By utilizing the method of correlation function (theory of Kubo), the ferrimagnetic resonance behaviour of the tight exchange coupled system was discussed. The general formulae of the magnetic susceptibility tensor were given, from which the resonance field H0 (or resonance frequency) and the line width 2△ω of the ferromagnetic branch and that of the exchange branch were determined. The results obtained show that the so-called fast relaxation and slow relaxation mechanisms are nothing but two branches (the transverse branch and the longitudinal branch) of the ferromagnetic resonance. The transverse branch corresponds to the coupled motion between the transverse componentsof J and S (J and S are the magnetic moments of rare earth ion and iron ion respectively), while the longitudinal branch corresponds to the coupled motion between thelongitudinal component of J and the transverse component of S. Owing to the action of crystal field and anisotropic exchange field, the direction of quantization of J deviates from that of S by an angle φ. Besides, owing to the aniso-tropy of exchange interaction, the nondiagonal elements of the tensor λ in the Hamil-tonian of exchange interaction J·λ·S may be quite large. It was shown that the contribution of the longitudinal branch to 2 △ω is approximately proportional to φ2 and λi3=1, 2). According to the general formula for 2△ω, the latter is determined mainly by the transverse branch at very low temperatures (below 4.2°K). Along certain crystal directions θa, when the two lowest energy levels of rare earth ion nearly cross over, anomalous peaks of H0 and 2△ω should appear, as it was verified experimentally. As the temperature increases, the longitudinal branch shall gradually dominate over the transverse branch. When the longitudinal relaxation frequency reaches the value of the frequency ω of the high frequency field, the line width possesses a maximum, which is the one ordinarily observed in experiments. As the temperature is increased further, the transverse branch shall play the dominant rolc again. When the transverse relaxation frequency approaches the frequency ω21, corresponding to the energy difference of the two lowest energy levels of the rare earth ion, the line width possesses a second maximum. Experimentally it is possible to observe the second maximum only in those directions θa, along which the two lowest levels have a near cross-over. When ω is high enough so that the condition |ω21(θa)-ω|?ω is satisfied, at very low temperatures there shall be a very sharp maximum of line width determined by the transverse branch. With the theoretical results obtained, in addition to the phenomena mentioned above, the following experimental facts observed in rare earth garnets can also be satisfactorily explained: the strong dependence of effective gyromagnetic ratio on temperature; the abrupt increase of line width near the compensation point; the abrupt increase of H0 for YbIG at the temperature where the line width reaches its maximum; etc.The limitation of classical equations of motion of magnetic moment was pointed out. For ferrites, in which the crystal field is comparable with the exchange field, it was shown that the results obtained by solving the classical equations of motion can qualitatively explain only those experimental facts, which are not concerned with the concrete spectrum of the energy levels of rare earth ions.
By utilizing the method of correlation function (theory of Kubo), the ferrimagnetic resonance behaviour of the tight exchange coupled system was discussed. The general formulae of the magnetic susceptibility tensor were given, from which the resonance field H0 (or resonance frequency) and the line width 2△ω of the ferromagnetic branch and that of the exchange branch were determined. The results obtained show that the so-called fast relaxation and slow relaxation mechanisms are nothing but two branches (the transverse branch and the longitudinal branch) of the ferromagnetic resonance. The transverse branch corresponds to the coupled motion between the transverse componentsof J and S (J and S are the magnetic moments of rare earth ion and iron ion respectively), while the longitudinal branch corresponds to the coupled motion between thelongitudinal component of J and the transverse component of S. Owing to the action of crystal field and anisotropic exchange field, the direction of quantization of J deviates from that of S by an angle φ. Besides, owing to the aniso-tropy of exchange interaction, the nondiagonal elements of the tensor λ in the Hamil-tonian of exchange interaction J·λ·S may be quite large. It was shown that the contribution of the longitudinal branch to 2 △ω is approximately proportional to φ2 and λi3=1, 2). According to the general formula for 2△ω, the latter is determined mainly by the transverse branch at very low temperatures (below 4.2°K). Along certain crystal directions θa, when the two lowest energy levels of rare earth ion nearly cross over, anomalous peaks of H0 and 2△ω should appear, as it was verified experimentally. As the temperature increases, the longitudinal branch shall gradually dominate over the transverse branch. When the longitudinal relaxation frequency reaches the value of the frequency ω of the high frequency field, the line width possesses a maximum, which is the one ordinarily observed in experiments. As the temperature is increased further, the transverse branch shall play the dominant rolc again. When the transverse relaxation frequency approaches the frequency ω21, corresponding to the energy difference of the two lowest energy levels of the rare earth ion, the line width possesses a second maximum. Experimentally it is possible to observe the second maximum only in those directions θa, along which the two lowest levels have a near cross-over. When ω is high enough so that the condition |ω21(θa)-ω|?ω is satisfied, at very low temperatures there shall be a very sharp maximum of line width determined by the transverse branch. With the theoretical results obtained, in addition to the phenomena mentioned above, the following experimental facts observed in rare earth garnets can also be satisfactorily explained: the strong dependence of effective gyromagnetic ratio on temperature; the abrupt increase of line width near the compensation point; the abrupt increase of H0 for YbIG at the temperature where the line width reaches its maximum; etc.The limitation of classical equations of motion of magnetic moment was pointed out. For ferrites, in which the crystal field is comparable with the exchange field, it was shown that the results obtained by solving the classical equations of motion can qualitatively explain only those experimental facts, which are not concerned with the concrete spectrum of the energy levels of rare earth ions.
In this paper, it is assumed that the left-cut of π-N scattering can be better approximated by four effective poles than by only one or two poles in the usual way. The author has made calculation for the contribution due to the short range interactions of the cross-diagram. The resulting phase-shift agrees with the experiment[3], and indicates that low-energy p-wave 3-3 resonance exists. Furthermore, from the calculated results, it can be seen that, to make better approximation, at least four poles must be taken, therefore the behaviour of the amplitude of the left-cut is very complicated.
In this paper, it is assumed that the left-cut of π-N scattering can be better approximated by four effective poles than by only one or two poles in the usual way. The author has made calculation for the contribution due to the short range interactions of the cross-diagram. The resulting phase-shift agrees with the experiment[3], and indicates that low-energy p-wave 3-3 resonance exists. Furthermore, from the calculated results, it can be seen that, to make better approximation, at least four poles must be taken, therefore the behaviour of the amplitude of the left-cut is very complicated.
The electrical conductivity, Hall coefficient, and magneto-resistance effect of n and p type InSb under temperatures 80-500°K have been measured, the impurity concentrations (after compensation) of samples varying in the range of 4×1013—7×1017cm-3.From results of measurement, values of intrinsic carrier concentrations, energy gap, and electron mobilities are presented. The scattering mechanisms for the electrons and the probable causes for the fact that the magneto-resistance is linearly field-dependent in large magnetic fields are discussed.
The electrical conductivity, Hall coefficient, and magneto-resistance effect of n and p type InSb under temperatures 80-500°K have been measured, the impurity concentrations (after compensation) of samples varying in the range of 4×1013—7×1017cm-3.From results of measurement, values of intrinsic carrier concentrations, energy gap, and electron mobilities are presented. The scattering mechanisms for the electrons and the probable causes for the fact that the magneto-resistance is linearly field-dependent in large magnetic fields are discussed.
In this paper, the problem of electromagnetic stress tensor of the oblate spheroidal conductor in an electric field is studied. By means of the similar corresponding relation of the stress tensor between the magnetostatic and the electrostatic case, the solution obtained here for electrostatics could be conveniently applied to the magnetostatic problem. It follows that some significant conclusions have been obtained.
In this paper, the problem of electromagnetic stress tensor of the oblate spheroidal conductor in an electric field is studied. By means of the similar corresponding relation of the stress tensor between the magnetostatic and the electrostatic case, the solution obtained here for electrostatics could be conveniently applied to the magnetostatic problem. It follows that some significant conclusions have been obtained.
A detailed study of the relation between diffraction points of various rhombohedral types and the type 6H of silicon carbide has been made, using the reciprocal lattice method. It was shown that there occur twelve possible relations. A method was proposed for determining the number of the close hexagonal packed layers in unit cell from the relations derived and the numbers of point between two Laue points of the type 6H. By using the method proposed, numerous SiC single crystals prepared in our laboratory were analysed and two new modifications of α-SiC 417R and 453R were found. These two new types are coalescent with the most common type 6H. The space group of the new types is R3m (C3v5). The unit cell dimensions in the hexagonal system for 417R and 453R are as follows respectively: 417R:αH=3.0806?,c=1050.7?,Z=417; 453R:αH=3.0806?,c=1141.4?,Z=453 or, in the rhombohedral unit cell: 417R:αR=350.4?,α=30.4′,Z=139; 453R:αR=380.6?,α=27.8′,Z=151.
A detailed study of the relation between diffraction points of various rhombohedral types and the type 6H of silicon carbide has been made, using the reciprocal lattice method. It was shown that there occur twelve possible relations. A method was proposed for determining the number of the close hexagonal packed layers in unit cell from the relations derived and the numbers of point between two Laue points of the type 6H. By using the method proposed, numerous SiC single crystals prepared in our laboratory were analysed and two new modifications of α-SiC 417R and 453R were found. These two new types are coalescent with the most common type 6H. The space group of the new types is R3m (C3v5). The unit cell dimensions in the hexagonal system for 417R and 453R are as follows respectively: 417R:αH=3.0806?,c=1050.7?,Z=417; 453R:αH=3.0806?,c=1141.4?,Z=453 or, in the rhombohedral unit cell: 417R:αR=350.4?,α=30.4′,Z=139; 453R:αR=380.6?,α=27.8′,Z=151.
This paper gives an analysis for the optical mechanism of the interferometric method of measuring the spectral slit width of the monochromator, suggested by V. J. Coates and H. Hausdorff. From the point of view of accuracy, moreover, it shows that the Michel-son interferometer is better than the Fabry-Perot interferometer.The spectral slit widths of type YM-2 monochromater for various slit widths were measured. The results are in agreement with the theoretical values.
This paper gives an analysis for the optical mechanism of the interferometric method of measuring the spectral slit width of the monochromator, suggested by V. J. Coates and H. Hausdorff. From the point of view of accuracy, moreover, it shows that the Michel-son interferometer is better than the Fabry-Perot interferometer.The spectral slit widths of type YM-2 monochromater for various slit widths were measured. The results are in agreement with the theoretical values.