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For considering the electron-phonon coupling in the problem of impurity absorption band, a set of normal modes of lattice vibration were formed by the linear combination of plane (running) waves in order to present fully the site symmetry of the impurity. The symmetric (standing) waves of a definite type are characterized by an irreducible representation of the site group. The frequency distribution function of the phonons of a certain symmetry type is that of the lattice vibration divided by a constant. The phonons involved in the transition of an absorption band are restricted to certain symmetry types but no selection on the frequency may be found. The configuration coordinate approximation of Williams et al. was critically examined at this stage. The dependence of the coupling strength on the frequency of phonons was qualitatively discussed and the possible importance of the critical points of the frequency distribution was remarked. The mathematical analysis of symmetric standing waves was given in details. The relation between this set of normal modes of lattice vibration and those of an isolated cluster containing a central ion and the ligands was demonstrated.

A general theoretical approach is developed to treat the effect of point imperfections on the spin waves in a ferromagnetic crystal. Special attention is paid to the formation of localized modes. As an example, the calculations have been carried out for a one-dimensional linear lattice. The main results obtained indicate the following features. A substitutional magnetic impurity atom may introduce more than one localized mode of spin waves. The conditions for the localized modes to appear and the positions of their energy levels are given in terms of J′S′/JS and J′/J. Here S′ and S are respectively the spin quantum number of the impurity and that of the normal atoms. J′ and J are respectively the exchange integral between an impurity and its neighbors and that between the normal neighboring atoms. Highly concentrated strains and interstitial atoms which cause the exchange interaction between the atoms in their neighborhood to increase lead also to the formation of localized modes. Furthermore, the dipole-dipole interaction has been taken into consideration with the conclusion reached that it should not destroy the existence of these localized modes. Discussions have been given to the discrete energy levels which appear below the continuous spectrum in case of J′

In this article the parametrically coupling of oscillations in a small ellipsoid of ferrite under the excitation of an uhf pumping of any spatial distribution is discussed. It is pointed out that the coupled oscillations may be induced through the two types of driving, field driving and magnetization driving. A special case of the former was recently discovered by Denton, who used a longitudinal pumping field uniform in space. A special example of the latter is found in Suhl's theoretical analysis and a number of experimental works after him. The pumping field transverse in direction and spatially uniform does not induce the coupled oscillations directly, but the rf magnetization of the Kittel precession excited by the pumping becomes the driving force of the oscillations. For each type of a uniform pumping we obtain from a set of differential equations the magnetostatic potential functions (the first order approximation) as linear combinations of Walker's functions. These solutions are different from those given by MOHOCOB. Making. use of the boundary conditions at the ferrire surface we find that for the Walker modes involved in the oscillations to be coupled, thtir indices must satisfy certain condi'ions. For the case of magnetostatic operations the dc magnetic field is tuned to a pair of the Walker modes, the potential functions may be reduced greatly. By studying the power drawn by the coupled oscillations from the pumping, we obtain the selection rules of a pair of magnetostatic modes excited by a pumping field of any given spatial distribution. We point out that for the determination of the amplitudes of the oscillations the equations derived from the conservation of energy and from the equality of the number of quanta emitted must be used. Finally, the threshold intensity of Denton's pumping field is derived using Suhl's method. We indicate that this method is based on a perturbation calculation.

In this paper, calculation has been carried out for the localized modes of spin waves around a magnetic impurity atom in a ferromagnetic of the simple cubic structure. There are three symmetry types, i.e., the s-type, the p-type and the dr-type mode. The wave functions and the curves of the energy levels against the parameter J'S'/JS of these modes are obtained. Next, the types of localized modes which may possibly exist in ferromagnetics of the bcc or the fcc structure are discussed. It is pointed out that probably the s-type mode is the only one to be expected in actual specimens. With the criterion that the Curie point of the specimen should increase with the concentration of impurity, several alloys are suggested for the experimental observation of the localized modes of spin waves. Finally, a general analysis of the spin quantum number of the spin wave states leads to the conclusion that it is impossible to excite the scattered modes with k0≠0 as well as the localized modes by the electromagnetic radiation.

By combining the equation of motion of a magneto-elastically coupled system derived from a classical hamiltonian and the Maxwell equations with the propagation factor neglected, we obtained a differential equation which determines the magnetic oscillations accompanying elastic vibrations of a ferrite specimen of the usual size for magnetic resonance experiments. To each normal mode of elastic vibration of the specimen there exists an associated magnetic oscillation (namely, a magneto-acoustic mode). We pointed out that the magneto-acoustic resonance phenomenon discovered by Spencer and Le Craw is a special case of the parametric oscillation involving a magnetoacoustic and a magnetostatic mode. The arrangements for observing the oscillation involving a certain magnetostatic mode and magnetoacoustic modes and the theoretical estimate of the threshold pumping power were discussed. We derived the equations coupling a magnetoacoustic and a magnetostatic mode under pumping. By analysing the (even or. odd) symmetry of the field quantities involved, we arrived at the selection rules for possible combinations of modes taking part in the parametric oscillations in a small sphere of ferrite. Finally, it was mentioned that attention should, be paid to the parametric amplification of the magnetic field accompanying thermal phonons as a possible source of noise in a ferrite microwave amplifier through the modulation of the pumping power.

The Bethe-Weiss method in the statistical theory of Heisenberg ferromagnetism is generalized and applied to the case of subtitutional solid solutions of random distribution. Calculations are carried out for binary solutions containing magnetic atoms of spin 1/2 and nonmagnetic ones. The Curie temperature v.s. composition and the paramagnetic susceptibility v.s. temperature curves are obtained for simple and body-centered cubic lattices. The degree of magnetic short-range order at the Curie point becomes higher as the concentration of non-magnetic atoms increases. The results are qualitatively applicable to solutions of two different kinds of magnetic atoms. It is also concluded that the method gives an useful approximation only for higher concentrations of magnetic atoms.