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A modified mean field theory is applied to the axial next nearest-neighbor Ising (ANNNI) model, where the model is treated exactly along the direction of competing axial interactions while the mean field approximation is made within the ferromagnetic layer. Particular attention is paid to the partially disordered states and the asymmetric states, which are predicted to be stabilized by the mean field theory if the intralayer interaction is weak. Both numerical and analytical calculations are made to find that neither the partially disordered states nor the asymmetric states are stabilized but only the conventional ordered states are stable.

Mean field calculations are made to study the effect of nonlinear terms with respect to the magnetization in the axial next-nearest neighbor Ising (ANNNI) model. The phase diagrams are calculated in both zero and nonzero magnetic fields, in which a large number of high-order commensurate phases is found. It is shown that the nonlinear effect makes the ordered phase stable at higher temperatures and larger fields. Partially disordered states which contain paramagnetic sites are also obtained, resulting from the nonlinear effect as well as the competition between the intralayer coupling and the entropy effect. In this connection, the theory is compared with the complex magnetic phase diagram of CeSb.

Magnetic properties of Cr–Fe alloy are studied on the basis of the two band model. It is assumed that the localized moment of Fe has the role of the scattering center and the role which enhances the magnetostrictive effect; The scattering effects of the intra- and the interband processes with the Coulomb and the s-d interactions are investigated in detail. The magnetostrictive effect is enhanced by the process in which electrons flow from the localized moment to the conduction band with the volume change. The phenomenological consideration shows that the magnetostrictive effect is equivalent to the negative electron reservoir. The phase diagram, the wave number of the spin density wave and the jump in the thermal expansion at the Neel temperature are calculated in satisfactory agreement with experiments.

A theoretical study is presented for the incommensurate ( I ) state and the incommensurate-commensurate ( C ) transition with McMillan's single charge-density-wave model. The I state is determined precisely by taking account of a sufficiently large number of harmonics. A domain-like I state is obtained if the fundamental wave number is close to that of the C state. At the domain boundary the amplitude of the order parameter decreases together with the change of the phase of the order parameter. The I - C transition of the model is shown to be of second order. A detailed study is also made on the collective modes for the domain-like I state. Modes associated with domain boundaries are obtained.

A study is made on an Ising spin system on a triangular (actually hexagonal) lattice which contains the couplings of the nearest neighbor ( J 1 ) and the next-nearest neighbor ( J 2

Three-dimensional structures of charge-density waves in 1T-Ta dichalcogenides are studied on the basis of a phenomenological free energy, in which interlayer couplings up to the second neighbor layer are considered. Special attention is paid to the commensurate (C) and striped discommensurate (DC) states. Several stable stackings are obtained both in the C and striped DC states, where some of them in the C states are found to be disordered. The theory is applied to 1T-TaS 2 , on which Tanda et al. have made an X-ray experiment recently. To explain the experimental data a novel model is proposed for the C phase. In addition the structure of the new phase appearing between the C and nearly C phases is discussed from the standpoint of the striped DC state.

The incommensurate (I) states of the triple charge density waves (CDW) in 1T-TaS 2 are studied in details by taking into account a sufficiently large number of harmonics. A domain-like structure of the I-CDW state is shown to be realized as the fundamental wave vector of the I state approaches to the commensurate (“3×1” superstructure) wave vector; the domain boundary is characterized generally by a change of the phase and amplitude of the CDW, and inside the domain an approximately commensurate CDW is stabilized. The nature of the commensurability energy and the coexistence of three CDW's are reflected in the pattern of the domain-like structure. The successive first-order transitions in 1T-TaS 2 are discussed in this connection. The presence of a domain-like structure, which our theory predicts for the nearly commensurate phase of 1T-TaS 2 , is consistent with the recent X-ray photoemission experiment by Hughes and Pollak.

Mean field calculations are performed to study an Ising spin model on a triangular (actually hexagonal) lattice in which the couplings up to the next nearest neighbor and the magnetic field are taken into account. Special attention is focused on possible long-period modulated structures at finite temperatures. It is shown that for antiferromagnetic couplings higher order commensurate structures with a triangular domain structure are stable in a wide temperature range. The mechanism stabilizing those structures is discussed explicitly by using domain boundaries as a key concept and the Ginzburg-Landau type free energy. Finally the theory is applied to the order-disorder transition of β-eucryptite (β-LiAlSiO 4 ) and compared with experiment.

The one-dimensional charge-density-wave (CDW) state containing impurities is studied theoretically. The localized large-amplitude excitation is taken into account to determine the ground state of the commensurate ( C )-CDW state at absolute zero. It is shown that the long-range order of the C -CDW is unstable against an arbitrarily weak impurity potential in spite of the existence of the commensurability energy. Investigations are also made on the impurity effect on the incommensurate ( I )- C transition as well as the temperature dependence of the wave number of the I -CDW. In this connection a mechanism is proposed for bringing the concave curvature in the temperature dependence of the wave number, which is observed in 2H-TaSe 2 .

Charge density wave (CDW) states of 2H-TaSe 2 are studied on the basis of Jacobs and Walker's free energy. Discommensuration (DC) structures are inspected in detail under the situation where the stable commensurate (C) state change from one to another as the interlayer coupling constant is increased. Numerical calculations, in which a sufficiently large number of harmonics are taken into account, exhibit double honeycomb, triangular and hexagonal DC structures. The formation mechanism of various DC structures is discussed and compared with McMillan's DC diagram. Crossing over between different DC structures is also studied. Phase diagrams in the temperature and interlayer coupling plane are constructed to explain the re-entrant lock-in transition of 2H-TaSe 2 . In this connection a suggestion is made on the nature of the high-pressure C state.