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In order to make clear a correlation between mesoscopic ferromagnetic cluster and the colossal magnetoresistance in perovskite based manganites, the systems (La 1- x Tb x ) 2/3 Ca 1/3 MnO 3 with x ...

The magnetization processes in ferromagnetic superconductors such as ErRh 4 B 4 are theoretically studied. Between superconducting electrons and localized spins, the s - f exchange interaction and the electromagnetic interaction are taken into account. On a basis of the theory, the unusual magnetization curves observed in ErRh 4 B 4 are explained. Various types of magnetization processes are predicted to occur in ferromagnetic superconductors.

The terahertz radiation from a rectangular mesa of single-crystalline Bi 2 Sr 2 CaCu 2 O 8+δ with dimensions of 80 ×320 ×1.6 µm 3 fabricated by Ar and focused ion bean milling techniques was studied by Fourier transform infrared (FTIR) spectroscopy and angular distribution measurement of the radiation intensity. The emission measured using the FTIR spectrometer is centered at 0.9219 THz, which corresponds to exactly twice of that previously observed from mesas of the same width. The spectral width was as narrow as 7.5 GHz, which is limited by the instrumental resolution. The radiation obeys the ac Josephson relation and has a tunability of about 7% in frequency. The angular distribution of the emission power was analyzed using the conventional patch antenna theory. Both results strongly suggest that the excitation mode with a standing full-wavelength may be observed across the mesa width as the fundamental mode, instead of the half-wavelength mode commonly observed previously.

The THz radiation emitted from rectangular mesas of single-crystal Bi 2 Sr 2 CaCu 2 O 8+δ was studied using angular distribution measurements and Fourier transform infrared spectroscopy. Unlike the recent theoretical predictions, the results provide strong evidence for a dual-source mechanism in which the uniform and non-uniform parts of the ac-Josephson current act as electric and magnetic current sources, respectively. The latter synchronizes with cavity modes of the mesa with integral harmonics of the fundamental radiation.

The lower and the upper critical fields H c1 and H c2 , and the slope of magnetization at H c2 , (∂ M /∂ H ) c2 , are calculated in ferromagnetic superconductors. The theory takes account of the electromagnetic and the s-f exchange interactions between conduction electrons and localized f-electrons. When temperature decreases, (∂ M /∂ H ) c2 in the mixed state increases and diverges at a certain temperature. This indicates that below this temperature, the transition at H c2 is of a first order. Near the spin ordering temperature, H c2 decreases more rapidly than H c1 with decreasing temperature. The theoretical results are compared with experimental results in single crystals ErRh 4 B 4 in detail.

Effective interaction between localized magnetic moments in ferromagnetic superconductors is studied microscopically by taking account of the interplay among the electromagnetic field, persistent current and magnetic moments. The obtained effective exchange coupling J i j ( q ) can stabilize the spin-spiral ordering with a finite wave number Q , which coexists with superconductivity. By using this J i j ( q ), the spin wave spectrum \(\hbar\omega_{\mbi{q}}\) in the spin-spiral state is calculated at zero temperature. Reflecting a characteristic anisotropy of J j i ( q ), \(\hbar\omega_{\mbi{q}}\) depends strongly on the direction of q ; for q // Q it has a prominent peak at q ∼ Q , but the peak vanishes as q deviates from the Q direction. It is also shown that \(\hbar\omega_{\mbi{q}}\) has many energy gaps characteristic of the magnetic superconductor.

The spin assisted phonon Raman scattering in EuS, EuSe and EuTe is Studied, based on the Raman Polarizability whose spin-phonon dependence originates from the cross effect of the 4 f spin-orbit interaction and the exciton-phonon interction. The phonon dispersions are calculated on the basis of the breathing shell model. The scattering spectrum consists of two parts: One part is a broad line assisted by the spin fluctuations. Most contribution for it comes from LO-phonon, but in EuTe TO-, LA- and TA-phonon contributions also become considerably large. The other part is the sharp line induced by the staggered magnetization. The result of calculation explains the observed results, such as the line shape, and its temperature and magnetic field dependence.

The giant thermopower in metals with Ce 3+ impurities is theoretically studied. The relaxation time of a conduction electron is calculated as a function of energy in the selfconsistent ladder approximation by applying Abrikosov's pseudofermion technique to the Coqblin-Schrieffer exchange model with crystal field. The thermopower as well as the electrical resistivity exhibit universal behaviors if the crystal field is neglected. The crystal field induces the characteristic features and the anisotropy in the thermopower versus temperature curve. However, the sign of the thermopower is always positive in Ce system in contrast with Yb systems.

Effects of tunneling motion of atoms characteristic in glass systems on superconductivity is theoretically studied. The pair-breaking mechanism of superconductivity proportional to [ln ( T / D )] 2 is derived in the fourth order of the Coulomb interaction between conduction electrons and atoms, where T is the temperature and D is the band width. We propose that the pair-breaking mechanism is an origin of the universal absence of the Maki term in the paraconductivity in amorphous superconductors.

The dependence of the line shapes on the excitation energy in the Raman scattering (RS) of EuTe at low temperatures is theoretically studied, and is interpreted in terms of the modulation of 5d spin-orbit interaction by lattice displacement. A sharp line induced by the staggered magnetization appears in the vicinity of the absorption edge. This line is observed in off-diagonal Raman polarization configuration. For the incident light with energy near the middle of the exciton absorption, the sharp line disappears and broad line assisted by the magnon excitation appears in both off-diagonal and diagonal polarization configurations. These calculated results are consistent with the experimental result. The RS spectra under a weak magnetic field are also calculated.

In mixed states of ferromagnetic superconductors, the spin polarization and the distortion of vortex line lattice form coupled fluctuation modes. The spin polarizability is enhanced by this coupling. When an external magnetic field is large, a mixed state with large vortex number appears. Spins are almost uniformly polarized in this state.When the applied field decreases, transition to a state with the smaller vortex number takes place. In this state divergence of the spin polarizability occurs. This indicates the appearance of a state with oscillatory spin polarization stabilized by the distortion of vortex line lattice from the triangular structure. Waved vortex lines also appear. The wave length increases as the vortex number increases.

A model for the mixed valence state is presented. The basic lattice is composed of N trivalent rare earth ions. Extra N electrons enter either the localized f level at each ion site or the conduction band. When an electron occupies the f level of rare earth ion, this ion becomes divalent ion. The electron can jump from the f level to the conduction band and vice versa through the hybridization between these states. The effect of the strong intra-atomic Coulomb and the exchange interactions between the f electrons on the hybridized states is studied by applying the coherent potential approximation. The gap in the density of states and/or the mobility gap appear around the f level, and the Fermi level is located within the gap. The energy of the paramagnetic state is shown to be lower than that of the ferromagnetic state.

An effective exchange interaction between rare-earth magnetic moments near the surface of ferromagnetic superconductors is calculated under various surface boundary conditions both for the persistent current and the original exchange coupling in the normal state. In the bulk system, the persistent current screens the exchange interaction through the electromagnetic interaction, but the screening effect is weakened in the vicinity of the surface. The behavior of the penetrated magnetic field is calculated by using the obtained effective exchange interaction. Some discussions are given on the comparison between the present calculation and our previous calculation made by the boson transformation method.

We present a theory for calculating the crystal field effects in Kondo systems of Ce compounds and alloys. By extending Abrikosov's pseudofermion method, the static and dynamical susceptibilities are formulated as functions of the self-energy of the pseudofermions. The self-energy is self-consistently treated in the ladder approximation. It is shown that the crystal field is not constant but depends on temperature through the renormalization of the exchange interaction between Ce 3+ ions and conduction electrons. The neutron quasi-elastic and inelastic scattering spectra and the static susceptibility are in good agreement with the experimental ones in the cubic Kondo system, Ce x La 1- x Al 2 . This agreement suggests that the present theory is applicable to many materials.

The effect of the electromagnetic interaction between the persistent current and the rare earth moments is theoretically studied in the film of ferromagnetic superconductors. Depending on the film thickness and temperature, the ferromagnetic-like order, the spin-spiral-like order and the spin-sinusoidal-like order are predicted to occur in coexistence with superconductivity. From the calculation of the free energies of these states and the normal ferromagnetic state, the phase diagram is obtained in the plane of temperature and film thickness.

The effect of crystal field on Kondo resistivity in metals with Ce impurities is theoretically studied. The T -matrix of conduction electron is calculated in the self-consistent ladder approximation by applying Abrikosov's pseudofermion technique to the Coqblin-Schrieffer exchange model. The numerical results of the resistivity in cubic and tetragonal crystals are compared with the experimental ones in Ce x La 1- x Al 2 and CeCu 2 Si 2 . Our theory provides a unified view of the magnetic and transport properties in Ce compounds and alloys.

Magnetization process in the mixed state of ferromagnetic superconductors is theoretically studied. By taking into account the electromagnetic and the s-f exchange interactions between conduction electrons and localized magnetic moments, the Ginzburg-Landau free energy is obtained. The polarization of localized magnetic moments depresses the stability of mixed state and causes a convex curvature in the magnetization versus magnetic field curve near the upper critical field H c 2 above the ferromagnetic transition temperature. This curvature becomes larger with decreasing temperature, and the magnetization jump occurs at low temperatures. The characteristic features of magnetization process are in good agreement with those experimentally obtained by Crabtree et al. in single crystals of ErRh 4 B 4 .

The magnetic susceptibility and antiferromagnetic resonance of CoO are studied on the basis of Kanamori's theory, in which the residual orbital angular momentum plays an important role in the magnetic properties of CoO. The parallel susceptibility does not vanish at 0°K due to the unquenched orbital angular momentum. The calculated parallel, perpendicular, and powder susceptibilities are in good agreement with measured values. The antiferromagnetic resonance modes and frequencies are calculated by the method of using fictitious magnetic fields. In the absence of an external field there are four modes, which are pair-wise degenerate. The obtained frequencies at 0°K are 5.76×10 12 sec -1 and 16.61×10 12 sec -1 , which correspond to far-infrared wavelengths of 52.0 microns and 18.1 microns, respectively.

In Cu(NO 3 ) 2 2.5H 2 O, the Cu 2+ ions are coupled in almost isolated pairs by antiferromagnetic exchange interaction, and the pairs are considered to be linked in one-dimensional way by weak inter-pair exchange interaction. In an external magnetic field, the ground singlet of the pair crosses the lowest component of the excited triplet at about H =36 kOe. In the vicinity of the point of level crossing, a large amount of the short range order of the spin component perpendicular to the field appears at sufficiently low temperatures. An anomaly found by Haseda et al . in their experiment of cooling by adiabatic magnetization of the crystal can be explained as the occurrence of this short range order.

Domain sizes of long period superlattices in alloys are calculated by minimizing the ordering energy which mainly originates from the energy of conduction electrons. The domain size M thus obtained has a strong tendency to be fixed at integral numbers. This tendency explains the experimental results that the periods are fixed at M =2 in A 3 B-type alloys, such as Au-Cd, Au-Zn, and Pd-Mn, independently of their electron-atom ratios. The anomalous dependence of M on the electron-atom ratio in the Ag-mg alloy system is also explained.

The D -value of Mn 2+ in CoCl 2 ·2H 2 O has been obtained to be -0.13 cm -1 by Date and Motokawa. The large negative D value is reasonably explained by introducing an effective exchange interaction of general form between the Mn 2+ and the ground Kramers doublet of Co 2+ , taking account of the crystal symmetry. It is shown that the interaction -2 J x z s x S z -2 J y z s y S z is responsible for the negative D -parameter. The effective exchange interaction is derived from the nondiagonal exchange between Mn 2+ and Co 2+ with respect to the cobaltous orbits by projecting the exchange to the ground Kramers doublet.

It has recently been shown, by using a molecular field theory, that in these systems a new type of spin ordering occurs under external magnetic fields. In the present paper, the physical properties of these systems at low temperatures are investigated on the basis of spin wave theory. In the ordered state, the spin wave frequency is proportional to the wave number when it is small, and the proportionality coefficient is strongly dependent on the intensity of external field. The field dependence of spin temperature in adiabatic magnetization process is modified from that obtained by the molecular field theory.

The ferroelectric single crystal of barium titanate exhibits a strong absorption in the ultra-violet region at any temperature including the three transition points. The threshold for the ultra-violet absorption shifts gradually towards longer wave-lengths as the temperature rises, and the temperature coefficient of it is about one Angstrom per degree centigrade. In addition to this ultra-violet absorption, the crystal exhibits another absorption in the visible region. The intensity of natural light with wave-lengths in the neighbourhood of 5000 A transmitted through the crystal is measured by means of a multiplier phototube. It shows quite steep and sudden changes near the transition temperatures, especially in thin crystals. Let I (T), I (O) and I (R) be the intensity of transmitted light in the tetragonal, orthorhombic and rhombohedral phases respectively. Then the following relations can be drawn out of the various curves for the thermal transition of transparency. They are \(I(\text{O}){\gtrsim}\frac...

The magnetic anisotropy constant Cr 2 O 3 arising from the dipolar interactions among the chromic ions was calculated to be -0.059 cm -1 per ion at absolute zero, and the magnetic anisotropy constant due to the crystalline field combined with the spin-orbit coupling was estimated from the fine-structure coupling constant of ruby and compared with that deduced from the antiferromagnetic resonance experiment by Dayhoff. The value from ruby is too large. The temperature dependence of the anisotorpy constant and that of the antiferromagnetic resonance frequency at zero field are discussed.

A new type of spin ordering in a spin-pair system is theoretically investigated. In the system, the intra-pair exchange interaction is antiferromagnetic and is much stronger than the inter-pair exchange interaction. In an external magnetic field, the excited triplet of the pair splits, and the lowest component of the triplet crosses the ground singlet at a certain magnitude of the field. In the vicinity of the point of level crossing, even the weak inter-pair exchange interaction causes a considerable amount of mixing between the singlet and the lowest component of the triplet. Due to the mixing, an ordering of the spin component perpendicular to the external field occurs. This ordering explains an anomaly which has been found by Haseda et al. in their experiment of cooling by adiabatic magnetization of Cu(NO 3 ) 2 2.5H 2 O.

+ A brief account of the present work is published in the proceedings of the International Conference on Magnetism and Crystallography in Kyoto, published by the Physical Society of Japan, 1962. A new approach to the calculation of the temperature dependence of spin wave frequencies in ordered spin state is proposed. The results for ferromagnets agrees with Keffer's expression. Spin wave frequencies in antiferromagnets in the presence of an anisotropy energy are also calculated. By the present approach it is shown that the antiferromagnetic resonance frequency can be expressed phenomenologically in terms of anisotropy constants and static susceptibilities. The obtained expression of the resonance frequency is valid in any statistical approximation. The observed temperature dependence of the resonance frequency in MnF 2 is discussed by use of this result.

The heat capacity was measured between 1.5 and 280 K. At liquid helium temperatures a heat capacity anomaly was observed and a new phase transition was found at 211.4 K with a secondary C p maximum at 215.5 K. The entropy and the enthalpy changes for the overall transition are Δ S t =13.778 J K -1 mol -1 and Δ H t =3322 J mol -1 , respectively. The infrared spectra were measured at 120,225 and 295 K. Many new absorption peaks appeared below the transition point. A mechanism for the phase transition is suggested in terms of ordering processes of crystalline water. A new model is proposed for explaining the heat capacity anomaly at liquid helium temperature: The cluster ions with equilateral triangle symmetry at room temperature are slightly distorted through the phase transition processes resulting two kinds of cluster ions forming isosceles triangles with different exchange parameters. The closest agreement with the experimental data was obtained by assuming J 0 =30 k and J 1 =4.5 k for half moles of the ...