Satoru Inagaki

Spin-Peierls State vs Néel State II. Interchain Exchange Interaction

The ground state of the quasi-one-dimensional Heisenberg antiferromagnet coupled with the lattice distortion is determined on the basis of the phase Hamiltonian. By treating the weak interchain exchange interaction in a mean field approximation, it is shown within the self-consistent harmonic approximation that the ground state is either the Neel state or the spin-Peierls state as in the case of the small Ising anisotropy in our former investigation, but the Neel state is much more stabilized. The case of the staggered magnetic field is also examined. The three mechanisms, the Ising anisotropy, the interchain interaction, and the staggered field, are shown to be quite different in their stabilizing the Neel state. Comparison of these results with those by the classical treatment reveals the essential importance of the quantum fluctuations in the present competition problem.

Spin-Peierls State vs Neel State I. Small Ising Anisotropy

The ground state of the one-dimensional antiferromagnetic Heisenberg-Ising model coupled with the lattice distortion is determined based on the phase Hamiltonian defined by the boson representation...

Spin-Peierls State vs Antiferromagnetic State.III.Effects of Magnetic Field

The phase diagram of the stable states in the presence of the magnetic field is obtained for the quasi-one-dimensional Heisenberg antiferromagnet coupled with the lattice distortion. The spin-flop state and the state having spin-solitons appear as the possible ground states besides the spin-Peierls state and the Neel state which are the ground state in the absence of the magnetic field. Three types of field-induced phase transitions are shown to exist depending on the relative strength of the weak interchain exchange interaction to the spin-lattice coupling.

Spin-Peierls state vs antiferromagnetic state in quasi-one-dimensional Heisenberg antiferromagnet. IV: Transition temperatures

The transition temperatures T SP and T N of the paramagnetic state to the spin-Peierls state and to the Neel state are derived on the basis of the phase Hamiltonian, which takes proper account of the quantum nature of the quasi-one-dimensional Heisenberg antiferromagnet coupled with the lattice distortion. The expressions of T SP and T N are essentially the same as those obtained by Cross and Fisher and by Fowler. The tendency of the competition betweern the spin-Peierls state and the Neel state for T c is in accordance with the phase diagram of the ground state obtained previously.

Ferromagnetism in Doubly Degenerate Hubbard Models near Quarter-Filled Band

Ferromagnetism of the Hubbard models with doubly degenerate orbitals is studied in the case of infinitely large intra-atomic Coulomb interactions. It is assumed that the hopping of electrons occurs between the same orbitals of the nearest-neighbor sites, and the band is almost quarter-filled or N e = N -1, where N e and N are the total number of electrons and the total number of the atomic sites, respectively. It is rigorously proved that the ground state energy is highly degenerate for any dimension and for any lattice structure. Not only states with the maximum total spin ( S spin) and the total orbital spin ( T spin) but also certain states with smaller total S and T spins have the same ground state energy. The degeneracy originates from the high symmetry of the hopping matrix elements. The introduction of off-diagonal hoppings between different orbitals makes the ground state unique, which becomes ferromagnetic with the maximum total S and T spins as well as T x for simple-cubic, body-centered-cubic, ...

Theory of the anomalous Hall effect in heavy-fermion systems

Abstract The Fermi-liquid theory is further developed for the anomalous Hall effect due to skew scattering on the basis of the periodic Anderson model with degenerate orbitals and spin-orbit coupling. In the low-temperature coherent regime, the skew-scattering contribution to the Hall coefficient is generally proportional to the square of the total resistivity. At low temperatures, this relation is in good agreement with experiments on several Ce and U compounds.

Magnetic Ordering with Small Moments

We discuss the reason why the magnetic ordering with small moments is realized in the heavy fermion systems. The reason is that almost full localized moments cannot be created without destroying the heavy fermion states but only small localized moments can be created within the heavy fermion states. Then, we discuss the conditions of the magnetic instability in the heavy fermion system and point out the tendency that the ordering temperature is inversely proportional to the enhanced electron mass. The critical temperature of the superconductivity is also reduced in the same way

Spin-Peierls state vs. magnetic state in the quasi-one-dimensional Heisenberg antiferromagnet

Abstract The competition between the spin-Peierls state and magnetic states in the quasi-one-dimensional Heisenberg antiferromagnet is discussed on the basis of the phase Hamiltonian, which takes proper account of the quantum fluctuations essential to the spin-Peierls transition. Various phase transitions induced by the magnetic field are also pointed out.

Analytical Solution of Scaling Equations in the Two-Dimensional Half-Filled Hubbard Model

We solve analytically the scaling equations in the half-filled Hubbard model on the two-dimensional square lattice. The equations are coupled differential equations for the vertex functions, which were derived independently by Schulz and Dzyaloshinskii to take the electron-correlation effects into account beyond the random phase approximation. Our analytical solution confirms the results so far obtained on the scaling equations.

Spin-Peierls State vs Antiferromagnetic State in Quasi-One-Dimensional Heisenberg Antiferromagnet

The competition between the spin-Peierls state and the antiferromagnetic Neel state in the quasi-one-dimensional Heisenberg antiferromagnet is discussed at zero and finite temperatures on the basis of the phase Hamiltonian, which takes proper account of the quantum nature of the one-dimensional spins. On lowering the temperature three types of the phase transitions occur depending on the relative strength of the weak interchain exchange interaction to the spin-lattice coupling.