotropy energy in an antiferromagnetic substance may be considered to consist of three parts: the first part arises from interactions of individual magnetic ions with their surrounding anisotropic crystalline field, the second part from magnetic dipole interactions between pairs of ions and the third part from the anisotropic exchange interactions between them. Magnetic dipole interactions do not produce any anisotropy in the first order ap­ proximation for crystals of cubic symmetry and the anisotropy arising from the crystalline field vanishes for crystals whose magnetic ions have a spin of 1/2. According to 'the calculation by Keffer,l)' the anisotropy energy of MnF2 having a crystal structure of rutile type arises mainly from the magnetic dipole interaction which makes spins point in the c-axis and those parts from the anisotropy of the crystalline field and the anisotropic exchange interaction amount only to ten percents of the experimental value. In the case of Mn02, however, which is similar to MnF2 in the crystal structure but different from it in the superstructure due to the antiferromagnetic spin orientation, the magnetic dipole interaction keeps the direction of spins in the plane perpendicular to the c-axis, but this interaction does not contribute to the anisotropy in this plane which may be considered to be arising from the crystalline field. 2) Therefore, both anisotropy from the magnetic dipole interaction and that from the anisotropy of the crystalline field are dominant in this substance. Thus, which is predominant among above mentioned three parts of anisotropy depends not only upon the crystal structure, but also upon the

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On the Origin of the Anisotropy Energy of CuCl2-2H2O

Spins in an antiferromagnet subjected to an external field perpendicular to the preferred axis of antiferromagnetic magnetization are not exactly aligned parallel and antiparallel to this axis. It is shown that a better approximation to the spin wave theory can be worked out, if one takes the equilibrium directions of the spins as the axes of quantization. One obtains the field·dependent resonance frequency of a microwave, which the usual spin wave theory fails to give, and also a higher approximation to the perpendicular susceptibility. The value of the latter in the limit of vanishing field strength agrees with the one obtained by Kubo. § l. Introduction Since Anderson1> has shown that the spin wave theory is a good approximate method for the ground state of antiferromagnetics, several authors2> have applied this method to the calculation of thermodynamic properties of these substances. The perpendicular susceptibility X..L calculated in the first approximation of the spin wave theory has the same value as that obtained on the basis of the molecular field theory, namely, it depends neither on temperature nor on field strength. However, Kubo3> has shown, by calculating the con­ tribution from terms neglected in the first approximation by the perturbation method, that X..L deviates at absolute zero from its classical value and also depends on temperature. On the other hand, Ziman•>, through a different approach, attained the result that X.1. in a higher approximation is still constant. Nak.amura5> discussed antiferromagnetic resonance absorption, and according to his results, for the case of perpendicular field, only one field-independent resonance frequency is obtained under the assumption of a uniaxial anisotropy. The classical theory developed by Nagamiya6> and Keffer and KitteF> yielded, however, two resonance frequencies, of which one corresponds to the frequency given by the spin wave theory and the other is a frequency which is field-dependent. Nakamura attributed this discrepancy to an insufficient approximation made in his spin wave theory. We propose here another method of treating these problems. Kubo8> suggests a similar method, but his statement is not so specific as ours. By this method the terms neglected in the usual spin wave theory can be taken into account to a certain extent and accordingly the discrepancy concerning the resonance frequency can be removed. We shall also derive X.1. and discuss the discrepancy between two conclusions attained by Kubo and Ziman. We are led to believe that Kubo' s result is more reasonable. We always confine ourselves to the case of two sublattices and to external field applied perpendicularly to the preferred axis. The spins on one sublattice are, in this case, not exactly antiparallel to the spins on the

Kei Yosida

Papers

On the Origin of the Magnetic Anisotropy Energy of Ferrites

The Effects of Covalency on the Nuclear Magnetic Resonance in Ionic Crystals

On the Antiferromagnetism of Single Crystals

On the Origin of the Anisotropy Energy of CuCl2-2H2O

Note on the Spin Wave Theory of Antiferromagnetism